ABSTRACT
This chapter discusses optimization-based methods for global motion planning to make robot efficient. The planning problem in interactive environments is introduced first, followed by the discussion of planning methods. The planning problem is formulated as a constrained optimization, which maximizes task efficiency given dynamic constraints, feasibility constraints, and interaction constraints. To solve the problem, we discuss an optimization-based trajectory planning method, an optimization-based speed profile planning method, and an optimization-based layered planning method which combines the previous two planning methods hierarchically. The planning problems are highly nonlinear and nonconvex due to dynamic and interactive constraints. To compute those problems efficiently online, we convexify the problems. The convex feasible set algorithm (CFS) and the slack convex feasible set algorithm (SCFS) are adopted to transform the non-convex optimization problems into quadratic programs. Various examples are discussed to illustrate the effectiveness of the methods.
