Parallel Complementary Strategies for Implementing Biological Principles into Mobile Robots

Roger D. Quinn Gabriel M. Nelson Richard J. Bachmann Daniel A. Kingsley John T. Offi Thomas J. Allen Department of Mechanical and Aerospace Engineering Case Western Reserve University Cleveland, Ohio, USA

Parallel Complementary Strategies For Implementing Biological Principles Into Mobile Robots

Roy E. Ritzmann Department of Biology Case Western Reserve University Cleveland, Ohio, USA

Abstract Our goal is to use intelligent biological inspiration to develop robots that capture the capacity of animals to traverse complex terrain. We follow two distinct but complementary strategies to meet this goal. In one, we have produced a series of robots that have mechanical and control designs increasingly more similar to those of a cockroach. The leg designs of these robots ensure that they can generate movements used by the cockroach to walk and climb over a range of objects. However, in order to take advantage of these complex designs, we must first solve difficult problems in actuation, proprioception and control. The second parallel strategy seeks to capture the principles of biological movement, but in an abstract form that does not require complex platforms. Following the second strategy, we designed and built two new robots that each use only one propulsion motor to generate a nominal tripod gait. Gait changes similar to those used by the animal are accomplished through passive mechanisms. Rearing movements in anticipation of climbing are accomplished by way of a body flexion joint, which also allows the robot to avoid high-centering. The parallel development of these robotic lines provides the best of both worlds. The multi-segmented leg designs will ultimately be more versatile and agile than the abstracted line, but will take more effort to perfect. The simplified line provides short-term solutions that can be deployed immediately and confirm, in principle, the value of biological properties for complex locomotion.

KEY WORDS—neuro-mechanics, biologically inspired, artificial muscle, reduced actuation, preflexes The International Journal of Robotics Research Vol. 22, No. 3–April, March–April 2003, pp. 169-186, ©2003 Sage Publications

1. Introduction The goal of our work in the Biorobotics Laboratory at Case Western Reserve University is to use principles of insect mechanical and control systems as inspiration for the development of robots with improved mobility and mission capability (Ritzmann et al. 2000). An effective strategy requires that all members of the team understand the goals of the project. In our case, we have two goals. First and foremost, we want to use biological principles to generate more effective robotic designs. Secondly, we want to further our understanding of the mechanisms used by animals to overcome locomotory challenges. These goals are inextricably linked. A greater understanding of animal locomotion will benefit biorobotic design. Although this strategy could lead to an apparently straightforward approach of copying animal designs, the reality is far from simple. Blind mimicry may never result in effective or efficient vehicles. The limbs of most animals are far more complex than they need be for most missions. For example, each leg on a cockroach has at least seven degrees of freedom (DoF). These DoF may be required for movements such as feeding or grooming that are not necessary for the missions to be performed by the robot. They may also be a product of the processes by which animal systems are designed and develop naturally. For example, insects are serially homologous, that is, each limb has the same segments and joints, but has been individually adapted to satisfy its own role in locomotion. The hind legs of the cockroach rarely if ever use all three DoF associated with the joint that joins the leg to the body (body-coxa or BC joint) as it walks and climbs. To include all three BC DoF in the hind legs would require the addition of 169

170

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

actuators that would rarely be used. These realities mean that at the very least, the robotic designer has to decide exactly which behaviors are to be captured and which leg movements are required to capture the essentials of those behaviors. To make efficient design decisions, a research team must first decide on the specific missions that the robot is to perform. The only reason for developing legged robots is to have vehicles that can negotiate very complex terrain. Clearly, if we need a vehicle to move on flat, hard surfaces, a legged vehicle is not required. Wheeled vehicles that are readily available can perform these functions better than any currently available legged device. However, as terrain approaches the complexity of many natural situations, wheeled vehicles and even tracked vehicles will fail. Solving these conditions should be the goal of legged robot development. Moreover, it is also clear that the specific leg structures of most animals are well suited to a range of environments. Given the properties of natural skeletal systems and actuators, it would be difficult to develop an animal with wheels, although animals that live in limited natural environments could get along perfectly well with simple paddle-like limbs like those seen in polycheate worms. Thus, an effective strategy for development of legged devices is to study animal locomotion in complex terrains and to attempt to capture the leg designs and movements that are necessary for similar movements in artificial devices. We are using two parallel but complementary strategies to develop systems that can readily negotiate complex terrain. We attempt to capture as closely as possible the minimal leg designs that an animal uses to move over, under and around various barriers while still being able to move efficiently through level regions. This approach requires detailed biological observation of biomechanics and movement and dynamic modeling to limit the DoF to those that are absolutely necessary for the behaviors that are needed for the prescribed missions. The second strategy attempts to capture the locomotory functions used by the animal, but in a more abstract form and with relatively simple mechanisms. Here biological data are required to establish how the animal performs the desired locomotion tasks. We then try to accomplish the same functions as simply as possible using readily available technology. In the remainder of this paper, we describe some of our efforts that exemplify these two strategies. We also discuss the advantages and disadvantages of each method and how we think they complement each other.

2. A Series Of Robots That Are Progressively More Similar To A Cockroach 2.1. Goal of the Project The goal of this project is to accurately capture the leg architecture that a cockroach uses to run and climb over a range of objects in a robot that is powerful enough to perform these functions. The project has generated a series of four robots that each solves problems on the way to achieving this goal.

Fig. 1. Robot I walked in a continuum of insect gaits.

2.2. Multi-segmented Legged Robots With Electric Motors Our Robot I (R-I) and Robot II (R-II) were both successful hexapods that used dc motors with their power and control systems off board. R-I (Figure 1) had two DoF in each of its six identical legs. Each leg could rotate about its hip in the sagittal plane and a linear joint permitted it to extend and retract radially. Maxon 2-Watt motors with integral transmissions drove all of the joints by means of proportional controllers with constant gains. Leg controllers solved the inverse kinematics problem and caused the feet to cycle in a nominal walking pattern. Two gait coordination controllers were demonstrated in the robot and they both caused it to walked well on relatively smooth terrain. The first was a neural network gait controller developed by Beer and Chiel (Beer 1990) and the second was the stick insect network reviewed by Cruse (1990). In fact, it was the first robot to successfully use the Cruse mechanisms to coordinate its gait. In both cases, it walked in a continuum of insect gaits from the wave to the tripod and its gait depended upon its speed (Quinn and Espenschied 1993; Espenschied et al. 1993). Its maximum speed was approximately 14 cm s−1 or 0.28 body lengths per second. R-II (Figure 2) had three revolute DoF in each of its six identical legs, which gave it a sprawled, insect-like posture (Espenschied et al. 1994). Each leg had three segments, coxa, femur and tibia, from proximal to distal. Maxon 6-Watt motors with integral transmissions activated each of its 18 revolute joints. In addition to these active DoF, the tibias were passively compliant along their axes. Potentiometers measured joint angle positions and strain gages were used to measure axial force in the tibias. R-II’s control system was distributed and hierarchical (Espenschied et al. 1996). Each joint was activated locally by a proportional controller with a software adjustable gain. The error signal was used as a measure of joint torque and when a large load was encountered the gain was reduced so that the

Quinn et al. / Parallel Complementary Strategies

Fig. 2. Robot II using the searching reflex to walk across a slatted surface.

joint actively complied. Each leg had a local controller, which coordinated its joints by solving the inverse kinematics problem and cycled its foot in a walking pattern. The stick insect network (Cruse 1990) was generalized for omnidirectional walking and used to coordinate the legs and form insect gaits. A central controller maintained the robot’s body height and orientation as the robot walked over irregular terrain. Several insect inspired local leg reflexes were implemented in each of the leg controllers to improve the robot’s locomotion over irregular terrain. An elevator reflex lifted a swinging leg higher when it encountered an obstacle. When a foot did not contact the substrate upon setting down, a searching reflex cycled the leg to find support. The mechanism that permitted ominidirectional walking also enabled a stepping reflex so that when a foot in stance was perturbed a distance away from its desired location it was lifted and returned to its nominal position. Because of the distributed nature of its control system, R-II could walk with one of its legs held and restricted from moving relative to the body. This distributed, hierarchical control system gave R-II mobility capabilities that earned it an IEEE award (Espenschied et al. 1995). As with R-I, it walked in a continuum of gaits. However, it also turned, yawed, and walked sideways, over irregular terrain and on slatted surfaces (Espenschied et al. 1996). Significantly it performed all of these behaviors with the same control system, no software or hardware needed to be changed to accomplish different tasks. Its maximum speed was 14 cm s−1 or 0.31 body lengths per second. Many gear-motor driven robots have been developed with a kinematic configuration similar to that of R-II. This configuration is often used because stick insects have been characterized with these DoF. Pfeiffer, Eltze, and Weidemann (1994) developed the TUM autonomous robot concurrently with our R-II. Its design was based on a stick insect, and it had 18 gearmotor driven joints. They also used the stick insect network for gait coordination and their results were similar.

