Many robotic tasks, such as human-robot interactions or the handling of fragile objects, require tight control and limitation of appearing forces and moments alongside sensible motion control to achieve safe yet high-performance operation. We propose a learning-supported model predictive force and motion control scheme that provides stochastic safety guarantees while adapting to changing situations. Gaussian processes are used to learn the uncertain relations that map the robot's states to the forces and moments. The model predictive controller uses these Gaussian process models to achieve precise motion and force control under stochastic constraint satisfaction. As the uncertainty only occurs in the static model parts -- the output equations -- a computationally efficient stochastic MPC formulation is used. Analysis of recursive feasibility of the optimal control problem and convergence of the closed loop system for the static uncertainty case are given. Chance constraint formulation and back-offs are constructed based on the variance of the Gaussian process to guarantee safe operation. The approach is illustrated on a lightweight robot in simulations and experiments.

翻译：许多机器人任务，如人机交互或易碎物品操作，需要在实现灵敏运动控制的同时，对出现的力和力矩进行严格限制，以确保安全且高性能的运行。我们提出一种学习支持的模型预测力与运动控制方案，该方案在适应变化场景的同时提供随机安全保证。采用高斯过程学习从机器人状态到力和力矩的不确定映射关系。模型预测控制器利用这些高斯过程模型，在随机约束满足条件下实现精准的运动与力控制。由于不确定性仅存在于静态模型部分（输出方程），我们采用计算高效的随机模型预测控制（MPC）公式。针对静态不确定性情况，给出了最优控制问题的递归可行性分析及闭环系统收敛性证明。基于高斯过程方差构建机会约束公式和调整参数，以确保安全运行。该方法在轻量级机器人上通过仿真和实验进行了验证。