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 user-friendly open-source implementation within CROCODDYL.

Multi-Contact Inertial Estimation and Localization in Legged Robots

Optimal estimation is a promising tool for multi-contact inertial estimation and localization. To harness its advantages in robotics, it is crucial to solve these large and challenging optimization problems efficiently. To tackle this, we (i) develop a multiple-shooting solver that exploits both temporal and parametric structures through a parametrized Riccati recursion. Additionally, we (ii) propose an inertial local manifold that ensures its full physical consistency. It also enhances convergence compared to the singularity-free log-Cholesky approach. To handle its singularities, we (iii) introduce a nullspace approach in our optimal estimation solver. We (iv) finally develop the analytical derivatives of contact dynamics for both inertial parametrizations. Our framework can successfully solve estimation problems for complex maneuvers such as brachiation in humanoids. We demonstrate its numerical capabilities across various robotics tasks and its benefits in experimental trials with the Go1 robot.