ABSTRACT
Generating a smooth path through an environment can be challenging because there are multiple competing constraints of total path length, path curvature, and static obstacle avoidance that must all be satisfied simultaneously. This chapter describes an approach that uses convex optimization to construct a smooth path that optimally balances all these competing constraints. The corridor map method introduced by Geraerts and Overmars, 2007 is used to construct an initial, nonoptimal path through the static obstacles in the environment. The corridor map representation makes it straightforward to constrain a path within the bounds of free space, which is crucial for the implementation of the path smoothing algorithm to ensure it does not result in a path that collides with static obstacles. The chapter describes just one particular application of the Chambolle–Pock algorithm. However, the algorithm itself is very general and can be adapted to solve a wide variety of optimization problems.
