# Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

arXiv: https://arxiv.org/abs/1912.10360 · HTML: https://mlsanity.com/paper/1912.10360/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2019.

## Built on by (most cited first, 17 of 17)

- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Approximate non-linear model predictive control with safety-augmented neural networks](https://mlsanity.com/paper/2304.09575/) (2023)
- [Safe Value Functions](https://mlsanity.com/paper/2105.12204/) (2021)
- [Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retraining](https://mlsanity.com/paper/2404.05835/) (2024)
- [Optimality Principles in Spacecraft Neural Guidance and Control](https://mlsanity.com/paper/2305.13078/) (2023)
- [Self-Supervised Learning of Iterative Solvers for Constrained Optimization](https://mlsanity.com/paper/2409.08066/) (2024)
- [The Mini Wheelbot: A Testbed for Learning-based Balancing, Flips, and Articulated Driving](https://mlsanity.com/paper/2502.04582/) (2025)
- [Vision-Language Model Predictive Control for Manipulation Planning and Trajectory Generation](https://mlsanity.com/paper/2504.05225/) (2025)
- [Safe Imitation Learning of Nonlinear Model Predictive Control for Flexible Robots](https://mlsanity.com/paper/2212.02941/) (2022)
- [Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributions](https://mlsanity.com/paper/2504.04603/) (2025)
- [Input Convex Lipschitz Recurrent Neural Networks for Robust and Efficient Process Modeling and Optimization](https://mlsanity.com/paper/2401.07494/) (2024)
- [Model-Free Predictive Control: Introductory Algebraic Calculations, and a Comparison with HEOL and ANNs](https://mlsanity.com/paper/2502.00443/) (2025)
- [Learning Predictive Control with Deep Koopman Operators for Autonomous Vehicle Motion Planning](https://mlsanity.com/paper/2606.08136/) (2026)
- [A stabilizing reinforcement learning approach for sampled systems with partially unknown models](https://mlsanity.com/paper/2208.14714/) (2022)
- [Nonlinear sparse variational Bayesian learning based model predictive control with application to PEMFC temperature control](https://mlsanity.com/paper/2404.09519/) (2024)
- [ReLU Networks for Model Predictive Control: Network Complexity and Performance Guarantees](https://mlsanity.com/paper/2601.16764/) (2026)
- [Robustness of Robotic Manipulation: Foundations and Frontiers](https://mlsanity.com/paper/2606.31494/) (2026)

## Abstract (arXiv)

Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.