This article proposes a roadmap to address the current challenges in small-scale testbeds for connected and automated vehicles (CAVs) and robot swarms. The roadmap is a joint effort of participants in the workshop “First Workshop on Small-Scale Testbeds for Connected and Automated Vehicles and Robot Swarms,” held on 2 June at the IEEE Intelligent Vehicles Symposium (IV) 2024 in Jeju, South Korea. The roadmap contains three parts: 1) enhancing accessibility and diversity, especially for underrepresented communities, 2) sharing best practices for the development and maintenance of testbeds, and 3) global testbed connectivity, e.g., through an abstraction layer, to support collaboration. The workshop features invited speakers, contributed papers, and a presentation of a survey paper on testbeds. The survey paper provides an online comparative table of more than 25 testbeds, available at https://bassamlab.github.io/testbeds-survey. The workshop’s own website is available at https://cpm.lrt.unibw.de/workshop.

Connected and automated vehicles and robot swarms hold transformative potential for enhancing safety, efficiency, and sustainability in the transportation and manufacturing sectors. Extensive testing and validation of these technologies is crucial for their deployment in the real world. While simulations are essential for initial testing, they often have limitations in capturing the complex dynamics of real-world interactions. This limitation underscores the importance of small-scale testbeds. These testbeds provide a realistic, cost-effective, and controlled environment for testing and validating algorithms, acting as an essential intermediary between simulation and full-scale experiments. This work serves to facilitate researchers' efforts in identifying existing small-scale testbeds suitable for their experiments and provide insights for those who want to build their own. In addition, it delivers a comprehensive survey of the current landscape of these testbeds. We derive 62 characteristics of testbeds based on the well-known sense-plan-act paradigm and offer an online table comparing 22 small-scale testbeds based on these characteristics. The online table is hosted on our designated public webpage www.cpm-remote.de/testbeds, and we invite testbed creators and developers to contribute to it. We closely examine nine testbeds in this paper, demonstrating how the derived characteristics can be used to present testbeds. Furthermore, we discuss three ongoing challenges concerning small-scale testbeds that we identified, i.e., small-scale to full-scale transition, sustainability, and power and resource management.

Distributing computations among agents in large networks reduces computational effort in multi-agent path finding (MAPF). One distribution strategy is prioritized planning (PP). In PP, we couple and prioritize interacting agents to achieve a desired behavior across all agents in the network. We characterize the interaction with a directed acyclic graph (DAG). The computation time for solving MAPF problem using PP is mainly determined through the longest path in this DAG. The longest path depends on the fixed undirected coupling graph and the variable prioritization. The approaches from literature to prioritize agents are numerous and pursue various goals. This article presents an approach for prioritization in PP to reduce the longest path length in the coupling DAG and thus the computation time for MAPF using PP. 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 propose a decentralized graph-coloring algorithm to determine priorities for the agents. We evaluate the approach by applying it to multi-agent motion planning (MAMP) for connected and automated vehicles (CAVs) on roads using, a variant of MAPF.

Multi-agent path finding (MAPF) in large networks is computationally challenging. An approach for MAPF is prioritized planning (PP), in which agents plan sequentially according to their priority. Albeit a computationally efficient approach for MAPF, the solution quality strongly depends on the prioritization. Most prioritizations rely either on heuristics, which do not generalize well, or iterate to find adequate priorities, which costs computational effort. In this work, we show how agents can compute with multiple prioritizations simultaneously. Our approach is general as it does not rely on domain-specific knowledge. The context of this work is multi-agent motion planning (MAMP) with a receding horizon subject to computation time constraints. MAMP considers the system dynamics in more detail compared to MAPF. In numerical experiments on MAMP, we demonstrate that our approach to prioritization comes close to optimal prioritization and outperforms state-of-the-art methods with only a minor increase in computation time. We show real-time capability in an experiment on a road network with ten vehicles in our Cyber-Physical Mobility Lab.

In the domain of Connected and Automated Vehicles (CAVs), small-scale testbeds bridge expensive testing in the real world and computer simulations. Meanwhile, they offer educational opportunities for students to acquire hands-on experience in areas like control, vehicle dynamics, trajectory planning, and real-time software. At RWTH Aachen University, we, the Cyber-Physical Mobility Group, built a small-scale testbed, the open-source and remotely accessible Cyber-Physical Mobility Lab (CPM Lab). We use it for one undergraduate course, one graduate course, and an international competition. Our literature research indicates that no similar publicly available testbed offers continuous educational applications for all academic levels, including postgraduate students. This paper presents (i) an educational umbrella concept designed to create a course portfolio suitable for undergraduate, graduate, and postgraduate needs, (ii) updates to the course concepts with an emphasis on previous publications, and (iii) lessons learned to develop an education portfolio based on small-scale testbeds. We base our results on evaluations conducted over four years involving over 370 students participating in our courses. Our findings indicate that small-scale testbeds can help students become more invested in the topic and may motivate them beyond course requirements.

