Distributing computations among agents in a networked control system (NCS) reduces computational effort. One distribution strategy is prioritized distributed model predictive control (P-DMPC). In P-DMPC, we couple and prioritize interacting agents to achieve a desired behavior of the NCS. We characterize the interaction with a directed acyclic graph (DAG). The computation time of the NCS is mainly determined through the longest path in the DAG. The longest path depends on the undirected coupling graph, which is fixed, and the prioritization, which is variable. The approaches to prioritize agents are numerous and pursue various goals. This article presents an approach to assign priorities in P-DMPC to reduce the longest path length in the coupling DAG and thus the computation time for the NCS. We prove that this problem can be mapped to a graph-coloring problem, in which the number of colors required corresponds to the longest path length in the coupling DAG. We further propose to reorder the colors, which decreases the number of constraints for agents along the longest path in the coupling DAG. We propose a decentralized graph-coloring algorithm to determine priorities for the agents. We evaluate the approach by applying it to trajectory planning for networked and autonomous vehicles on roads.

Self-driving laboratories receive increasing acceptance as they are used in research and education. For research, they mainly serve as a platform on which algorithms can be tested under realistic conditions before getting deployed into the real world. In education, they can add value by creating a reference to reality as they o er an application for theoretical knowledge. In combination with the fact that practical work is well appreciated among students, such setup helps to motivate and thus enhance the learning experience. However, not every institution has the capabilities to create a self-driving lab on its own. Instead, open-source and remotely accessible laboratories, like our Cyber-Physical Mobility Lab (CPM Lab) can be used to engage with the domain of networked and autonomous vehicles. By means of two of our courses, we demonstrate the capabilities of the CPM Lab. These two courses can either be used as groundwork to develop own lectures in this domain, or used directly since the course materials are open-source.

Nonconvex optimal control problems for large-scale networked control systems (NCSs) can be distributed to accelerate computation time. One distribution strategy is priority-based non-cooperative distributed model predictive control. The priorities assigned to agents determine if a feasible solution for all agents exists. This problem has been investigated in the domain of robotics for many years, and has recently been picked up in the domain of road vehicles. We develop a dynamic priority assignment algorithm for road vehicles based on an approach from the domain of robotics. In our algorithm, each vehicle determines its priority in a distributed fashion. The priority of a vehicle increases with the number of potential collisions on its planned path to increase the success of the distributed control problem. We further propose an approach for priority-based non-cooperative distributed model predictive control with dynamic priorities and prove recursive feasibility for the NCS. This paper presents the first evaluation in experiment of the priority assignment algorithm. We compare the algorithm’s performance to dynamic random priorities and to static priorities.

Rapid prototyping of Connected and Automated Vehicles (CAV) is challenging because of the physical distribution of vehicles. Furthermore, experiments with CAV may be subject to external influences which prevent reproducibility. This article presents an architecture for the experimental testing of CAVs with a focus on decision-making. Our architecture for experiments of CAV is strictly modular and hierarchical, and therefore it supports an easy and rapid exchange of every single controller as well as of optimization libraries. Additionally, the architecture synchronizes the whole network of sensors, computation devices, and actuators. Thus, it achieves deterministic and reproducible results, even for time-variant network topologies. Using this architecture, we are able to include active and passive vehicles and vehicles with heterogeneous dynamics in the experiments. The architecture also allows for handling communication uncertainties, e.g., data packet drop and time delay. The resulting architecture supports performing different in-the-loop tests and experiments. We demonstrate the architecture in the Cyber-Physical Mobility Lab (CPM Lab) using 20 vehicles in 1:18 scale. The architecture can be applied to other domains.

Optimization problems for trajectory planning in autonomous vehicle racing are characterized by their nonlinearity and nonconvexity. Instead of solving these optimization problems, usually a convex approximation is solved instead to achieve a high update rate. We present a real-time-capable model predictive control (MPC) trajectory planner based on a nonlinear single-track vehicle model and Pacejka’s magic tire formula for autonomous vehicle racing. After formulating the general nonconvex trajectory optimization problem, we form a convex approximation using sequential convex programming (SCP). The state of the art convexifies track constraints using sequential linearization (SL), which is a method of relaxing the constraints. Solutions to the relaxed optimization problem are not guaranteed to be feasible in the nonconvex optimization problem. We propose sequential convex restriction (SCR) as a method to convexify track constraints. SCR guarantees that resulting solutions are feasible in the nonconvex optimization problem. We show recursive feasibility of solutions to the restricted optimization problem. The MPC is evaluated on a scaled version of the Hockenheimring racing track in simulation. The results show that an MPC using SCR yields faster lap times than an MPC using SL, while still being real-time capable.

It is hard to find the global optimum to general nonlinear, nonconvex optimization problems in reasonable time. This paper presents a method to transfer the receding horizon control approach, where nonlinear, nonconvex optimization problems are considered, into graph-search problems. Specifically, systems with symmetries are considered to transfer system dynamics into a finite state automaton. In contrast to traditional graph-search approaches where the search continues until the goal vertex is found, the transfer of a receding horizon control approach to graph-search problems presented in this paper allows to solve them in real-time. We proof that the solutions are recursively feasible by restricting the graph search to end in accepting states of the underlying finite state automaton. The approach is applied to trajectory planning for multiple networked and autonomous vehicles. We evaluate its effectiveness in simulation as well as in experiments in the Cyber-Physical Mobility Lab, an open source platform for networked and autonomous vehicles. We show real-time capable trajectory planning with collision avoidance in experiments on off-the-shelf hardware and code in MATLAB for two vehicles.