Optimization-based control and planning for highly dynamic legged locomotion in complex environments

Legged animals can dynamically traverse unstructured environments in an elegant and efficient manner, whether it be running down a steep hill or leaping between branches. To harness part of the animal agility to the legged robot would unlock potential applications such as disaster response and planetary exploration. The unique challenge of these tasks is that the robot has to produce highly dynamic maneuvers in complex environments with minimum human guidance. This thesis explores how an optimization-based method can be applied in the control and planning of highly dynamic legged motions to address the locomotion problem in complex environments. Specifically, this work first describes the design synthesis of a small and agile quadrupedal robot \panther. Based on the quadruped platform, we developed a model predictive control (MPC) control framework to realize complex 3D acrobatic motions without resorting to switching among controllers. We present the MPC formulation that directly uses the rotation matrix, which avoids the singularity issue associated with Euler angles. Motion planning algorithms are developed for planar-legged robot traversing challenging terrains. Dynamic trajectories that simultaneously reason about contact, centroidal dynamics, and joint torque limit are obtained by solving mixed-integer convex programs (MICP) without requiring any initial guess from the operator. We further reduce the computational expense of long-horizon planning by leveraging the benefits of both optimization and sampling-based approaches for a simple legged robot. Finally, we present experimental results for each topic on legged robot hardware to validate the proposed method. It is our hope that the results presented in this thesis will eventually enable legged robots to achieve mobility autonomy at the level of biological systems