Endpoint-Explicit Differential Dynamic Programming via Exact Resolution

We introduce a novel method for handling endpoint constraints in constrained differential dynamic programming (DDP). Unlike existing approaches, our method guarantees quadratic convergence and is exact, effectively managing rank deficiencies in both endpoint and stagewise equality constraints. It is applicable to both forward and inverse dynamics formulations, making it particularly well-suited for model predictive control (MPC) applications and for accelerating optimal control (OC) solvers. We demonstrate the efficacy of our approach across a broad range of robotics problems and provide a userfriendly open-source implementation within Crocoddyl.