Standing Balance Control

Standing balance control is an important control problem for humanoid robots. It is shown that a single optimization criterion can be used to generate multiple balance recovery strategies. We employ a library of optimal trajectories and the neighboring optimal control method to compute local approximations to the optimal control. We take advantage of a parametric nonlinear optimization method, SNOPT, to generate initial trajectories and then use Differential Dynamic Programming (DDP) to refine them. A library generation method is proposed, which keeps the trajectory library to a reasonable size. We compare the proposed controller with an LQR based gain scheduled controller with the same optimization criterion. Simulation results demonstrate the performance of the proposed method.

Nonparameteric Controller Using a Trajectory Library

We employ a library of optimal trajectories and local models of the optimal cost function and the control policy to generate an nonparametric representation of the optimal control laws. We take advantage of a combination of a direct method, that finds coarse initial trajectories, and an indirect method, that further refines these trajectories. The indirect method we used is Differential Dynamic Programming (DDP). By designing an appropriate terminal penalty term, DDP generate physically correct solutions and consistent time-invariant local models of control laws at the same time. Coming soon.

Practical Issues:

1) Physical Parameter Identification.

2) Filter Design.

Case study of trajectory optimization