AbstractThe computation time required to solve nonconvex, nonlinear optimization problems increases rapidly with their size. This poses a challenge in trajectory planning for multiple networked vehicles with collision avoidance. In the centralized formulation, the optimization problem size increases with the number of vehicles in the networked control system (NCS), rendering the formulation unusable for experiments. We investigate two methods to decrease the complexity of networked trajectory planning. First, we approximate the optimization problem by discretizing the vehicle dynamics with an automaton, which turns it into a graph-search problem. Our search-based trajectory planning algorithm has a limited horizon to further decrease computation complexity. We achieve recursive feasibility by design of the automaton which models the vehicle dynamics. Second, we distribute the optimization problem to the vehicles with prioritized distributed model predictive control (P-DMPC), which reduces the problem size. To counter the incompleteness of P-DMPC, we propose a framework for time-variant priority assignment. The framework expands recursive feasibility to every vehicle in the NCS. We present two time-variant priority assignment algorithms for road vehicles, one to improve vehicle progress and one to improve computation time of the NCS. We evaluate our approach for online trajectory planning of multiple networked vehicles in simulations and experiments.

AbstractTrajectory planning techniques form a central step to enable autonomous driving. The motion primitives method generates an automaton of precomputed maneuvers with structure-exploiting properties. Thereby, the trajectory planning problem can be reduced to finding an admissible/optimal sequence of motion primitives. In this chapter, we present ways to designing maneuver automata based on different system models and on either analytical or data-based approaches for automaton generation. Moreover, numerical methods for computing optimal maneuvers are listed and we discuss graph-based planning techniques. A subsequent chapter shows the evaluation of motion primitives automata in the Cyber-Physical Mobility Lab.

Connected and automated vehicles (CAVs) and robot swarms (RSs) hold transformative potential for enhancing safety, efficiency, and sustainability in the transportation and manufacturing sectors. Extensive testing and validation of these technologies are crucial for their deployment in the real world. While simulations are essential for initial testing, they often have limitations in capturing the complex dynamics of real-world interactions. This limitation underscores the importance of small-scale testbeds. These testbeds provide a realistic, cost-effective, and controlled environment for testing and validating algorithms, acting as an essential intermediary between simulation and full-scale experiments. This work serves to facilitate researchers' efforts in identifying existing small-scale testbeds suitable for their experiments and provide insights for those who want to build their own. In addition, it delivers a comprehensive survey of the current landscape of these testbeds. We derive 62 characteristics of testbeds based on the well-known sense-plan-act paradigm and offer an online table comparing 23 small-scale testbeds based on these characteristics. The online table is hosted on our designated public webpage, https://bassamlab.github.io/testbeds-survey, and we invite testbed creators and developers to contribute to it. We closely examine nine testbeds in this article, demonstrating how the derived characteristics can be used to present testbeds. Furthermore, we discuss three ongoing challenges concerning small-scale testbeds that we identified, i.e., small-scale to full-scale transition, sustainability, and power and resource management.

In prioritized planning for vehicles, vehicles plan trajectories in parallel or in sequence. In parallel prioritized planning, the computation time remains approximately constant with an increasing number of vehicles, but it is difficult to guarantee collision-free trajectories. Although sequential prioritized planning can guarantee collision-free trajectories, the computation time increases with the number of sequentially computing vehicles, which we call computation levels. This number is determined by the directed coupling graph which results from the coupling and prioritization of vehicles. This work's contribution is twofold. First, we guarantee safe trajectories in parallel planning through reachability analysis. Although these trajectories are collision-free, they tend to be conservative. Second, we address this conservativeness by planning with a subset of vehicles in sequence. We formulate the problem of selecting this subset as a graph partitioning problem, in which we limit the size of the resulting subgraphs. Consequently, we can choose the number of computation levels independently from the directed coupling graph, and thus are able to limit the computation time in prioritized planning. In our simulations, we reduce the number of computation levels to approximately 64% compared to sequential prioritized planning while maintaining the solution quality.

