A Distributed Neural Network Architecture for Hexapod Robot Locomotion

Communicated by Rodney Brooks A Distributed Neural Network Architecture for Hexapod Robot Locomotion Randall D. Beer Departments of Computer Engineering and Science and Biology, Case Western Reserve University, Cleveland, OH 44106 USA Hillel J. Chiel Departments of Biology and Neuroscience, Case Western Reserve University, Cleveland, OH 44106 USA Roger D. Quinn Kenneth S. Espenschied Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106 USA Patrik Larsson Department of Electrical Engineering and Applied Physics, Case Western Reserve University, Cleveland, OH 44106 USA We present a fully distributed neural network architecture for controlling the locomotion of a hexapod robot. The design of this network is directly based on work on the neuroethology of insect locomotion. Previously, we demonstrated in simulation that this controller could generate a continuous range of statically stable insect-like gaits as the activity of a single command neuron was varied and that it was robust to a variety of lesions. We now report that the controller can be util- ized to direct the locomotion of an actual six-legged robot, and that it exhibits a range of gaits and degree of robustness in the real world that is quite similar to that observed in simulation. 1 Introduction Even simpler animals are capable of feats of sensorimotor control that exceed those of our most sophisticated robots. Insects, for example, can walk rapidly over rough terrain with a variety of gaits and can immedi- ately adapt to changes in load and leg damage, as well as developmental changes (Graham 1985). Even on flat horizontal surfaces, insects walk with a variety of different gaits at different speeds (Wilson 1966). These gaits range from the wave gait, in which only one leg steps at a time in a back-to-front sequence on each side of the body (this sequence is called Neural Computation 4,356-365 (1992) @ 1992 Massachusetts Institute of Technology Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/neco.1992.4.3.356 by guest on 01 October 2021 Neural Network Architecture for Hexapod Robot Locomotion 357 Figure 1: A comparison of simulated and robot gaits. Black bars represent the swing phase of a leg and the space between bars represents its stance phase. (Top) Leg labeling conventions. (Left) Selected gaits observed in simulation as the activity of the command neuron is varied from lowest (top) to highest (bottom) (Beer 1990). (Right) Gaits generated by the robot under corresponding conditions. Here the duration of a swing bar is 0.5 seconds. a metachronal wave), to the tripod gait, in which the front and back legs on each side of the body step in unison with the middle leg on the op- posite side (see left side of Fig. 1). While most current research in legged robot locomotion utilizes centralized control approaches that are compu- tationally expensive and brittle, insect nervous systems are distributed and robust. What can we learn from biology? In previous work (Beer et at. 1989), we described a neural network architecture for hexapod locomotion. The design of this network was based on work on the neuroethology of insect locomotion, especially Pearson's flexor burst-generator model for walking in the American cockroach (Periplaneta americana) (Pearson et al. 1973; Pearson 1976). Through simulation, we demonstrated that this network was capable of generat- ing a continuous range of statically stable gaits similar to those observed Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/neco.1992.4.3.356 by guest on 01 October 2021 358 Randall D. Beer et al. in insects (see left side of Fig. 11, as well as smooth transitions between these gaits. The different gaits were produced simply by varying the tonic level of activity of a single command neuron. In addition, a lesion study of this network demonstrated both its surprising robustness and the subtlety of the interaction between its central and peripheral compo- nents (Chiel and Beer 1989). A natural question to ask is whether these results were just artifacts of the many physical simplifications of the simulation or whether they are robust properties of the network that persist in the presence of such physical realities as delay, friction, inertia, and noise. This is a difficult question to resolve given the subtle dependencies of this controller on sensory feedback (Chiel and Beer 1989). The only way to determine whether this distributed controller had any practical utility was to design and build a six-legged robot and interface it to the locomotion network. 