171

A series of three hexapod robots, Lauron, Lauron II, and Lauron III, have been developed with the same stick insect configuration and using 18 dc motors. Berns, Cordes, and Ilg (1994) developed Lauron concurrently with TUM and R-II. It had a hierarchical control system with its joint and leg controllers on board and its central controller on an off-board PC. The controller selected from a discrete set of gaits. Lauron was most remarkable because all of its control systems were implemented in neural networks and a learning algorithm was applied to the leg controllers. Lauron II was mechanically similar to Lauron, but it was autonomous and had more sensors on board (Kepplin and Berns 1999). In addition to the sensors that we used on R-II, Lauron II used inclinometers to help determine its internal state and a stereo camera system to determine the distance to objects in the environment. A visual information reduction strategy was used so that the vision problem was solved on board the vehicle. Lauron III is also autonomous and has the sensory suite found on Lauron II (Kepplin and Berns 1999). It has a hierarchical control system with many of the leg reflexes that we implemented in R-II such as compliance, elevator and searching. Lauron III has successfully walked in many real world environments such as in forests and mountainous terrain. Kirchner and Spenneberg (2001) recently developed another similar robot called Scorpion, which has all of its systems self-contained. The DoF of each leg are the same as those of R-II. It has eight legs, but its systems are modular and it is easily converted to a hexapod. This autonomous robot has also performed many of the behaviors we demonstrated in R-II, including omnidirectional turning. As successful as R-II was, it had some problems. Its Maxon gear-motors, although the most efficient then commercially available, did not have sufficient power-to-mass ratios to allow the robot to carry a significant payload. We concluded that a considerable improvement in performance required a change in actuator technology. In fact, because of this drawback, autonomous legged robots using dc motors and multi-segmented legs tend to be slow relative to their animal counterparts. Table 1 in Saranli, Buehler, and Koditschek (2001) illustrates this fact. However, there are some notable exceptions. Pratt, Dilworth, and Pratt (1997) overcame some of the disadvantages of dc motors by placing springs in series with them so that the springs could absorb, store and release energy during a stance cycle. The resulting vehicles walk quickly and promise energy efficiency at a particular vehicle speed. Robot III (R-III) incorporated two distinct changes from our previous designs. After investigating the various actuation systems that were commercially available at the time, we chose to use double acting pneumatic cylinders manufactured by Bimba. In our second major departure from our previous designs we sought to capture the essence of cockroach leg morphology in the designs of R-III’s legs. We chose the cockroach rather than the stick insect because cockroaches are better suited to rapid locomotion. We did not seek to

172

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

simply copy the leg designs of the cockroach. Rather we used the concept of intelligent biological inspiration to identify the joint movements that were critical to efficient walking and climbing movements and we used this information in guiding our implementation. 2.3. Biological Observations In order to make intelligent decisions regarding leg design, we recorded side and ventral views of cockroaches (Blaberus discoidalis) walking on a treadmill (Figure 3) or climbing over barriers of varying heights. We recorded joint actions with high-speed video systems operating at 250 or 500 frames per second and digitized specific landmarks on the legs that defined joint actions (Watson and Ritzmann 1998). These data were then implemented into a dynamic model of a cockroach in which each leg was simplified to have three segments: coxa, femur and tibia (Nelson and Quinn 1995). This simulation allowed us to examine the necessity of various DoF in each leg. We froze individual DoF and compared the resulting leg actions to normal behavior during normal walking. In this way, we determined that all but three of the seven DoF could be eliminated in the hind legs. In order to accomplish climbing movements, a fourth DoF was implemented in the middle legs. The arm-like actions of the front legs required five DoF, because these legs make complex movements of the BC joint as they reach forward during walking and climbing behaviors. In summary, each leg’s femur-tibia and coxa-femur joints have a single DoF. However, the BC joints have one, two and three DoF in the rear, middle and front legs, respectively.

Fig. 3. Cockroach walking on treadmill. Note that the animal’s front and rear right legs and middle left leg are in extreme anterior positions. The remaining legs are in extreme posterior positions.

2.4. Robot III Design Implementation The robot’s dimensions were determined by scaling the cockroach model up by a factor of 17. The design also preserved ranges of motion at each leg joint that the cockroach used in walking and climbing. In the resulting design, R-III’s rear legs are the largest and most powerful and well suited for propelling the robot forward; its middle legs are smaller and more agile and suited for lifting and turning the robot; and its front legs are the smallest and most agile for reaching to find footholds, while also contributing to climbing and turning. The structure of R-III was designed to withstand loads predicted by a scaled-up dynamic model and its air cylinders were sized to produce the predicted joint torques. The kinematic and inertial properties of the robot were input to a dynamic simulation (Nelson and Quinn 2000), along with joint angles that produced a reasonable tripod posture. Five sets of joint angles were chosen to represent the robot at different positions in the stance phase. From analysis of the digitized cockroach walking video, joint angles were chosen at the beginning and end of stance, as well as 25%, 50%, and 75% of the way through stance. These values were minimally adjusted so that the three stance feet were at the same elevation, and would

Fig. 4. Graphical output from the simulation. The model robot is dropped onto three legs that form a tripod: front left, middle right, and rear left. The lines under the substrate represent the ground reaction force vectors.

therefore hit the ground simultaneously when the simulated robot was dropped. The model robot was then dropped from a height of 2.54 cm. This was done to approximate large loading conditions for the robot. The stiffness of the joints was set such that the ensuing motion would be anatomically possible, i.e., there was joint flexure, but the coxa-femur joints did not hit the ground. Figure 4 shows the graphical output from the simulation, including vectors from the center of mass to each BC joint, the 18 leg segments, and the three ground reaction forces. Table 1 shows the resulting joint torques from five drop tests. The air cylinders and their moment arms were sized to produce torques that met the maximum torques specified in the last row of the table. The robot was fabricated from aluminum with steel being used sparingly for high-stress parts such as joint axles. A total

Quinn et al. / Parallel Complementary Strategies

173

Table 1. Torques in N m Predicted by the Dynamic Model from Drop Testing the Simulated Robot % Front (T1) Leg Middle (T2) Leg Rear (T3) Leg Stance
β α CF FT β α CF FT β CF FT 0 25 50 75 100 Max

5.09 1.47 4.41 4.87 5.32 5.32

8.94 3.62 10.5 12.6 12.7 12.7

3.28 2.38 8.49 15.2 5.66 15.2

9.28 4.30 12.3 11.8 16.2 16.2

2.26 0.68 3.28 5.77 1.24 5.77

28.4 12.2 29.9 29.1 30.4 30.4

3.28 5.32 17.0 22.3 19.4 22.3

25.7 10.8 17.4 14.9 11.5 25.7

4.87 1.24 3.51 2.94 2.38 4.87

21.9 13.4 23.0 22.1 22.7 23.0

18.4 9.50 8.49 4.98 9.62 18.4

7.58 3.39 7.69 6.68 4.07 7.69

The rows show maximum torques encountered for five different leg configurations and the last row shows the maximum from those five tests.

of six blocks each containing eight three-way valves were installed on the robot. The matrix valves were placed on the abdomen to locate the center of mass in a biologically accurate location above the BC joints of the rear leg. The power and control systems are off-board. The robot is 0.75 m long and weighs 13.6 kg (Bachmann et al. 1998). Our choice of valves constrained the control system. The 48 three-way valves can be energized to inlet high-pressure air to the actuators or de-energized to exhaust the actuators to the ambient atmosphere. However, air cannot be trapped in the cylinders to provide passive compliance. If we wished to trap the air, we would have used 96 two-way valves, which would have increased the weight of the robot and the complexity of the control system.

