# Safe Machine-Learning-supported Model Predictive Force and Motion Control in Robotics

arXiv: https://arxiv.org/abs/2303.04569 · HTML: https://mlsanity.com/paper/2303.04569/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 65 references that are in the map.
- First posted on arXiv 8 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Learning-based Model Predictive Control for Safe Exploration and Reinforcement Learning](https://mlsanity.com/paper/1906.12189/) (2019)
- [Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars](https://mlsanity.com/paper/1711.06586/) (2017)
- [Deep Haptic Model Predictive Control for Robot-Assisted Dressing](https://mlsanity.com/paper/1709.09735/) (2017)
- [On Simulation and Trajectory Prediction with Gaussian Process Dynamics](https://mlsanity.com/paper/1912.10900/) (2019)
- [Gaussian Process Model Predictive Control of An Unmanned Quadrotor](https://mlsanity.com/paper/1707.04515/) (2017)
- [Safe Trajectory Tracking in Uncertain Environments](https://mlsanity.com/paper/2001.11602/) (2020)
- [Nonlinear Model Predictive Control for Constrained Output Path Following](https://mlsanity.com/paper/1502.02468/) (2015)
- [Learning References with Gaussian Processes in Model Predictive Control applied to Robot Assisted Surgery](https://mlsanity.com/paper/1911.10793/) (2019)

## Built on by (most cited first, 3 of 3)

- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems](https://mlsanity.com/paper/2509.18404/) (2025)
- [On the role of Artificial Intelligence methods in modern force-controlled manufacturing robotic tasks](https://mlsanity.com/paper/2409.16828/) (2024)

## Abstract (arXiv)

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.