2 Locomotion Controller The circuit responsible for controlling each leg is shown in Figure 2. Each leg controller operates in the following manner: Normally, the foot motor neuron is active (i.e., the leg is down and supporting weight) and excitation from the command neuron causes the backward swing motor neuron to move the leg back, resulting in a stance phase. Periodically, this stance phase is interrupted by a burst from the pacemaker, which inhibits the backward swing and foot motor neurons and excites the forward swing motor neuron, resulting in a swing phase. The time between bursts in the pacemaker, as well as the velocity output of the backward swing motor neuron during a stance phase, depend on the level of excitation provided by the command neuron. In addition, sensory feedback is capable of resetting the pacemaker neuron, with the forward angle sensor encouraging the pacemaker to terminate a burst when the leg is at an extreme forward position and the backward angle sensor encouraging the pacemaker to begin a burst when the leg is at an extreme backward position. There are six copies of the leg controIler circuit, one for each leg, ex- cept that the single command neuron makes the same two connections on each of them. Following Pearson’s model, the pacemakers of all adjacent leg controllers mutually inhibit one another, discouraging adjacent legs from swinging at the same time (Fig. 3). At high speeds of walking, this architecture is sufficient to reliably generate a tripod gait. However, at lower speeds of walking, the network is underconstrained, and there is no guarantee that the resulting gaits will be statically stable. To enforce the generation of metachronal waves, we added the additional constraint that the natural periods of the pacemakers are arranged in a gradient, with longer periods in the back than in the front (Graham 1977). Under these conditions, the pacemakers phase-lock into a stable metachronal Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/neco.1992.4.3.356 by guest on 01 October 2021 Neural Network Architecture for Hexapod Robot Locomotion 359 Command Backward Angle Sensor r Pacemaker Swing uw Forward Angle Sensor t- t- Excitatory Connection c Inhibitory Connection Figure 2: The leg control circuit. Each leg is monitored by two sensory neurons that signal when it has reached an extreme forward or backward position. Each leg is controlled by three motor neurons responsible for the state of the foot, the velocity with which the leg swings forward, and the velocity with which the leg swings backward, respectively. The motor neurons are driven by a pacemaker neuron whose output rhythmically oscillates. A single command neuron makes the same two connections on every leg controller. The architecture also includes direct connections from the forward angle sensor to the motor neurons, dupli- cating a leg reflex known to exist in the cockroach. The state of each neuron is governed by the equation CidVildt = -Vi/Ri + cj~jifj(Vj)+ INTi + EXTi, where Vi, Ri, and Ci, respectively, represent the voltage, membrane resistance, and membrane capacitance of the ith neuron, wji is the strength of the connection from the jth to the ith neuron, f is a saturating linear threshold activation function, and EXTi is the external current injected into the neuron. INTi is an intrinsic current present only in the pacemaker neurons that causes them to oscillate. This current switches between a high state of fixed duration and a low state whose duration depends linearly on the tonic level of synaptic input, with excitation decreasing this duration and inhibition increasing it. In addition, a brief inhibitory pulse occurring during a burst or a brief excitatory pulse occurring between bursts can reset the bursting rhythm of the pacemaker. Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/neco.1992.4.3.356 by guest on 01 October 2021 360 Randall D. Beer et al. Figure 3: The pacemaker neurons of adjacent leg controllers are coupled by mutual inhibition. relationship. We chose to enforce this constraint by making the range of motion of the rear legs slightly larger than that of the middle legs, whose range of motion in turn is slightly larger than that of the front legs. A complete discussion of the design of this network and its relationship to Pearson’s model can be found in Beer (1990). 3 Robot To examine the practical utility of this locomotion controller, we designed and built a six-legged robot (Fig. 4, top). The network was simulated on a personal computer using the C programming language and interfaced with the robot via A/D and D/A boards. Because the controller was originally designed for a simpler simulated body (see top of Fig. l), two main issues had to be addressed in order to connect this controller to the robot. First, the locomotion controller assumes that the swing and lift motions of the leg are independent, whereas in the robot these two degrees of freedom are coupled (Fig. 4, bottom). In simulation, this prob- lem was dealt with by having a stancing leg passively stretch between its joint and foot.

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