This article presents the testing of distributed trajectory planning algorithms using our rapid prototyping platform, the Cyber-Physical Mobility Lab (CPM Lab). We propose two algorithms for distributed trajectory planning which plan trajectories at intersections, highway on- and off-ramps, and lane changes for networked and autonomous vehicles. The algorithms avoid collisions between vehicles using a synchronization-based and a prioritized Distributed Model Predictive Control (DMPC) strategy. We test two algorithms in the CPM Lab which is able to handle parallel, sequential, and hybrid computations. The CPM Lab achieves reproducible experiments under non-deterministic computation times and stochastic communication times. Our evaluation shows that different algorithms for distributed trajectory planning can be efficiently tested in different in-the-loop tests.

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.

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, focusing 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 can 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 on a 1:18 scale. The architecture can be applied to other domains.

As the capabilities of connected and autonomous vehicles (CAVs) advance, they will successively enter traffic. Algorithms to control CAVs require extensive testing before they can be deployed to vehicles interacting with human-driven vehicles (HDVs) in mixed traffic. Testing an algorithm in simulation requires simulating human behavior, which is difficult, if not intractable. Testing in real traffic is dangerous and expensive. A scaled laboratory is a testing platform which allows testing of algorithms in controlled environments. Our Cyber-Physical Mobility Lab (CPM Lab) is such a laboratory to evaluate algorithms for CAVs. This paper presents how we incorporate a HDV in our CPM Lab. It shows how we replicate the dynamics and haptic of a real vehicle in our scaled laboratory via a steering wheel and a first-person-view. We demonstrate the capabilities of the CPM Lab with a mixed-traffic scenario composed of an HDV and several CAVs. We plan trajectories for the CAVs with prioritized distributed model predictive control and interact with the HDV using reachability analysis and responsibility-sensitive safety rules.

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 MPC using SCR yields faster lap times than 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.

Rapid prototyping of a Networked Control System (NCS) is challenging because of the physical distribution of agents. Furthermore, experiments with NCS may be subject to external influences which prevent reproducibility. This article presents an architecture for experimental testing of NCS with focus on decision-making. Our architecture for experiments of NCS is strictly modular and hierarchical, and therefore it supports an easy and rapid exchange of each 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 agents and agents with heterogeneous dynamics in the experiments. The architecture also allows handling communication uncertainties, e.g., data packet drop and time delay. The resulting architecture supports performing in-the-loop tests on the model, software, and hardware levels. We demonstrate the architecture in the Cyber-Physical Mobility Lab (CPM Lab) using 20 agents. The architecture can be applied to other domains.

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.

<p>Networked control problems of multi-agent systems can be distributed to the agents to reduce computational effort. One distribution strategy is priority-based non-cooperative distributed model predictive control (P-DMPC), in which the computation time is mainly determined by the longest path in the coupling directed acyclic graph (DAG). The longest path is dependent on the undirected coupling graph, which is fixed, and the priority assignment, which is variable. This article presents an approach to assign priorities in P-DMPC to reduce the longest path length in the coupling DAG and therefore the computation time for the networked control system (NCS). We proof that this problem can be mapped to a graph-coloring problem, in which the number of needed colors corresponds to the longest path length in the coupling DAG. We present an efficient graph-coloring algorithm from which we determine priorities for the agents. We evaluate effect and effort of the approach before applying it to trajectory planning for networked vehicles at intersections.</p>

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.

This paper introduces our Cyber-Physical Mobility Lab (CPM Lab). It is an open-source development environment for networked and autonomous vehicles with focus on networked decision-making, trajectory planning, and control. The CPM Lab hosts 20 physical model-scale vehicles ({\mu}Cars) which we can seamlessly extend by unlimited simulated vehicles. The code and construction plans are publicly available to enable rebuilding the CPM Lab. Our four-layered architecture enables the seamless use of the same software in simulations and in experiments without any further adaptions. A Data Distribution Service (DDS) based middleware allows adapting the number of vehicles during experiments in a seamless manner. The middleware is also responsible for synchronizing all entities following a logical execution time approach to achieve determinism and reproducibility of experiments. This approach makes the CPM Lab a unique platform for rapid functional prototyping of networked decision-making algorithms. The CPM Lab allows researchers as well as students from different disciplines to see their ideas developing into reality. We demonstrate its capabilities using two example experiments. We are working on a remote access to the CPM Lab via a webinterface.