Optimal biped walking with a complete dynamical model

We solve the problem of generating symmetric, periodic minimum energy gaits for a 5-link biped robot moving in the sagittal plane of forward motion. We seek to approximate natural walking motion through the minimization of actuation energy. The model we use has considerably more structure than those previously studied. We deal with a fully nonlinear minimum energy path planning problem on a 14-dimensional state space. Also, a large number of constraints must be considered, including contact and collision effects. Our solution required development of various symbolic, dynamical algorithms relating to multibody systems and use of powerful numerical optimal control software. Solving the minimum energy walking problem including saturation and algebraic constraints amounts to solving a Hamilton-Jacobi-Bellman type equation along the optimal path. We use the path planning software DIRCOL which provides a substantial decrease in computing time required for generating solutions. We discuss numerical optimization and other modeling issues.