2.5. Hardware Control System for Pneumatic Robots The philosophy behind the design of R-III’s control system was to maintain control architecture flexibility. This has been achieved because the low level code that was developed for RIII has been used successfully for Robot IV (R-IV) and other pneumatic robots. This approach meant avoiding dedicated control system hardware that has applicability to only one robot. This goal was achievable because a 1 GHz Pentium-III PC, with standard timer/interrupt, digital I/O, and A/D expansion cards, can read the robot’s 42 sensors, perform control calculations, and activate the robot’s 48 bandwidth-limited valves at a real-time speed that exceeds the response time of the valves. Continuous pulsing of the Matrix solenoid valves activates the actuators. The valves are rated at 200 Hz and are driven at a pulse width modulation (PWM) frequency in the 50-100 Hz range with a 1% resolution in duty cycle. This frequency is the fundamental, or fastest, control system update rate, which, via time-division-multiplexing across valves, is readily performed by a single 1 GHz Pentium PC. However, the control system used for R-III used two slower PCs. The original system architecture was optimized for the centralized posture controller described below. This was a trian-

gular configuration consisting of two PCs in a master-slave system and the physical robot. The master PC (450 MHz Pentium) read sensory information from the physical robot, performed all the control calculations, and exported commanded duty cycles to the slave PC. The slave (127 MHz) was responsible for driving the robot’s valves with PWM based on these commands. The planned hierarchical control system indicated a hierarchical hardware architecture as well, one that had distinct high and low level controllers which could each perform separate yet overlapping tasks at different speeds. Thus, the system was rearranged in a serial configuration in which a local controller (the PC closest to the physical robot) would perform stereotyped yet adjustable tasks as rapidly as possible. This piece of the control system would also be responsible for reading the sensors of the robot, rapidly adjusting the duty cycles and valve commands to the robot in response to this feedback, and making the afferent sensor data available to the higher level controller or PC. Thus, the control system was transitioned to this hierarchical configuration, which parallels the distributed control architecture of animals, having central and local algorithms. Posture control is a more centralized computation and is therefore serviced by the higher-level PC. Its outputs provide feedforward commands for the local servo loops performed by the lower level controller residing in the local PC. The bandwidth for R-III’s joint control using this system was found to be 4.5 Hz with 80 Hz PWM. 2.6. Distributed, Hierarchical Controller for Robot III The biologically similar kinematic design of R-III suggested that biological inspiration be used for its control design as well. We developed a distributed control system and its hierarchical design reflects that of the animal. 2.6.1. Posture Controller A central circuit controls R-III’s body movement. Our previous robots used dc motors and we could simply use proportional control and increase the gains until they lifted

174

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

themselves. This is not possible with R-III because the bandwidth of pneumatic actuators is much lower than for dc motors. For this reason, a posture controller was developed using the language of virtual model control (Pratt 1999) and concepts from postural studies on cats (Horak and Macpherson 1996). It is a centralized system that estimates the current posture of the robot’s body from joint position data and distributes the load responsibility among the stance legs such that the desired center of pressure is attained and the strain energy in the legs is minimized (Nelson and Quinn 1999). It encourages lateral ground reaction forces similar to those observed in the cockroach (Full, Blickhan, and Ting 1991). This posture control system has been shown to be robust to large external disturbances and, using it, R-III’s actuators have been shown to be powerful. As designed it can perform “push-ups” while lifting a payload equal to its own weight (Nelson and Quinn 1998). This control component can be used to move the body in all six DoF relative to the stance feet. 2.6.2. Local Controller The local circuit consists of a hierarchy of joint, leg and gait controllers. A localized proportional controller causes the joints of each leg to follow a desired trajectory, which is determined from inverse kinematics and a desired foot path. Because the front and middle legs are kinematically redundant, the inverse problem described below is solved by minimizing the muscle-like actuator strain energy in each leg as is hypothesized in the case of mammals and amphibians (Mussa-Ivaldi and Hogan 1991). The inverse kinematics solution is implemented in a neural network that coordinates the joints in a leg (Nelson and Quinn 2001). Residing in the highest layer of the local controller, the stick insect distributed network (Cruse 1990) is used to coordinate the legs of the robot. The redundant kinematics of the front and middle legs of R-III complicate the inverse kinematics problem. We have developed a simple algorithm that, given a desired foot position, can provide joint angle set-points for a redundant limb and do so in a manner that has an integrable differential form, maximizes the mobility of the leg by avoiding joint limits and is computationally efficient (Nelson and Quinn 2001). Pseudo-inverses of the Jacobian matrix are often used to solve a redundant inverse kinematics problem (Hollerback and Suh 1985). A common pseudo-inverse approach is to minimize joint-space velocity in a constant weighted fashion. Yet, as Mussa-Ivaldi and Hogan (1991) have shown, unless special care is taken, constant weight pseudo-inverse schemes suffer from non-integrability: a closed path in task-space is not guaranteed to produce a closed path in joint-space. For instance, a leg of a walking robot having redundant DoF may not return to the same configuration after a cycle of foot motion. Animal limbs have redundant DoF, yet we observe (in steady-state behavior) repeatable configurations over many cycles of motion. One compelling explanation is that animals

move their limbs in such a way as to minimize the potential energy stored in the compliance of the actuators (muscles, tendons, etc.). Taking this observation as inspiration, we considered the quasi-static motion of a redundant limb with imagined jointspace springs (i.e., virtual torsional springs) acting on the joints. The unloaded equilibrium positions for the springs are the mid-range joint positions. The virtual spring stiffnesses are chosen based on the joint ranges of motion as observed from high-speed video of a cockroach. The virtual energy cost of driving any joint to a joint limit is homogeneous across all joints, which imbues animal-like motion into the final results. The unloaded joint positions correspond to an unloaded foot position. When the foot is forced away from this equilibrium position, the redundant limb assumes a configuration that minimizes potential energy in the virtual springs. Mathematically, this problem is equivalent to minimizing deviations from the preferred mid-range positions, thus minimizing the chances of encountering joint limits. This, in a sense, maximizes the mobility of the leg. For simplicity, the spring rates are assumed linear and gravity is neglected. Once the foot is driven to a desired Cartesian position, the joint configuration that results depends on the stiffness of the springs and their unloaded equilibrium positions. The configuration will also depend on whether during the motion a singularity of the Jacobian was encountered. However, there is a simply connected region in joint-space in which an integrable differential map exists, which means that a unique map from the desired foot position to joint angles also exists. We used a simple quasi-static numerical approach to solve for the equilibrium configurations off-line. Results were tabulated and a single-hidden-layer feedforward neural network was trained to reproduce the results (a mapping from desired Cartesian foot positions to optimal joint angles). Three hidden-layer neurons, with sigmoidal activation functions, were used for each joint on the robot. The coordinate system convention used with R-III (Figure 5(a)) is as follows: +x = forward, +y = left, +z = up. The reachable workspace of the left front leg of R-III (in this case, the foot is taken as the tibia-tarsis joint), from the shoulder or BC joint, is a complex shape contained inside a box of approximately: +22 > x > −32 cm, +31 > y > −18 cm, +8 > z > −31 cm. Inside this workspace, the quasi-static simulation was used to find optimal solutions for 152 desired foot positions in a Cartesian grid with 5.08 cm spacing. The simulations were completed with typical final errors between actual and desired foot positions of less than 0.25 mm, although some foot positions on the fringes of the workspace resulted in greater errors. After neural network training, typical foot position error was less than 1.3 cm. Figure 5(b) shows a test of the neural network for a given foot trajectory in the x-y plane (zfoot = −15.24 cm below shoulder). The foot traces a square of 17.8 × 17.8 cm. The

Quinn et al. / Parallel Complementary Strategies

175

30 20 10 0

-10

y x (a)

(b)

- 30 - 20 - 10

0

10

20

Fig. 5. (a) Partial overhead view of R-III with left front leg x-y coordinate system. (b) Desired square foot path versus neural network output.

maximum ±z error was +0.65 cm / −0.43 cm. These results are typical throughout the workspace with errors increasing slightly at the fringes. Neural network implementations of this inverse kinematics solution were installed in the leg controllers for each of the six legs of R-III. Proportional joint control was implemented using 80 Hz PWM. The leg controllers supply jointspace set-points for the joint controllers. Inter-leg coordination was achieved using the stick insect coordination mechanisms (Cruse 1990) that we have used successfully in our previous robots. With the robot suspended by tethers, this hierarchical control system caused the robot to move its legs in a smooth cockroach tripod gait (Figure 6). As described above, the front, middle and rear leg pairs model those of the cockroach and therefore have different designs. Thus, to form a tripod gait the foot paths and joint movements are also very different.

