Planning over discontinuous dynamics is needed for robotics tasks like contact-rich manipulation, which presents challenges in the numerical stability and speed of planning methods when either neural network or analytical models are used. On the one hand, sampling-based planners require higher sample complexity in high-dimensional problems and cannot describe safety constraints such as force limits. On the other hand, gradient-based solvers can suffer from local optima and convergence issues when the Hessian is poorly conditioned. We propose a planning method with both sampling- and gradient-based elements, using the Cross-entropy Method to initialize a gradient-based solver, providing better search over local minima and the ability to handle explicit constraints. We show the approach allows smooth, stable contact-rich planning for an impedance-controlled robot making contact with a stiff environment, benchmarking against gradient-only MPC and CEM.

翻译：针对接触丰富操作等机器人任务，需要在非连续动力学上进行规划。当使用神经网络或分析模型时，规划方法在数值稳定性和速度方面面临挑战。一方面，基于采样的规划器在高维问题中需要更高的采样复杂度，且无法描述力约束等安全限制。另一方面，基于梯度的求解器在Hessian矩阵条件数不佳时可能陷入局部最优或出现收敛问题。我们提出一种融合采样与梯度元素的规划方法：利用交叉熵方法初始化梯度求解器，从而实现对局部最小值更优的搜索，并具备处理显式约束的能力。实验证明，该方法能够使阻抗控制机器人与刚性环境接触时实现平滑稳定的接触丰富规划，并与纯梯度MPC及CEM方法进行了基准对比。