Trajectory optimization via continuous-time constraint satisfaction

Trajectory optimization via continuous-time constraint satisfaction

This paper proposes a trajectory optimization method that guarantees continuous-time feasibility of state and control trajectories with respect to path constraints. It achieves this by reformulating path constraints into an auxiliary dynamical system with periodic boundary conditions. The method converges to an approximate Karush-Kuhn-Tucker point via sequential convex programming using a technique called prox-linear optimization. It is applicable to a wide range of nonlinear optimal control problems with nonconvex dynamics and constraints. The approach does not require a dense discretization grid or mesh refinement heuristics to ensure constraint satisfaction between discretization nodes.