2.6.3. Discussion of Robot III’s Control System We might expect that the combination of the posture component and the local component should produce a good locomotion controller. The posture controller has been shown to produce the large leg forces required to oppose gravity and accelerate the body in a desired direction. It has also been shown to be robust to large disturbances. The local component has been shown to coordinate the joints and the legs and cycle the legs in insect walking gaits. However, when these controllers were combined and walking was attempted, the results were disappointing. Walking was achieved, but the robot tended to stumble when legs were rapidly lifted in spite of the fact that the robot can easily produce enough force in three legs to support itself. The problem is that the posture controller can-

Fig. 6. R-III cycling its legs in a tripod gait.

not react quickly enough to counteract disturbances caused by sudden changes in the number of stance legs. The local controller reacts more quickly, but the bandwidth of the joint controllers is insufficient for them to generate significant stabilizing torques. We plan to add force feedback to the local circuit. Positive load feedback is known to be an important component in mammalian and cockroach control circuits (Prochazka, Gillard, and Bennett 1997). It is a local circuit and reacts rapidly to sudden changes in load. Cockroaches have many campaniform sensilla on their legs that act as strain gages for load measurement (Kaliyamoorthy et al. 2001). In preparation for implementing load feedback, we installed six strain gages on each of the robot’s legs to form load cells. Results show that these provide an accurate measure of the three-dimensional foot forces. Implementation of this local force feedback circuit remains as future work on R-III.

176

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

As in the animal, the locomotion control entities are intertwined into an overall hierarchical control scheme illustrated by Figure 7. The posture component controls overall body configuration and motion and therefore resides at the highest level. The local controller includes joint, intra-leg and interleg circuits in a bottom-up hierarchy. However, all of these circuits are inextricably linked because they share proprioceptive sensory data and ultimately all control authority must be implemented at the joint level. Furthermore, during stance, all three components will be active and must be orchestrated for efficient movement. The passive mechanical properties of the vehicle are an equally important component in the neuro-mechanical system depicted in Figure 7 (Alexander 1990). Based upon their experiments with cats, Prochazka, Gritsenko, and Yakovenko (2002) assert that “the intrinsic stiffness of limb muscles, when activated with optimized cyclical patterns can generate stable locomotions.” Loeb, Brown, and Cheng (1999) explain that biological muscles produce large instantaneous forces when kinematic conditions change but respond sluggishly to changes in neural activation. They define a three-component hierarchical control system in vertebrates similar to Figure 7 in which the intrinsic muscle properties are at the lowest level. Responses they term “preflexes” are mediated by the central nervous system (CNS) and cause a zero delay change in muscle force in response to perturbations in length and velocity. These “preflexes appear to provide substantial and immediate responses to perturbations, which tend to stabilize the system.” Jindrich and Full (2002) demonstrate that this is true in invertebrates as well. Others have developed legged robots concurrently with RIII that are also actuated with air cylinders and similar conclusions can be drawn from their work. Protobot used air cylinders and three-way valves (Delcomyn and Nelson 2000). Its geometry was also similar to a scaled-up cockroach, however all of its legs have three DoF. Despite this simplification, its walking was limited. Another example of a robot that uses air cylinders is Robug IV, which has eight identical legs with three DoF each (Cooke et al. 1999). Four two-way valves are used to activate each joint DoF so that air can be trapped in the cylinders giving it passive joint stiffness or preflexes. It can walk and tow payloads. With its current valve configuration R-III is incapable of stiffness preflexes. We could double the number of valves on the robot, trap air in its cylinders, and thereby implement passive joint stiffness. However, this joint stiffness is not similar to that exhibited by muscle. Instead we concluded that its successor robots should have mechanics more like the animal. For example, they should have actuators with passive, tunable stiffness and preferably other properties that are similar to those of muscle. This advance is consistent with this line of robots where each successive generation uses more of the important locomotion mechanisms found in the cockroach and solves locomotion problems revealed in previous research.

Posture

Interleg Intraleg Joint

Mechanics

Fig. 7. The controller entities are intertwined with each other and with the mechanics of the robot in a hierarchical structure.

2.7. Robot IV Uses Artificial Muscles Braided pneumatic actuators (BPAs), also known as McKibben artificial muscles, pneumatic muscle actuators or Rubbertuators, have several desirable properties similar to muscle (Nickel, Perry, and Garrett 1963; Chou and Hannaford 1996; Caldwell, Medrano-Cerda, and Goodwin 1995; Inoue 1987). They can apply tensile force, have a higher force-toweight ratio than motors, air cylinders or muscle (Davis and Caldwell 2001), are structurally flexible, and their force output approaches zero at their minimum length. Furthermore, when they are used in antagonistic pairs, a joint’s stiffness can be tuned independent of its motion (Colbrunn, Nelson, and Quinn 2001). Air cylinders share this property, but BPAs are more easily tuned over a wider range of conditions. Powers (1996) developed the first hexapod robot that used BPAs. Berns et al. (2001) have developed Airbug, a larger (28 kg) robot that uses a variant of the BPA developed by FESTO called fluidic muscle. While capable of locomotion the robot moves slowly. The inability of the controller to compensate for the dynamic effects of the moving limb masses was cited as the cause of this slow speed. Before beginning the construction of R-IV, we investigated ways of controlling BPAs by adjusting their passive stiffness. A planar leg with two joints was constructed with antagonistic pairs of BPAs. The leg was suspended from a horizontal track so that it could cycle during swing, then push the trolley forward in the stance phase. Results indicate that it should be able to walk with its valves closed 90% of the time (Colbrunn,

Quinn et al. / Parallel Complementary Strategies

177

Fig. 9. Robot IV. Fig. 8. R-IV front legs on hybrid robot.

Nelson, and Quinn 2001). This demonstrated the promise of energy efficient locomotion with BPAs. In a further test of the viability of BPAs for activating complex robotic legs, prototype front legs of R-IV, with antagonistic BPAs installed, were attached to a frame with wheels to form a hybrid wheel-leg robot (Kingsley 2001). The legs have the same DoF and dimensions as the front legs of RIII. The structural flexibility of the BPAs permitted their insertion into the legs’ exoskeleton structures. When its actuators are pressurized, this hybrid robot stands (Figure 8) and remains standing with no additional energy expense. It is a passive system and so is robust to external disturbances. Using open-loop, on-off valve sequencing the robot performed cockroach-like walking and climbing movements. This good performance with such a simple control system demonstrates one merit of muscle-like actuators. They act as mechanical filters to smooth the motion that is activated by on-off valve signals. R-IV has been constructed (Figure 9) and some preliminary tests have been performed on it. The kinematic design and dimensions of R-IV are the same as R-III. The major differences are that it uses antagonistic pairs of BPAs and it has 96 two-way valves. Standard Matrix valves are used for the inlets and we have modified Matrix valves for the outlets. Because of improvements by Matrix and our modifications, the valve mass is about 1.4 times the valve mass on R-III, even though the number of valves has been doubled. Another improvement to R-IV is that its mass is 8.09 kg, less than two-thirds that of R-III, because BPAs are much less massive than air cylinders. In preliminary tests of R-IV, pressurized air was inlet to its extensors and it stood passively while resisting external disturbances. Furthermore, it has walked using a simple open-loop, on-off valve sequencing. We believe that some of the problems encountered by R-III will be eliminated by design changes in R-IV. For example, the BPAs coupled with twice as many valves provide R-IV

with preflexes that have been shown to be important for animal locomotion. It has passive stability properties that R-III cannot achieve.

