Linear Contact Modeling and Stochastic Parameter Optimization for LQR-Based Whole-Body Push Recovery

In this paper we extend the line of research that aims at applying linear optimal control approaches with quadratic cost (LQR) to the inherently non-linear control problem of whole-body balancing for push recovery of humanoid robots. The non-linearity of the system is addressed in the controller design by optimization in the weight-space of the cost function in order to maximize balancing performance. We use stochastic sampling-based, gradient-free optimization over the large design parameter space of the whole-body controller to efficiently cope with the unknown relation between the cost function and the balancing performance. We further investigate three different linear ground contact models and evaluate their influence on the overall controller performance. We demonstrate that parameter optimization and novel ground contact models can be used to design a linear balancing controller that produces human-like whole-body motions in physics simulation-based push recovery experiments, simultaneously considering joint angles, center of mass and angular momentum.