Legged robots require fast and reliable motion planners and controllers to satisfy real-time implementation requirements. In this dissertation, we investigate the model-based motion planning and control techniques for robotics problems involving contact, including multi-legged robot walking and vertical climbing, item manipulation inside a cluttered environment, and self-reconfigurable robot systems. Each of them can be formulated into a mixed-integer nonlinear (non-convex) program problem for optimization solvers to resolve.

In general, mixed-integer nonconvex programs are challenging to solve. In this dissertation, we adopted several approaches including the decoupling approach, coupled approaches such as ADMM, and data-driven approaches. In the end, we benchmark the performance of the proposed approaches on the bookshelf manipulation problem. Through comparison of various approaches, we show that the data-driven approach can potentially achieve a high success rate, fast solving speed, and good objective function value, given that the new problem is within the trained distribution. Planned trajectories are validated on the hardware showing the planner's capability of generating real-world feasible trajectories.