3. Robots Designed With Abstracted Biological Principles 3.1. Goal of the Project Although we are confident that a future generation of the line of cockroach-like robots represented by R-III and R-IV will ultimately be able to function remarkably well in a wide range of environments, there remain some technical barriers to overcome. These include control issues that may be solved with current technology and other components such as actuators and sensors that will require new developments in order to reach optimal capability. These impediments led us to simultaneously pursue another line of robots, which could benefit from biological principles more immediately using available technology. For this new type of robot, we distilled out the basic walking principles of the animal and designed the simplest platform we could imagine to incorporate those properties. We then identified fundamental aspects of locomotion over complex terrain where the animal could outperform the simplified robot design. By examining movement in these situations, we identified the strategies that the animal used and implemented mechanical solutions in the robot. For these robots we do not try to accomplish the desired capability in the same way as the cockroach. Rather, we abstract the animal’s mechanisms and make an adaptation that is appropriate for the standard drive mechanisms of the robot. 3.2. Initial Biological Observations and Basic Vehicle Design The nominal locomotion pattern found in cockroaches and most other insects is the tripod gait in which the front and

178

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

rear legs on one side move in approximate synchrony with the middle leg on the opposite side (Figure 3). This tripod alternates with a second tripod made up of the remaining legs. Each leg moves rapidly through the swing phase and then slows down as it enters the stance phase and pushes the body forward. The front legs move through a 6 mm arc (on the order of the animal’s height) in order to reach the top of small barriers without the need for any change in leg movement (Watson et al. 2002). Saranli, Buehler, and Koditschek (2001) have developed a very capable robot called RHex that implements these ideas while using just six motors. Each leg can be thought of as a single compliant spoke that rotates 360º. A leg rotates quickly through the swing phase and slows down as it enters the stance phase. It is capable of walking at one body length per second in a tripod gait and moving its legs independently to form other gaits. It can move rapidly through rough and broken terrain and, with specially designed legs, it can readily climb stairs. We have shown that the cockroach’s nominal tripod gait can be accomplished with an even simpler hexapod design that uses only one conventional dc motor to propel it and two small servos for steering. Our new robot line based upon this principle is named Whegs (Quinn 2003) after an appendage design that is a hybrid between WHEels and leGS (Quinn et al. 2001). Because gear-motors are one of the most massive components on most electrically-actuated legged vehicles, a onemotor design reduces the weight and increases the payload capacity. Furthermore, when one leg encounters an obstacle and the other legs are slipping, the single leg with a solid foothold requires a great amount of torque to propel the robot. In this one drive-motor design, all of the motor’s torque is available for that leg. When individual legs or joints are driven by individual motors, each motor must be powerful enough for the worst case scenario. This requirement results in many large, heavy motors. The motor for the single-motor robot design can weigh much less than the combined weight of all of the motors on a robot with legs or joints driven by individual motors (see Section 4). The one-motor design also eliminates individual control of joints, which simplifies the controller. Of course, this simplification also reduces the possible behaviors that the robot can perform. Other mechanisms described below mitigate some of these limitations. A major advantage of legs is their ability to gain discontinuous footholds, i.e., they alternate between the stance phase, in which they contact the substrate, and swing in which they do not. This aspect is particularly beneficial on irregular, discontinuous terrain. After its stance phase, a leg should rapidly move through its swing phase to return to stance and again support the body. A single segment leg rotating continuously, as used in RHex, must change speed between stance and swing to accomplish this kind of movement (Saranli, Buehler, and Koditschek 2001). A control circuit is required to perform

this motion and such accelerations of the motor are not energy efficient. However, the principles of the leg cycle can be accomplished with an appendage we call a “wheg”, which is made of compliant spokes distributed about a hub. The wheg in Figure 10(a) has three spokes separated by 120º. The desired leg cycle motion is accomplished with this appendage driven at constant speed continuously over its full 360 degrees of rotation. As shown in Figure 10(a), this configuration permits the leg to obtain a foothold on an obstacle that is higher than the length of a spoke. If the motor and leg are strong enough, then the leg can drive the robot over such an obstacle. This design is greatly superior to the climbing ability of a conventional wheel, as shown in Figure 10(b), where the wheel’s radius is comparable to the length of one spoke of the wheg. The wheel makes continuous contact with the substrate, which is a disadvantage on irregular terrain. Although the addition of knobby tires or treads can increase traction, they cannot overcome this fundamental limitation of wheels. Given that the goal is for the motor to run at a constant speed to drive the robot forward, a three-spoke wheg is a compromise between climbing capability and ride smoothness. A two-spoke wheg would have better climbing abilities, but walking would be difficult. A four-spoke wheg would be less capable for climbing steps, but would provide a smoother ride. As shown in Figure 10(a), the three-spoke wheg has good potential for climbing. The ride smoothness can also be acceptable as discussed below. It would appear that a wheg with only three spokes would provide a very rough ride on smooth terrain. However, if the hexapod walks in a tripod gait on flat terrain, each spoke will be in stance during only 60 degrees of its rotation. During the remaining 60◦ prior to the following spoke entering stance, spokes on the adjacent whegs will support the body. This property is demonstrated in Figure 11, which shows a contralateral wheg pair. When the dark gray wheg is vertical and supporting the body, the hub is at its highest position. When the light gray wheg next contacts the ground, both whegs have rotated 30◦ . Therefore, if the spokes were rigid, the hub would translate vertically only about 13% of the spoke length or body height. This percentage of body height movement is less than that of an insect during a typical walk. Leg compliance can further reduce this vertical movement. Whegs I (Figure 12) is the first generation in this new line of robots that benefits from abstracted biological principles. It uses three-spoke compliant whegs for all six of its appendages. Whegs I is 50 cm long, 50 cm wide and weighs 2.9 kg. All six whegs have 11.4 cm long spokes. The wheg spokes are angled outward 30◦ from the sagittal plane to give the vehicle a sprawled posture. Spring steel 0.635 mm thick was bent to form compliant feet. It uses an RC car motor for propulsion and two hobby servos for steering. It carries a 7.2 V Ni-Cad battery pack and its speed and steering are controlled remotely by radio. Its top speed is about 5.5 km h−1 or three body lengths per second measured while it moved through a thick lawn.

Quinn et al. / Parallel Complementary Strategies

(a)

179

(b)

Fig. 10. (a) A three-spoke wheg can reach the top of a barrier that is higher than the length of a spoke, but (b) a wheel cannot do this.

(a)

(b)

Fig. 11. A pair of three-spoke whegs. The robot is moving to the left. The lighter gray tri-spoke wheg is on the opposite side of the body. Note that there is a 60◦ separation between the spokes when the whegs are out-of-phase as is the case when the robot is in a tripod gait. (a) As the robot moves to the left, the light gray wheg is ending its support phase and the darker gray wheg is beginning its support phase. (b) The height of the hub drops only 13% during this transition.

Whegs I is steered by rotating the front and rear whegs in opposite directions. This alters the direction of ground reaction forces of the feet and causes the robot to change its direction of motion. Similar mechanisms are found in turning cockroaches. However, the animal accomplishes this by altering joint movements especially in the front legs in order to direct the resulting forces laterally across the long axis of the direction of movement (Jindrich and Full 1999). Whegs I has a turning radius of 1.2 m. This undesirably large radius is caused by interference in the mechanisms. The turning radius of subsequent models was reduced. 3.3. Further Biological Observations to Improve Agility in Whegs Observations made on climbing cockroaches inspired mechanisms for improving the climbing ability of Whegs. Although cockroaches do not alter their tripod gait as they climb small obstacles, when the obstacle is about shoulder high or taller

Fig. 12. Whegs I is a hexapod and uses tri-spoke appendages. Each spoke can support and propel the body. It is power autonomous and controlled remotely via radio.

