On Koopman-based surrogate models for non-holonomic robots

Data-driven surrogate models of dynamical systems based on the extended dynamic mode decomposition are nowadays well-established and widespread in applications. Further, for non-holonomic systems exhibiting a multiplicative coupling between states and controls, the usage of bi-linear surrogate models has proven beneficial. However, an in-depth analysis of the approximation quality and its dependence on different hyperparameters based on both simulation and experimental data is still missing. We investigate a differential-drive mobile robot to close this gap and provide first guidelines on the systematic design of data-efficient surrogate models.

Cooperative Distributed MPC via Decentralized Real-Time Optimization: Implementation Results for Robot Formations

Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approaches formation control of mobile robots via a cooperative DMPC scheme. We discuss the implementation via decentralized optimization algorithms. To this end, we combine the alternating direction method of multipliers with decentralized sequential quadratic programming to solve the underlying optimal control problem in a decentralized fashion. Our approach only requires coupled subsystems to communicate and does not rely on a central coordinator. Our experimental results showcase the efficacy of DMPC for formation control and they demonstrate the real-time feasibility of the considered algorithms.

Time-Optimal Handover Trajectory Planning for Aerial Manipulators based on Discrete Mechanics and Complementarity Constraints

Planning a time-optimal trajectory for aerial robots is critical in many drone applications, such as rescue missions and package delivery, which have been widely researched in recent years. However, it still involves several challenges, particularly when it comes to incorporating special task requirements into the planning as well as the aerial robot's dynamics. In this work, we study a case where an aerial manipulator shall hand over a parcel from a moving mobile robot in a time-optimal manner. Rather than setting up the approach trajectory manually, which makes it difficult to determine the optimal total travel time to accomplish the desired task within dynamic limits, we propose an optimization framework, which combines discrete mechanics and complementarity constraints (DMCC) together. In the proposed framework, the system dynamics is constrained with the discrete variational Lagrangian mechanics that provides reliable estimation results also according to our experiments. The handover opportunities are automatically determined and arranged based on the desired complementarity constraints. Finally, the performance of the proposed framework is verified with numerical simulations and hardware experiments with our self-designed aerial manipulators.

Model Predictive Control of Non-Holonomic Vehicles: Beyond Differential-Drive

Non-holonomic vehicles are of immense practical value and increasingly subject to automation. However, controlling them accurately, e.g., when parking, is known to be challenging for automatic control methods, including model predictive control (MPC). Combining results from MPC theory and sub-Riemannian geometry in the form of homogeneous nilpotent system approximations, this paper proposes a comprehensive, ready-to-apply design procedure for MPC controllers to steer controllable, driftless non-holonomic vehicles into given setpoints. It can be ascertained that the resulting controllers nominally asymptotically stabilize the setpoint for a large-enough prediction horizon. The design procedure is exemplarily applied to four vehicles, including the kinematic car and a differentially driven mobile robot with up to two trailers. The controllers use a non-quadratic cost function tailored to the non-holonomic kinematics. Novelly, for the considered example vehicles, it is proven that a quadratic cost employed in an otherwise similar controller is insufficient to reliably asymptotically stabilize the closed loop. Since quadratic costs are the conventional choice in control, this highlights the relevance of the findings. To the knowledge of the authors, it is the first time that MPC controllers of the proposed structure are applied to non-holonomic vehicles beyond very simple ones, in particular (partly) on hardware.