High-Order Control Barrier Functions: Insights and a Truncated Taylor-Based Formulation

We examine the complexity of the standard High-Order Control Barrier Function (HOCBF) approach and propose a truncated Taylor-based approach that reduces design parameters. First, we derive the explicit inequality condition for the HOCBF approach and show that the corresponding equality condition sets a lower bound on the barrier function value that regulates its decay rate. Next, we present our Truncated Taylor CBF (TTCBF), which uses a truncated Taylor series to approximate the discrete-time CBF condition. While the standard HOCBF approach requires multiple class K functions, leading to more design parameters as the constraint's relative degree increases, our TTCBF approach requires only one. We support our theoretical findings in numerical collision-avoidance experiments and show that our approach ensures safety while reducing design complexity.

Small-Scale Testbeds for Connected and Automated Vehicles and Robot Swarms: Challenges and a Roadmap

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 "1st Workshop on Small-Scale Testbeds for Connected and Automated Vehicles and Robot Swarms," held on June 2 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) connecting testbeds through an abstraction layer to support collaboration. The workshop features eight invited speakers, four contributed papers [1]-[4], and a presentation of a survey paper on testbeds [5]. 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-remote.lrt.unibwmuenchen.de/iv24-workshop.

Learning-Based Control Barrier Function with Provably Safe Guarantees: Reducing Conservatism with Heading-Aware Safety Margin

We propose a learning-based Control Barrier Function (CBF) to reduce conservatism in collision avoidance of car-like robots. Traditional CBFs often use Euclidean distance between robots' centers as safety margin, neglecting headings and simplifying geometries to circles. While this ensures smooth, differentiable safety functions required by CBFs, it can be overly conservative in tight environments. To address this limitation, we design a heading-aware safety margin that accounts for the robots' orientations, enabling a less conservative and more accurate estimation of safe regions. Since the function computing this safety margin is non-differentiable, we approximate it with a neural network to ensure differentiability and facilitate integration with CBFs. We describe how we achieve bounded learning error and incorporate the upper bound into the CBF to provide formal safety guarantees through forward invariance. We show that our CBF is a high-order CBF with relative degree two for a system with two robots whose dynamics are modeled by the nonlinear kinematic bicycle model. Experimental results in overtaking and bypassing scenarios reveal a 33.5 % reduction in conservatism compared to traditional methods, while maintaining safety. Code: https://github.com/bassamlab/sigmarl

XP-MARL: Auxiliary Prioritization in Multi-Agent Reinforcement Learning to Address Non-Stationarity

Non-stationarity poses a fundamental challenge in Multi-Agent Reinforcement Learning (MARL), arising from agents simultaneously learning and altering their policies. This creates a non-stationary environment from the perspective of each individual agent, often leading to suboptimal or even unconverged learning outcomes. We propose an open-source framework named XP-MARL, which augments MARL with auxiliary prioritization to address this challenge in cooperative settings. XP-MARL is 1) founded upon our hypothesis that prioritizing agents and letting higher-priority agents establish their actions first would stabilize the learning process and thus mitigate non-stationarity and 2) enabled by our proposed mechanism called action propagation, where higher-priority agents act first and communicate their actions, providing a more stationary environment for others. Moreover, instead of using a predefined or heuristic priority assignment, XP-MARL learns priority-assignment policies with an auxiliary MARL problem, leading to a joint learning scheme. Experiments in a motion-planning scenario involving Connected and Automated Vehicles (CAVs) demonstrate that XP-MARL improves the safety of a baseline model by 84.4% and outperforms a state-of-the-art approach, which improves the baseline by only 12.8%. Code: github.com/cas-lab-munich/sigmarl

Limiting Computation Levels in Prioritized Trajectory Planning with Safety Guarantees

In prioritized planning for vehicles, vehicles plan trajectories in parallel or in sequence. Parallel prioritized planning offers approximately consistent computation time regardless of the number of vehicles but struggles to guarantee collision-free trajectories. Conversely, sequential prioritized planning can guarantee collision-freeness but results in increased computation time as the number of sequentially computing vehicles, which we term computation levels, grows. This number is determined by the directed coupling graph resulted from the coupling and prioritization of vehicles. In this work, we guarantee safe trajectories in parallel planning through reachability analysis. Although these trajectories are collision-free, they tend to be conservative. We address this by planning with a subset of vehicles in sequence. We formulate the problem of selecting this subset as a graph partitioning problem that allows us to independently set computation levels. Our simulations demonstrate a reduction in computation levels by approximately 64% compared to sequential prioritized planning while maintaining the solution quality.

A Survey on Small-Scale Testbeds for Connected and Automated Vehicles and Robot Swarms

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.

SigmaRL: A Sample-Efficient and Generalizable Multi-Agent Reinforcement Learning Framework for Motion Planning

This paper introduces an open-source, decentralized framework named SigmaRL, designed to enhance both sample efficiency and generalization of multi-agent Reinforcement Learning (RL) for motion planning of connected and automated vehicles. Most RL agents exhibit a limited capacity to generalize, often focusing narrowly on specific scenarios, and are usually evaluated in similar or even the same scenarios seen during training. Various methods have been proposed to address these challenges, including experience replay and regularization. However, how observation design in RL affects sample efficiency and generalization remains an under-explored area. We address this gap by proposing five strategies to design information-dense observations, focusing on general features that are applicable to most traffic scenarios. We train our RL agents using these strategies on an intersection and evaluate their generalization through numerical experiments across completely unseen traffic scenarios, including a new intersection, an on-ramp, and a roundabout. Incorporating these information-dense observations reduces training times to under one hour on a single CPU, and the evaluation results reveal that our RL agents can effectively zero-shot generalize. Code: github.com/cas-lab-munich/SigmaRL