180

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

Fig. 13. Rearing movement of cockroach. Note that the middle legs extend in phase to push the animal upward (two arrows).

they change their leg motion and exit the tripod gait. Their middle legs move in phase as they rear their body upward (Figure 13) so that their front legs can be readily placed upon the top of the barrier (Watson et al. 2002). The front legs also often move in phase during climbing. Similarly, it would be beneficial for Whegs to transiently bring its wheg pairs into phase so that it can climb larger obstacles. To accomplish this task, we installed passive mechanisms in all six axles of Whegs I that permit its whegs to comply rotationally and change their phase relative to the other whegs when they encounter a large disturbance torque. The single propulsion gear-motor is directly connected to front, middle and rear inner axles via sprockets and chains. Each of the six wheg hubs is attached to its respective outer axle. A torsionally compliant mechanism serially connects each outer axle to its corresponding inner axle. The compliant mechanisms consist of torsional springs that have been pretensioned so that a disturbance torque below a threshold value will not cause the wheg to change its phase. The threshold torque is approximately 25% of the robot weight multiplied by the spoke length. Furthermore, the phase retarding of a wheg is limited to 60◦ by mechanical stops so that the contralateral wheg can move into phase with it. The compliant mechanisms can improve the climbing ability of a whegs robot. Consider the situation when the robot approaches a barrier head-on from the left as in Figure 15. This is a side view, which only shows the front whegs for simplicity. The arrow pointing to the right in Figure 15(a) indicates a force applied by the middle and rear legs that drives the robot toward the right. This force continues throughout this process, but is not shown in the other stills. In Figure 15(a) the right (dark) wheg has just made contact with the obstacle and the front whegs are in their nominal out-of-phase configuration. In Figure 15(b) the right wheg axle is complying because of the large external force applied by the barrier on its foot and this wheg is not rotating, but the left (light) wheg continues

Fig. 14. Body flexion joint between first and second thoracic segment allows the animal to position legs properly during climbing.

to rotate. In Figure 15(c) this process continues, but the right wheg is sliding up the obstacle because of the force from the middle and rear whegs. In Figure 15(d) the left wheg is almost in phase with the right wheg and the sliding up the barrier continues. In Figure 15(e) the front whegs are in phase and have their feet on top of the barrier, and the robot has begun to climb. Once the front whegs have surpassed the obstacle, the springs in the axles cause them to move out of phase once again and the robot can return to its nominal tripod gait. The installation of torsional compliance in all six axles has an additional benefit. Although the vehicle will walk in a nominal tripod gait, its gait will adapt to irregular terrain because of these compliant mechanisms. This compliance captures much of what the cockroach accomplishes with actions of its distal leg joints. Hence, the vehicle will have more whegs in contact with the ground and be more stable. These passive leg adjustments are similar to the preflexes described by Loeb, Brown, and Cheng (1999). Like the cockroach, the hexapod Whegs I can climb small barriers with little changes to its nominal tripod gait. When a large obstacle is encountered, the wheg pairs passively move into phase from their nominal out-of-phase tripod gait (Figure 16). Results of this compliance are that the robot passively changes its gait as it walks over natural terrain and its climbing ability is enhanced. It has climbed rectangular obstacles with a height greater than 1.5 times the wheg radius (Figure 16). Furthermore, when moving rapidly on relatively level terrain the vehicle uses the tripod gait and moves with little vertical body motion. In fact, rather than bouncing, its body pitches cyclically. Note that these gait adaptations are entirely due to passive mechanisms and the only control inputs are speed and direction via a radio.

Quinn et al. / Parallel Complementary Strategies

(a)

(b)

(d)

181

(c)

(e)

Fig. 15. Five stills illustrating an example of how its compliant axles can help Whegs climb tall barriers. The hexapod Whegs approaches the barrier from the left. Only the front whegs are shown. (a) The right (darker) front wheg has encountered the barrier. The arrow represents the force being applied by the middle and rear whegs. This force continues throughout this process, but is not shown in the other stills. (b) The axle on the right wheg complies and it does not rotate. The left (lighter) front wheg continues to rotate, but the robot does not move. (c) The left wheg continues to rotate, and the right wheg complies more as the robot moves forward. (d) The robot begins to lift as the right wheg continues to slide up the face of the barrier, and the left wheg continues to rotate. (e) The front whegs are in phase. The right wheg has surmounted the barrier, and the left wheg has joined it, in preparation for lifting the robot over the barrier.

Whegs I is three times faster than legged vehicles of similar size such as RHex (Saranli, Buehler, and Koditschek 2001) and it can climb higher barriers than wheeled vehicles of similar size. However, its climbing capabilities are limited as compared to the cockroach because it cannot change its body posture. The rearing movement of the cockroach is critical to its capacity to climb over objects that are taller than it could normally reach with its front legs (Watson et al. 2002). To rear up, a cockroach rotates its middle legs so that their extension pitches the front of its body upward (Figure 13). Clearly, Whegs cannot rear up using its middle whegs. However, it can accomplish the same type of postural adjustment by flexing a body joint. Indeed, cockroaches use a body flexion joint located between their front and middle leg attachments to extend their front legs downward in the later stages of a climb (Figure 14). We have implemented a body flexion joint in Whegs II, a second-generation vehicle (Figure 17). Whegs II is 47 cm long, 38 cm wide and weighs 3.86 kg. All six wheg axles have passive torsional compliant devices similar to those in Whegs I. The whegs have internal linear springs (2280 N m−1 ) that permit them to comply radially. Its radial wheg-spoke length is 10 cm when no load is applied. It uses a 90 W Maxon motor with a 26:1 integral transmission to propel it, two small hobby servos for steering, and a larger hobby servo to activate the

body joint. It has two 7.2 V battery packs onboard. Speed, steering and body joint motion are controlled via a hobby RC system. The body can flex 30◦ in each direction about the middle leg axle (Figure 17(b) and (c)). Using this joint to rear the front whegs upward, the robot can readily climb a series of steps (Figure 17(d)) that are 1.38 spoke lengths high and 0.8 body lengths deep. Whegs II can also run on its middle and rear whegs while holding its front whegs airborne. RHex (Saranli, Buehler, and Koditschek 2001) preceded Whegs and a direct comparison of these vehicles is instructive. Whegs is similar to RHex in that they are both hexapods of similar size that employ single segmented legs that rotate their feet in a circular path relative to their respective bodies. However, there are many differences. RHex uses six motors, one to drive each of its legs, whereas Whegs uses just one large motor for propulsion. RHex uses a 17.5 cm long single spoke leg, so that its control system must accelerate and decelerate each leg during a cycle so that it can move its body at a constant speed. Whegs uses three 10 cm long spokes for each leg and its motor runs at a constant speed to move the body at a near constant speed. RHex has a locomotion control system that can change its gait for movement over different terrains. The locomotion control system for Whegs is embedded into its mechanics and its gait adapts passively to different substrates. RHex turns by skid steering whereas

182

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

A

B

C

D

E Fig. 16. Sequential stills from video showing Whegs I beginning to climb an obstacle that is greater than 1.5 times taller than the radius of its whegs. (a) The robot is running toward the obstacle. (b) The right front wheg has made contact with the barrier and has stopped rotating while the left front wheg continues to rotate. (c) The left front wheg has made contact with the barrier and is in phase with the right front wheg. (d) The front whegs are beginning to lift the robot while the middle and rear whegs continue to push it forward. (e) The robot is climbing the barrier.

Quinn et al. / Parallel Complementary Strategies

(a)

(c)

183

(b)

(d)

Fig. 17. (a) Top view of Whegs II. (b) Whegs II can flex its body joint up so that its front legs can reach higher. (c) It can flex its body joint down to prevent high centering in the later stages of climbing. (d) It can climb stairs using this joint.

Whegs has two small servos that turn its front and rear whegs for more cockroach-like steering. Whegs II also has a body flexion joint, which RHex does not have. A comparison of the performance of RHex and Whegs is also interesting. Both vehicles have remarkable climbing and running abilities. For example, they can climb staircases that are higher than 1.3 times the length of one leg-spoke. According to Saranli, Buehler, and Koditschek (2001) RHex can run at one body length per second and when that paper was published it was the fastest legged vehicle of its size. However, both Whegs I and Whegs II have exceeded three body lengths per second. In RHex the gait software is changed to accomplish different behaviors such as running or climbing, whereas Whegs passively adapts its gait according to the terrain in real time. The reason that Whegs can be faster than RHex despite their having similar climbing abilities is addressed in the next section.

