Koptev Mikhail, Figueroa Nadia, Billard Aude
Learning Algorithms and Systems Laboratory (LASA), École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
Department of Aeronautics and Astronautics, University of Pennsylvania, Philadelphia, PA, USA.
Int J Rob Res. 2024 Nov;43(13):2049-2069. doi: 10.1177/02783649241246557. Epub 2024 Apr 12.
Dynamical system (DS) based motion planning offers collision-free motion, with closed-loop reactivity thanks to their analytical expression. It ensures that obstacles are not penetrated by reshaping a nominal DS through matrix modulation, which is constructed using continuously differentiable obstacle representations. However, state-of-the-art approaches may suffer from local minima induced by non-convex obstacles, thus failing to scale to complex, high-dimensional joint spaces. On the other hand, sampling-based Model Predictive Control (MPC) techniques provide feasible collision-free paths in joint-space, yet are limited to quasi-reactive scenarios due to computational complexity that grows cubically with space dimensionality and horizon length. To control the robot in the cluttered environment with moving obstacles, and to generate feasible and highly reactive collision-free motion in robots' joint space, we present an approach for modulating joint-space DS using sampling-based MPC. Specifically, a nominal DS representing an unconstrained desired joint space motion to a target is locally deflected with obstacle-tangential velocity components navigating the robot around obstacles and avoiding local minima. Such tangential velocity components are constructed from receding horizon collision-free paths generated asynchronously by the sampling-based MPC. Notably, the MPC is not required to run constantly, but only activated when the local minima is detected. The approach is validated in simulation and real-world experiments on a 7-DoF robot demonstrating the capability of avoiding concave obstacles, while maintaining local attractor stability in both quasi-static and highly dynamic cluttered environments.
基于动态系统（DS）的运动规划能够提供无碰撞运动，由于其解析表达式，具有闭环反应性。它通过使用连续可微的障碍物表示构建的矩阵调制来重塑标称DS，从而确保不穿透障碍物。然而，现有方法可能会受到非凸障碍物引起的局部极小值的影响，因此无法扩展到复杂的高维关节空间。另一方面，基于采样的模型预测控制（MPC）技术在关节空间中提供可行的无碰撞路径，但由于计算复杂度随空间维度和预测时域长度呈立方增长，仅限于准反应场景。为了在存在移动障碍物的杂乱环境中控制机器人，并在机器人的关节空间中生成可行且高反应性的无碰撞运动，我们提出了一种使用基于采样的MPC来调制关节空间DS的方法。具体而言，一个表示向目标的无约束期望关节空间运动的标称DS会通过障碍物切向速度分量进行局部偏转，这些分量引导机器人绕过障碍物并避免局部极小值。这种切向速度分量由基于采样的MPC异步生成的滚动时域无碰撞路径构建而成。值得注意的是，MPC不需要持续运行，仅在检测到局部极小值时才激活。该方法在一个7自由度机器人的模拟和实际实验中得到了验证，展示了在准静态和高动态杂乱环境中避免凹形障碍物的能力，同时保持局部吸引子稳定性。
