In this article, we address the task and safety performance of data-driven model predictive controllers (DD-MPC) for systems with complex dynamics, i.e., temporally or spatially varying dynamics that may also be discontinuous. The three challenges we focus on are the accuracy of learned models, the receding horizon-induced myopic predictions of DD-MPC, and the active encouragement of safety. To learn accurate models for DD-MPC, we cautiously, yet effectively, explore the dynamical system with rapidly exploring random trees (RRT) to collect a uniform distribution of samples in the state-input space and overcome the common distribution shift in model learning. The learned model is further used to construct an RRT tree that estimates how close the model's predictions are to the desired target. This information is used in the cost function of the DD-MPC to minimize the short-sighted effect of its receding horizon nature. To promote safety, we approximate sets of safe states using demonstrations of exclusively safe trajectories, i.e., without unsafe examples, and encourage the controller to generate trajectories close to the sets. As a running example, we use a broken version of an inverted pendulum where the friction abruptly changes in certain regions. Furthermore, we showcase the adaptation of our method to a real-world robotic application with complex dynamics: robotic food-cutting. Our results show that our proposed control framework effectively avoids unsafe states with higher success rates than baseline controllers that employ models from controlled demonstrations and even random actions.

In this paper, we address the safety of data-driven control for contact-rich manipulation. We propose to restrict the controller's action space to keep the system in a set of safe states. In the absence of an analytical model, we show how Gaussian Processes (GP) can be used to approximate safe sets. We disable inputs for which the predicted states are likely to be unsafe using the GP. Furthermore, we show how locally designed feedback controllers can be used to improve the execution precision in the presence of modelling errors. We demonstrate the benefits of our method on a pushing task with a variety of dynamics, by using known and unknown surfaces and different object loads. Our results illustrate that the proposed approach significantly improves the performance and safety of the baseline controller.