Robust Low Torque Biped Walking Using Differential Dynamic Programming With a Minimax Criterion

We developed a control policy design method for robust low torque biped walking 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. Future work will implement these controllers on a robot we are currently developing. Recent humanoid robots using Zero Moment Point (ZMP) control strategies have demonstrated impressive biped walking [7, 11, 8]. However, robots using ZMP control are often neither robust nor energy efficient and can generate large joint torques. McGeer [9] demonstrated that passive dynamic walking was possible. His robots walked down a slight incline without applying any torques at the joints. Recently, several studies have explored how to generate energy efficient biped walking [1, 10]. Many studies using optimization methods [4, 2] focus on finding optimal biped walk trajectories, but do not provide control laws to cope with disturbances. Our strategy is to use differential dynamic programming [3, 6], an optimization method, to find both a low torque biped walk and a policy or control law to handle deviations from the nominal trajectory. We use a minimax reward to insure the policy is robust. 1 BIPED ROBOT MODEL In this paper, we use a simulated five link biped robot (Fig. 1) to explore our approach. Kinematic and dynamic parameters of the simulated robot are chosen to match those of a biped robot we are currently developing (Fig. 2) and which we will use to further explore our approach. Height and total weight of the robot are about 0.4 [m] and 2.0 [kg] respectively. Table 1 shows the parameters of the robot model. Table 1: Physical parameters of the robot model link1 link2 link3 link4 link5 mass [kg] 0.05 0.43 1.0 0.43 0.05 length [m] 0.2 0.2 0.01 0.2 0.2 inertia [kg·m ×10] 1.75 4.29 4.33 4.29 1.75