Optimal biped walking with a complete dynamical model

Abstract

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. This forces us to a fully nonlinear minimum energy path planning problem on a 14dimensional 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 can handle the many constraints, as well as the high degree of nonlinearity and high dimensionality. A newly available version of this software provided a substantial decrease in computing time required for generating solutions. We discuss numerical optimization and other modeling issues in this paper.

Hybrid direct collocation and control in the constraint-consistent subspace for dynamic legged robot locomotion

“…Our method achieves this without adding artificial decision variables as in [8]. With a similar motivation, early work on optimal biped walking using minimal coordinates models was explored by Hardt et al [22]. However, this modeling approach is only valid for simple cases.…”

Clustered Regression Control of a Biped Robot Model

“…It can, however, describe the walking motion rather well and is therefore applied in slightly different forms by many researchers (see e.g. Chevallereau et al, 2003;Hardt et al, 1999;Juang, 2000). Fig.…”

Minimax differential dynamic programming: application to a biped walking robot

“…This property is one of the advantage over other optimization methods used to generate biped walking trajectories [1,3].…”