4. Discussion The Whegs vehicles are more energetic than other legged robots of similar size despite the fact that they are all actuated with dc motors. For example, besides running fast and climbing tall obstacles, Whegs II can rear up on horizontal ground such that its front and middle legs are airborne and its body makes a 30◦ angle with the substrate. These vehicles use single-segmented spoke-like legs. Does this success mean

that we should return to the use of motors for multi-segmented legs rather than continue to work with artificial muscle? No. The following analysis suggests that we should maintain our present course of research. Table 1 compares the actuator power-to-weight ratios of four robots that all use Maxon dc motors with integral transmissions. The motor power is that rated by the manufacturer and this number can be safely exceeded. However, this is true for all four robots and it would affect the absolute power-toweight ratio not the trend. The clear trend is that the actuator power-to-weight ratio increases corresponding to a decrease in the number of gear-motors. This explains the relatively energetic behaviors of RHex and Whegs and also explains why Whegs is even more energetic than RHex. The trade-off for reducing the number of gear-motors and thereby increasing the power-to-weight ratio is fewer independent DoF. For example, both RHex and Whegs have single-segment legs. The success of Whegs and RHex leads to another important question. Given the remarkable locomotion capabilities of Whegs and RHex, what are the advantages of multisegmented legs such as those used by animals? In fact, there are many advantages. Given a particular body pose, a leg with a single segment and single DoF can place its foot on at most two locations on a planar substrate without passing through the ground. On the other hand, multi-segmented, multi-DoF legs have a workspace that permits them to place their feet in many different locations. For example, cockroaches use seven active joints and ten segments in their forelimbs to

184

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

reach forward and on top of obstacles for climbing. Reaching is particularly important for sparse substrates. Stick insects and locusts use the searching reflex to cycle their legs to find a foothold. Robot II used its three DoF legs to perform this behavior and walk across slatted surfaces. RHex and Whegs cannot do this. Another advantage is that insects can use their multi-segmented legs to rotate their legs and push in different directions to enable more efficient turning than that possible in simplified vehicles. A further advantage is that vehicles with multi-segmented legs can walk with their bodies in different postures. Animals can use this mechanism to lower their body height to walk under low clearances. As another example, cockroaches change their body posture while climbing to improve their stability. Furthermore, animals use their legs in general and forelimbs in particular for more than just locomotion. For example, praying mantises hold their prey with their forelimbs while ingesting it and other animals use their legs for digging. Vehicles with few gear-motors such as Whegs can move with great agility and speed on certain terrains because their simplified designs enable them to have high power-to-weight ratios. Hexapod robots that use many gear-motors to drive multi-segmented legs have multi-functional legs, but poorer power-to-weight ratios. This is the reason that we are pursuing other types of actuators for our cockroach robots and in particular we are interested in artificial muscles. Table 3 shows the actuator power-to-weight ratios of two of our 75 cm long pneumatic hexapod robots, R-III and R-IV. The actuation system mass includes the weight of the valves. The McKibbens on R-IV are much less massive than the air cylinders on R-III, which more than makes up for the weight of the 48 additional valves on R-IV. The actuator power output was calculated at six bar air pressure and at 2 Hz joint motion. Only one of the two antagonistic actuator groups was used in the power calculations for R-IV because its antagonists cannot simultaneously develop power. The power rating and power-to-weight ratio for R-III is very high compared to the electric robots in Table 2. This explains its ability to perform push-ups at a 60% duty cycle while lifting a payload equal to its own weight. R-III also has a much higher power-toweight ratio than R-IV, but that of R-IV is superior to Whegs. In moving from R-III to R-IV we have lost some power-toweight advantage, but gained tunable preflexes.

5. Comparison of Our Two Robot Lines The two lines of robots that we are developing are in fact complementary. The Whegs vehicles are ready for near-term deployment while we continue to develop the cockroach robot line. The Whegs vehicles are currently capable of rapid locomotion and climbing on various substrates using remote control. They are excellent platforms for the development and implementation of navigational behaviors that will enable au-

tonomous locomotion over real world terrains. The cockroach robot line will eventually lead to a vehicle with superior locomotion and manipulation capabilities at which time the navigational behaviors can be implemented in it. The cockroach robot line (RI, RII, RIII and R-IV) will progress and ultimately outperform Whegs. Their multisegmented leg architectures enable them to move their legs with the agility to solve a range of terrain problems as well as perform manipulation tasks. The actuator power-to-weight ratios of R-III and R-IV are promising for energetic movements. Furthermore, the preflexes exhibited by R-IV are encouraging for robust cockroach-like locomotion. Thus, we expect that future robots in this line will achieve the goal of capturing the cockroach’s ability to run efficiently through a range of complex terrains. However, this goal requires more research. One technology that needs more work is the energy-poweractuation system. BPAs have many important characteristics similar to muscle. Their main drawback is that they are activated by compressed gas and conventional methods of compressing gas are inefficient. Therefore, it remains to be shown that a robot with a BPA can operate autonomously for long periods of time. If this can be done, a vehicle such as R-IV or Airbug (Berns et al. 2001) will have great promise. However, regardless of this, our work in locomotion control of robots with BPAs can be transferred directly to a similar robot with another type of artificial muscle. Therefore, when a superior artificial muscle is available we can readily implement it in a robot and apply the locomotion control methods that we have developed in our research. Fundamental control issues also remain to be solved. For example, what role should positive load feedback play in the locomotion control system? The efficient interaction of central and local control as a vehicle moves over various barriers and carries payloads of various sizes and shapes also presents a challenge. The solutions to locomotion control problems can be found in cockroach biology. However, discovering those solutions can take years of biological research. Whegs provides a simpler solution that can be implemented immediately. Although future generations of the cockroach robot will outperform them, current Whegs robots are remarkably agile considering their simplicity. Because much of their locomotion control system is imbedded in their mechanics, they can be used immediately to test higher-level control strategies. For example, head sensors can be mounted on them and cockroach inspired rules can be implemented in an onboard navigation system to guide them through complex terrain. This will make them useful, mission capable vehicles in the near term. It will also pave the way for the implementation of these same devices on the cockroach-like robot line. Thus, the two parallel robot lines represent a near-term and far-term line of vehicles. Far from being conflicting systems, they are complementary to the ultimate goal of achieving legged robots that can move easily through tortuous terrain in a manner reminiscent of animal locomotion.

Quinn et al. / Parallel Complementary Strategies Table 2. Actuator Power-to-mass Ratios for Robots That Use Different Numbers of DC Motors Robot II Robot I Rhex Number of motors Motor power Gear-motor mass Power/mass

18 6 × 18 = 108W 2.7 kg 40 W kg−1

12 12 × 2 = 24W 0.444 kg 54 W kg−1

6 6 × 20 = 120W 1.8 kg 67 W kg−1

185

Whegs II 1 1 × 90 = 90W 0.87 kg 103 W kg−1

The motor power is that rated by the motor manufacturer. The gear-motor mass includes the mass of all of the motors and integral transmissions onboard the robot. This value for Whegs also includes the mass of its servos and drive chains. The values for RHex are from Saranli, Buehler, and Koditschek (2001) and Maxon.

Table 3. The Actuator Power-to-mass Ratio for Two Pneumatic Robots Robot III Robot IV Number of actuators Total power Valve+actuator mass Power/mass

36 1677 W 5.24 kg 320 W kg−1

88 519 W 3.79 kg 137 W kg−1

R-III uses double acting air cylinders and 48 three-way valves. R-IV uses McKibben artificial muscles and 96 two-way valves. The valve mass is included in these calculations.

Acknowledgments This work was supported by the Office of Naval Research (N0014-99-1-0378), DARPA (DAAN02-98-C-4027), JPL and the Air Force (F08630-01-C-0023).

References Alexander, R. McN. 1990. Three uses for springs in legged locomotion. International Journal of Robotics Research 9(2):53–61. Bachmann, R. J., Nelson, G. M., Quinn, R. D., Watson, J., Tryba, A. K., and Ritzmann, R. E. 1998. Construction of a Cockroach-like Hexapod Robot. In Proc. 6th IASTED Int. Conf. on Robotics and Automation, Banff, Canada, pp. 22–27. Beer, R. D. 1990. Intelligence as Adaptive Behavior: An Experiment in Computational Neuroethology, Academic Press, New York. Berns, K., Cordes, S., and Ilg, W. 1994. Adaptive, neural control architecture for the walking machine lauron. In Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, München, pp. 1172-1177. Berns, K., Albiez, J., Kepplin, V., and Hillenbrand, C. 2001. Airbug—Insect-like machine actuated by fluidic muscle. In Proc. 4th Int. Conf. on Climbing and Walking Robots, K. Berns and R. Dillman, eds, pp. 237–244. Caldwell, D. G., Medrano-Cerda, G. A., and Goodwin, M. J. 1995. Control of pneumatic muscle actuators. IEEE Con-

