Online Motion Generation via Tangential Sampling-Based MPC Around Nonconvex Obstacles

Collision-free motion planning has a well-established research history, but the majority of studies have been centered around Euclidean space and conducted offline. The primary challenge in online motion planning lies in circumventing local minima, which become more pronounced in configuration space. We propose an online method for generating collision-free motion in configuration space that effectively avoids local minima. Our approach decomposes the optimal velocity into nominal and tangential components, with the tangential velocity optimized to facilitate escape from local minima. The tangential velocity is defined in the tangential space, with its normal direction determined by the gradient of the nearest distance between the robot and obstacles, relative to the robot's states. Direct optimization of the tangential velocity is challenging due to its dependence on varying tangent spaces. To address this, we represent the tangential velocity using the orthogonal basis of the tangent space, decoupling it from the varying tangent space. This allows explicit optimization of the tangential velocity by optimizing its components. Additionally, we introduce a warm-start operator in the tangent space to ensure the consistency and convergence. Furthermore, we propose a dynamic weight based on proximity to local minima to balance the tangential and nominal velocities, forming the optimal velocity. The effectiveness of our approach in avoiding local minima is validated through simulations and physical experiments.