-- Multi-vehicle trajectory planning (MVTP) is one of the key challenges in multi-robot systems (MRSs) and has broad applications across various fields. This paper presents ESCoT, an enhanced step-based coordinate trajectory planning method for multiple car-like robots. ESCoT incorporates two key strategies: collaborative planning for local robot groups and replanning for duplicate configurations. These strategies effectively enhance the performance of step-based MVTP methods. Through extensive experiments, we show that ESCoT 1) in sparse scenarios, significantly improves solution quality compared to baseline step-based method, achieving up to 70% improvement in typical conflict scenarios and 34% in randomly generated scenarios, while maintaining high solving efficiency; and 2) in dense scenarios, outperforms all baseline methods, maintains a success rate of over 50% even in the most challenging configurations. The results demonstrate that ESCoT effectively solves MVTP, further extending the capabilities of step-based methods. Research on multi-robot systems (MRSs) has attracted growing attention in recent years, for its capability of accomplishing complicated missions more effectively and efficiently [1], [2]. MRSs involve many critical problems, one of which is multi-agent path finding (MAPF). MAPF focuses on finding conflict-free paths for multiple agents in a shared environment, ensuring that each agent can navigate from its start position to its goal without colliding with others [3].

Autonomous navigation of car-like robots on uneven terrain poses unique challenges compared to flat terrain, particularly in traversability assessment and terrain-associated kinematic modelling for motion planning. This paper introduces SEB-Naver, a novel SE(2)-based local navigation framework designed to overcome these challenges. First, we propose an efficient traversability assessment method for SE(2) grids, leveraging GPU parallel computing to enable real-time updates and maintenance of local maps. Second, inspired by differential flatness, we present an optimization-based trajectory planning method that integrates terrain-associated kinematic models, significantly improving both planning efficiency and trajectory quality. Finally, we unify these components into SEB-Naver, achieving real-time terrain assessment and trajectory optimization. Extensive simulations and real-world experiments demonstrate the effectiveness and efficiency of our approach. The code is at https://github.com/ZJU-FAST-Lab/seb_naver.

This work proposes a hybrid framework for car-like robots with obstacle avoidance, global convergence, and safety, where safety is interpreted as path invariance, namely, once the robot converges to the path, it never leaves the path. Given a priori obstacle-free feasible path where obstacles can be around the path, the task is to avoid obstacles while reaching the path and then staying on the path without leaving it. The problem is solved in two stages. Firstly, we define a ``tight'' obstacle-free neighborhood along the path and design a local controller to ensure convergence to the path and path invariance. The control barrier function technology is involved in the control design to steer the system away from its singularity points, where the local path invariant controller is not defined. Secondly, we design a hybrid control framework that integrates this local path-invariant controller with any global tracking controller from the existing literature without path invariance guarantee, ensuring convergence from any position to the desired path, namely, global convergence. This framework guarantees path invariance and robustness to sensor noise. Detailed simulation results affirm the effectiveness of the proposed scheme.

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

This paper investigates the planning and control for accurate positioning of car-like robots. We propose a solution that integrates two modules: a motion planner, facilitated by the rapidly-exploring random tree algorithm and continuous-curvature (CC) steering technique, generates a CC trajectory as a reference; and a nonlinear model predictive controller (NMPC) regulates the robot to accurately track the reference trajectory. Based on the $\mu$-tangency conditions in prior art, we derive explicit existence conditions and develop associated computation methods for a special class of CC paths which not only admit the same driving patterns as Reeds-Shepp paths but also consist of cusp-free clothoid turns. Afterwards, we create an autonomous vehicle parking scenario where the NMPC endeavors to follow the reference trajectory. Feasibility and computational efficiency of the CC steering are validated by numerical simulation. CarSim-Simulink joint simulations statistically verify that with exactly same NMPC, the closed-loop system with CC trajectories as references substantially outperforms the case where Reeds-Shepp trajectories are used as references.

We propose a design method for a robust safety filter based on Input Constrained Control Barrier Functions (ICCBF) for car-like robots moving in complex environments. A robust ICCBF that can be efficiently implemented is obtained by learning a smooth function of the environment using Support Vector Machine regression. The method takes into account steering constraints and is validated in simulation and a real experiment.

This paper presents the design of a research platform for autonomous driving applications, the Delft's Autonomous-driving Robotic Testbed (DART). Our goal was to design a small-scale car-like robot equipped with all the hardware needed for on-board navigation and control while keeping it cost-effective and easy to replicate. To develop DART, we built on an existing off-the-shelf model and augmented its sensor suite to improve its capabilities for control and motion planning tasks. We detail the hardware setup and the system identification challenges to derive the vehicle's models. Furthermore, we present some use cases where we used DART to test different motion planning applications to show the versatility of the platform. Finally, we provide a git repository with all the details to replicate DART, complete with a simulation environment and the data used for system identification.

Multi-robot teams have attracted attention from industry and academia for their ability to perform collaborative tasks in unstructured environments, such as wilderness rescue and collaborative transportation.In this paper, we propose a trajectory planning method for a non-holonomic robotic team with collaboration in unstructured environments.For the adaptive state collaboration of a robot team to catch and transport targets to be rescued using a net, we model the process of catching the falling target with a net in a continuous and differentiable form.This enables the robot team to fully exploit the kinematic potential, thereby adaptively catching the target in an appropriate state.Furthermore, the size safety and topological safety of the net, resulting from the collaborative support of the robots, are guaranteed through geometric constraints.We integrate our algorithm on a car-like robot team and test it in simulations and real-world experiments to validate our performance.Our method is compared to state-of-the-art multi-vehicle trajectory planning methods, demonstrating significant performance in efficiency and trajectory quality.

Autonomous navigation of ground robots on uneven terrain is being considered in more and more tasks. However, uneven terrain will bring two problems to motion planning: how to assess the traversability of the terrain and how to cope with the dynamics model of the robot associated with the terrain. The trajectories generated by existing methods are often too conservative or cannot be tracked well by the controller since the second problem is not well solved. In this paper, we propose terrain pose mapping to describe the impact of terrain on the robot. With this mapping, we can obtain the SE(3) state of the robot on uneven terrain for a given state in SE(2). Then, based on it, we present a trajectory optimization framework for car-like robots on uneven terrain that can consider both of the above problems. The trajectories generated by our method conform to the dynamics model of the system without being overly conservative and yet able to be tracked well by the controller. We perform simulations and real-world experiments to validate the efficiency and trajectory quality of our algorithm.

Distributionally Robust Optimal Control (DROC) is a technique that enables robust control in a stochastic setting when the true distribution is not known. Traditional DROC approaches require given ambiguity sets or a KL divergence bound to represent the distributional uncertainty. These may not be known a priori and may require hand-crafting. In this paper, we lift this assumption by introducing a data-driven technique for estimating the uncertainty and a bound for the KL divergence. We call this technique D3ROC. To evaluate the effectiveness of our approach, we consider a navigation problem for a car-like robot with unknown noise distributions. The results demonstrate that D3ROC provides robust and efficient control policies that outperform the iterative Linear Quadratic Gaussian (iLQG) control. The results also show the effectiveness of our proposed approach in handling different noise distributions.