trol Systems Journal 15(1):40–48. Chou, C., and Hannaford, B. 1996. Measurement and modeling of McKibben pneumatic artificial muscles. IEEE Transactions on Robotics and Automation 12(1):90–102. Colbrunn, R. W., Nelson, G. M., and Quinn R. D. 2001. Design and control of a robotic leg with braided pneumatic actuators. In Proc. IEEE IROS, Maui, Hawaii. Cooke, D. S., Hewer, N. D., White, T. S., Galt, S., and Luk, B. L. 1999. Implementation of modularity in Robug IV— Preliminary results. In CLAWAR99, G. S. Virk, M. Randall, and D. Howard, eds, Professional Engineering Publishing, London, pp. 393–404. Cruse, H. 1990. What mechanisms coordinate leg movement in walking arthropods? Trends in Neurosciences 13:15–21. Davis, S. T., and Caldwell, D. G. 2001. The bio-mimetic design of a robot primate using pneumatic muscle actuators. In Proc. 4th Int. Conf. on Climbing and Walking Robots, K. Berns and R. Dillman, eds, Professional Engineering Publishing, London, pp. 197–204. Delcomyn, F., and Nelson, M. E. 2000. Architectures for a biomimetic hexapod robot. Robotics and Autonomous Systems 30:5–15. Espenschied, K. S., Quinn, R. D., Chiel, H. J., and Beer, R. D. 1993. Leg coordination mechanisms in stick insect applied to hexapod robot locomotion. Adaptive Behavior 1(4):455–468. Espenschied, K. S., Quinn, R. D., Chiel, H. J., and Beer, R. D. 1994. Robotics and Manufacturing, M. Jamshidi, C. Nguyen, R. Lumia, and J. Yuh, eds, ASME, New York, Vol. 5. Espenschied, K. S., Quinn, R. D., Chiel, H. J., and Beer, R. D. 1995. Biologically-inspired hexapod robot project: Robot II. In IEEE Int. Conf. on Robotics and Automation (ICRA) Video Proceedings, Nagoya Congress Center, Nagoya, Japan. Espenschied, K. S., Quinn, R. D., Chiel, H. J., and Beer, R. D. 1996. Biologically-based distributed control and local reflexes improve rough terrain locomotion in a hexapod robot. Robotics and Autonomous Systems 18:59–64. Full, R. J., Blickhan, R., and Ting, L. H. 1991. Leg design in hexapedal runners. Journal of Experimental Biology 158:369–390.

186

THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / March–April 2003

Gassmann, B., Scholl, K. U., and Berns, K. 2001. Locomotion of LAURON III in rough terrain. In Proc. IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics (2):959–964. Hollerbach, J. M., and Suh, K. C. 1985. Redundancy resolution of manipulators through torque optimization. In Proc. IEEE Int. Conf. on Robotics and Automation, St Louis, IEEE, New York, pp. 1016–1021. Horak, F. B., and Macpherson, J. M. 1996. Postural orientation and equilibrium. In Handbook of Physiology, Oxford University Press, New York, pp. 255–292. Inoue, K. 1987. Rubbertuators and applications for robots. In Proc. 4th Symp. on Robotics Research, Tokyo, pp. 57–63. Jindrich, D. L., and Full, R. J. 1999. Many-legged maneuverability: dynamics of turning in hexapods. Journal of Experimental Biology 202(12):1603–23. Jindrich, D. L., and Full R. J. 2002. Dynamic stabilization of rapid hexapedal locomotion. Journal of Experimental Biology 205:2803–2823. Kaliyamoorthy, S., Zill, S. N., Quinn, R. D., Ritzmann, R. E., and Choi, J. 2001. Finite element analysis of strains in a Blaberus cockroach leg during climbing. In Proc. Int. Conf. on Intelligent Robots and Systems (IROS’01), Maui, HI, pp. 833–838. Kepplin, V., and Berns, K. 1999. A concept for walking behavior in rough terrain. In Climbing and Walking Robots, G. S. Virk, M. Randall, and D. Howard, eds, Professional Engineering Publishing, London. Kingsley, D. A. 2001. A study of the viability of braided pneumatic actuators for use on walking robots. M.S. Thesis. Case Western Reserve University, Ohio, USA. Kirchner F., and Spenneberg, D. 2001. Omnidirectional walking in multi-pod-robots based on feedback driven oscillators and local reflex mechanisms. In Proc. 4th Int. Conf. on Climbing and Walking Robots, K. Berns and R. Dillman, eds, Professional Engineering Publishing, London, pp. 197–204. Loeb, G. E., Brown, I. E., and Cheng, E. J. 1999. A hierarchical foundation for models of sensorimotor control. Experimental Brain Research 126:1–18. Mussa-Ivaldi, F. A., and Hogan, N. 1991. Integrable solutions of kinematic redundancy via impedance control, International Journal of Robotics Research 10(5):481–491. Nelson, G. M., and Quinn, R. D. 1995. A Lagrangian formulation in terms of quasicoordinates for dynamic simulations of multibody systems such as insects and robots. In Proc. ASME Int. Mechanical Engineering Congress and Expo., San Francisco, CA. Nelson, G. M., and Quinn, R. D. 1998. Posture control of a cockroach-like robot. In IEEE Int. Conf. on Robotics and Automation (ICRA’98) Video Proceedings, Belgium. Nelson, G. M., and Quinn, R. D. 1999. Posture control of a cockroach-like robot. IEEE Control Systems 19(2): 9–14. Nelson, G. M., and Quinn, R. D. 2000. A Lagrangian quasicoordinate formulation for dynamic simulations of multibody systems. Journal of the Chinese Society of Mechanical En-

gineers 21(1):25–33. Nelson, G. M., and Quinn, R. D. 2001. A numerical solution to inverse kinematics for swing control. In Proc. CLAWAR 2001. Nickel, V. L., Perry, J., and Garrett, A. L. 1963. Development of useful function in the severely paralyzed hand. Journal of Bone and Joint Surgery 45A(5):933–952. Pfeiffer, F., Eltze, J., and Weidemann. 1994. The TUM walking machine. In Intelligent Automation and Soft Computing 2, M. Jamshidi, C. Nguyen, R. Lumia, and J. Yuh, eds, TSI Press, Albuquerque, NM. Powers, A. C. 1996. Research in the design and construction of biologically-inspired robots. M.S. Thesis, University of California, Berkeley. Pratt, J., Dilworth, P., and Pratt, G. 1997. Virtual model control of a bipedal walking robot. In Proc. IEEE Int. Conf. on Robotics and Automation, Albuquerque, NM. Pratt, G. A. 1999. Legged robots at MIT—What’s new since Raibert? In Proc. 1999 Int. Conf. on Climbing and Walking Robots, G. S. Virk, M. Randall, and D. Howard, eds, Professional Engineering Publishing, London, pp. 393–404. Prochazka, A., Gillard D., and Bennett D. J. 1997. Implications of positive feedback in the control of movement. Journal of Neurophysiology 77(6):3237–3251. Prochazka, A., Gritsenko, V., and Yakovenko, S. 2002. Sensory control of locomotion: reflexes versus higher-level control. In Sensorimotor Control, S. G. Gandevia. U. Proske, and D. G. Stuart, eds, Kluwer Academic/Plenum, London. Quinn, R. D., Kingsley, D. A., Offi, J. T., and Ritzmann, R. E. 2002. Vehicle with compliant drive train. Patent pending. Quinn, R. D., and Espenschied, K. S. 1993. Control of a hexapod robot using a biologically inspired neural network. In Biological Neural Networks in Invertebrate Neuroethology and Robotics, R. D. Beer, R. E. Ritzmann, and T. M. McKenna, eds, Academic, New York, pp. 365–382. Quinn, R. D., Nelson, G. M., Bachmann, R. J., Kingsley, D. A., Offi, J., and Ritzmann, R. E. 2001. Insect designs for improved robot mobility. In Proc. 4th Int. Conf. on Climbing and Walking Robots, K. Berns and R. Dillman, eds, Professional Engineering Publishing, London, pp. 69–76. Ritzmann, R. D., Quinn, R.D., Watson, J. T., and Zill, S. N. 2000. Insect walking and biorobotics: A relationship with mutual benefits. Bioscience 50(1):23–33. Saranli, U., Buehler, M., and Koditschek, D. 2001. RHex a simple and highly mobile hexapod robot. International Journal of Robotics Research 20(7):616–631. Watson, J. T., and Ritzmann R. D. 1998. Leg kinematics and muscle activity during treadmill running in the cockroach, Blaberus discoidalis: I. Slow running. Journal of Computational Physiology A 182:11–22. Watson, J. T, Ritzmann, R. E., Zill, S. N., and Pollack, A. J. 2002. Control of obstacle climbing in the cockroach, Blaberus discoidalis I. Kinematics. Journal of Computational Physiology A 188:39–53.