Robust Optimal Motion Planning for Nonlinear Systems in the Context of Neural Abstraction

Robotic automation provides a great contribution to increase efficiency and precision of several tasks. However, most of the solutions used rely on the perfect knowledge of the system's model. While this requirement could be easily fulfilled in industrial setup, this cannot be assumed as true in more general scenarios, like daily living environment. To this aim, in this study, we present a novel theoretical framework for optimal motion planning in unknown nonlinear dynamical systems using neural abstraction. The proposed approach establishes an ϵ-approximate simulation relation, leveraging deep neural networks to create an abstracted representation of the system with quantified approximation errors. The state space is partitioned into polyhedral regions using neural networks with ReLU activation functions, resulting in piecewise linear dynamical models. A hybrid control scheme combining Tube Model Predictive Control and Sliding Mode Control is incorporated into this framework to generate optimal trajectories and control signals while ensuring stability in the presence of unknown external disturbances and model inaccuracies. Its effectiveness is demonstrated through a case study on object manipulation using a Franka arm equipped with a Pisa/IIT SoftHand gripper in a ROS/Gazebo simulation environment.