Optimal Dynamically Stable Quadruped Walking for Different Gaits


The problem of finding optimal, dynamically stable gaits for a quadruped robot is considered. Trajectories are sought which minimize the actuation energy required for walking in an attempt to approximate natural motion. The number of possible gaits for a quadruped is quite large when one considers varied orders of leg motion, different liftoff times, and various ground contact combinations for the legs. The problem is treated as a fully nonlinear optimal hybrid path planning problem on a 22-dimensional state space.

The model of the multi-body dynamics describing the motion in the sagittal plane consists of 9 rigid bodies. The resulting nonlinear dynamical systems consists of 22 independent, continuous state variables (i.e. 22 first order ordinary differential equations) and 8 continuous control variables. The objective of the nonlinear, hybrid optimal control problem for optimal walking at different gaits is to minimize the total energy required per step length. Computational results are presented using a recursive, articulated body algorithm for the formulation of the legged robot dynamics and a direct collocation and sparse nonlinear programming SQP method for the solution of the nonlinear, hybrid optimal control problem.

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Relevant Publications

Fachgebiet Simulation und Systemoptimierung, TU Darmstadt