Programmable Central Pattern Generators: an Application to Biped Locomotion Control

We present a system of coupled nonlinear oscillators to be used as programmable central pattern generators, and apply it to control the locomotion of a humanoid robot. Central pattern generators are biological neural networks that can produce coordinated multidimensional rhythmic signals, under the control of simple input signals. They are found both in vertebrate and invertebrate animals for the control of locomotion. In this article, we present a novel system composed of coupled adaptive nonlinear oscillators that can learn arbitrary rhythmic signals in a supervised learning framework. Using adaptive rules implemented as differential equations, parameters such as intrinsic frequencies, amplitudes, and coupling weights are automatically adjusted to replicate a teaching signal. Once the teaching signal is removed, the trajectories remain embedded as the limit cycle of the dynamical system. An interesting aspect of this approach is that the learning is completely embedded into the dynamical system, and does not require external optimization algorithms. We use our system to encapsulate rhythmic trajectories for biped locomotion with a simulated humanoid robot, and demonstrate how it can be used to do online trajectory generation. The system can modulate the speed of locomotion, and even allow the reversal of direction (i. e. walking backwards). The integration of sensory feedback allows the online modulation of trajectories such as to increase the basin of stability of the gaits, and therefore the range of speeds that can be produced

Authors

• Ludovic Righetti
• Auke Jan Ijspeert

Keywords

• Legged locomotion
• Centralized control
• Couplings
• Oscillators
• Humanoid robots
• Education
• Nonlinear control systems
• Control systems
• Signal generators
• Biological neural networks
• Central Pattern Generator
• Locomotor Control
• System Dynamics
• Optimization Algorithm
• Sensory Feedback
• Limit Cycle
• Humanoid Robot
• Trajectory Generation
• Locomotion Speed
• Simulated Robot
• Backward Walking
• Teaching Signal
• Phase Difference
• Oscillation Frequency
• Frequency Components
• Negative Feedback Loop
• Walking Speed
• Pendulum
• Aperiodic
• Feedback Pathway
• Bipedal Locomotion
• Periodic Input
• Sample Trajectories
• Stable Limit Cycle
• External Processes
• General Architecture
• Phase Resetting
• Network Oscillations
• Learning Trajectories