Contact-Implicit Optimal Planning and Iterative Learning Control for Quadrupedal Robots

In this article, we propose a novel approach for motion planning and control in quadruped robots that simultaneously optimizes the base trajectory and contact sequence along the longitudinal direction. The method relies on a simplified 2-D single rigid body model to compute an optimal trajectory, which is then mapped at the joint level. To compensate for model approximations and environmental uncertainties, we introduce an iterative learning control (ILC) scheme that progressively improves tracking performance across repetitions. Compared to existing approaches, our formulation unifies contact planning and trajectory optimization in a learning-while-doing framework, enhancing robustness to disturbances. We validate the method on the quadruped robot Solo-12, demonstrating adaptive gait generation and stable locomotion across different terrains and perturbations.