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.

Terrain analysis is critical for the practical application of ground mobile robots in real-world tasks, especially in outdoor unstructured environments. In this paper, we propose a novel spatial-temporal traversability assessment method, which aims to enable autonomous robots to effectively navigate through complex terrains. Our approach utilizes sparse Gaussian processes (SGP) to extract geometric features (curvature, gradient, elevation, etc.) directly from point cloud scans. These features are then used to construct a high-resolution local traversability map. Then, we design a spatial-temporal Bayesian Gaussian kernel (BGK) inference method to dynamically evaluate traversability scores, integrating historical and real-time data while considering factors such as slope, flatness, gradient, and uncertainty metrics. GPU acceleration is applied in the feature extraction step, and the system achieves real-time performance. Extensive simulation experiments across diverse terrain scenarios demonstrate that our method outperforms SOTA approaches in both accuracy and computational efficiency. Additionally, we develop an autonomous navigation framework integrated with the traversability map and validate it with a differential driven vehicle in complex outdoor environments. Our code will be open-source for further research and development by the community, https://github.com/ZJU-FAST-Lab/FSGP_BGK.

Dynamic jumping on high platforms and over gaps differentiates legged robots from wheeled counterparts. Compared to walking on rough terrains, dynamic locomotion on abrupt surfaces requires fusing proprioceptive and exteroceptive perception for explosive movements. In this paper, we propose SF-TIM (Simple Framework combining Terrain Imagination and Measurement), a single-policy method that enhances quadrupedal robot jumping agility, while preserving their fundamental blind walking capabilities. In addition, we introduce a terrain-guided reward design specifically to assist quadrupedal robots in high jumping, improving their performance in this task. To narrow the simulation-to-reality gap in quadrupedal robot learning, we introduce a stable and high-speed elevation map generation framework, enabling zero-shot simulation-to-reality transfer of locomotion ability. Our algorithm has been deployed and validated on both the small-/large-size quadrupedal robots, demonstrating its effectiveness in real-world applications: the robot has successfully traversed various high platforms and gaps, showing the robustness of our proposed approach. A demo video has been made available at https://flysoaryun.github.io/SF-TIM.

The tractor-trailer robot consists of a drivable tractor and one or more non-drivable trailers connected via hitches. Compared to typical car-like robots, the addition of trailers provides greater transportation capability. However, this also complicates motion planning due to the robot’s complex kinematics, high-dimensional state space, and deformable structure. To efficiently plan safe, time-optimal trajectories that adhere to the kinematic constraints of the robot and address the challenges posed by its unique features, this paper introduces a lightweight, compact, and high-order smooth trajectory representation for tractor-trailer robots. Based on it, we design an efficiently solvable spatial-temporal trajectory optimization problem. To deal with deformable structures, which leads to difficulties in collision avoidance, we fully leverage the collision-free regions of the environment, directly applying deformations to trajectories in continuous space. This approach not requires constructing safe regions from the environment using convex approximations through collision-free seed points before each optimization, avoiding the loss of the solution space, thus reducing the dependency of the optimization on initial values. Moreover, a multi-terminal fast path search algorithm is proposed to generate the initial values for optimization. Extensive simulation experiments demonstrate that our approach achieves severalfold improvements in efficiency compared to existing algorithms, while also ensuring lower curvature and trajectory duration. Real-world experiments involving the transportation, loading and unloading of goods in both indoor and outdoor scenarios further validate the effectiveness of our method. The source code is accessible at https://github.com/Tracailer/Tracailer.

Just as humans can become disoriented in featureless deserts or thick fogs, not all environments are conducive to the Localization Accuracy and Stability (LAS) of autonomous robots. This paper introduces an efficient framework designed to enhance LiDAR-based LAS through strategic trajectory generation, known as Perception-aware Planning. Unlike vision-based frameworks, the LiDAR-based requires different considerations due to unique sensor attributes. Our approach focuses on two main aspects: firstly, assessing the impact of LiDAR observations on LAS. We introduce a perturbation-induced metric to provide a comprehensive and reliable evaluation of LiDAR observations. Secondly, we aim to improve motion planning efficiency. By creating a Static Observation Loss Map (SOLM) as an intermediary, we logically separate the time-intensive evaluation and motion planning phases, significantly boosting the planning process. In the experimental section, we demonstrate the effectiveness of the proposed metrics across various scenes and the feature of trajectories guided by different metrics. Ultimately, our framework is tested in a real-world scenario, enabling the robot to actively choose topologies and orientations preferable for localization. The source code is accessible at https://github.com/ZJU-FAST-Lab/LF-3PM.

As a fundamental component of autonomous driving systems, motion planning has garnered significant attention from both academia and industry. This paper focuses on efficient and spatial-temporal optimal trajectory optimization in unstructured environments using compact convex approximations of vehicle shapes. Conventional approaches typically model the task as an optimal control problem by discretizing the motion process in state configuration space. However, this often results in a tradeoff between optimality and efficiency since generating high-quality motion trajectories often requires high-precision discretization of the dynamic process, which imposes a substantial computational burden. To address this issue, we leverage the differential flatness property of car-like robots to simplify the trajectory representation and analytically formulate the spatial-temporal joint optimization problem with flat outputs in a compact manner, while ensuring the feasibility of nonholonomic dynamics. Moreover, we achieve efficient obstacle avoidance with a collision-free driving corridor for unmodelled obstacles and signed distance approximations for dynamic moving objects. We present comprehensive benchmarks with State-of-the-Art methods, demonstrating the significance of the proposed method in terms of efficiency and trajectory quality. Real-world experiments verify the practicality of our algorithm. We will release our codes for the research community.

With the development of robotics, ground robots are no longer limited to planar motion. Passive height variation due to complex terrain and active height control provided by special structures on robots require a more general navigation planning framework beyond 2D. Existing methods rarely considers both simultaneously, limiting the capabilities and applications of ground robots. In this paper, we proposed an optimization-based planning framework for ground robots considering both active and passive height changes on the z-axis. The proposed planner first constructs a penalty field for chassis motion constraints defined in$\mathbb{R}^{3}$such that the optimal solution space of the trajectory is continuous, resulting in a high-quality smooth chassis trajectory. Also, by constructing custom constraints in the z-axis direction, it is possible to plan trajectories for different types of ground robots which have z-axis degree of freedom. We performed simulations and real-world experiments to verify the efficiency and trajectory quality of our algorithm.

Robot swarm is a hot spot in robotic research community. In this paper, we propose a decentralized framework for car-like robotic swarm which is capable of real-time planning in cluttered environments. In this system, path finding is guided by environmental topology information to avoid frequent topological change, and search-based speed planning is leveraged to escape from infeasible initial value's local minima. Then spatial-temporal optimization is employed to generate a safe, smooth and dynamically feasible trajectory. During optimization, the trajectory is discretized by fixed time steps. Penalty is imposed on the signed distance between agents to realize collision avoidance, and differential flatness cooperated with limitation on front steer angle satisfies the non-holonomic constraints. With trajectories broadcast to the wireless network, agents are able to check and prevent potential collisions. We validate the robustness of our system in simulation and real-world experiments. Code will be released as open-source packages.

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.