Minimax differential dynamic programming: application to a biped walking robot

We developed a robust control policy design method in high-dimensional state space by using differential dynamic programming with a minimax criterion. As an example, we applied our method to a simulated five link biped robot. The results show lower joint torques from the optimal control policy compared to a hand-tuned PD servo controller. Results also show that the simulated biped robot can successfully walk with unknown disturbances that cause controllers generated by standard differential dynamic programming and the hand-tuned PD servo to fail. Learning to compensate for modeling error and previously unknown disturbances in conjunction with robust control design is also demonstrated. We also applied proposed method to a real biped robot for optimizing swing leg trajectories.

Authors

• Jun Morimoto
• Garth Zeglin
• Christopher G. Atkeson

Keywords

• Legged locomotion
• Minimax techniques
• Dynamic programming
• Orbital robotics
• Robust control
• Optimal control
• Servomechanisms
• Design methodology
• State-space methods
• PD control
• Bipedal Walking
• Differential Dynamic Programming
• High-dimensional
• Control Design
• Error Model
• Differentiation Program
• Unknown Disturbances
• Robust Control Design
• High-dimensional State Space
• Time Step
• Value Function
• Optimization Method
• Number Of Steps
• Square Deviation
• Local Optimum
• Local Policy
• Penalty Function
• Nominal Trajectory
• Trajectory Optimization
• Cost Control
• Output Control
• Real Robot
• Number Of Time Steps
• Error Dynamics
• Walking Trajectory
• Lower Torque
• Local Optimization Methods