Vector fields are advantageous in handling nonholonomic motion planning as they provide reference orientation for robots. However, additionally incorporating curvature constraints becomes challenging, due to the interconnection between the design of the curvature-bounded vector field and the tracking controller under underactuation. In this paper, we present a novel framework to co-develop the vector field and the control laws, guiding the nonholonomic robot to the target configuration with curvature-bounded trajectory. First, we formulate the problem by introducing the target positive limit set, which allows the robot to converge to or pass through the target configuration, depending on different dynamics and tasks. Next, we construct a curvature-constrained vector field (CVF) via blending and distributing basic flow fields in workspace and propose the saturated control laws with a dynamic gain, under which the tracking error's magnitude decreases even when saturation occurs. Under the control laws, kinematically constrained nonholonomic robots are guaranteed to track the reference CVF and converge to the target positive limit set with bounded trajectory curvature. Numerical simulations show that the proposed CVF method outperforms other vector-field-based algorithms. Experiments on Ackermann UGVs and semi-physical fixed-wing UAVs demonstrate that the method can be effectively implemented in real-world scenarios.

Recent advancements in Text-to-3D modeling have shown significant potential for the creation of 3D content. However, due to the complex geometric shapes of objects in the natural world, generating 3D content remains a challenging task. Current methods either leverage 2D diffusion priors to recover 3D geometry, or train the model directly based on specific 3D representations. In this paper, we propose a novel method named DirectGaussian, which focuses on generating the surfaces of 3D objects represented by surfels. In DirectGaussian, we utilize conditional text generation models and the surface of a 3D object is rendered by 2D Gaussian splatting with multi-view normal and texture priors. For multi-view geometric consistency problems, DirectGaussian incorporates curvature constraints on the generated surface during optimization process. Through extensive experiments, we demonstrate that our framework is capable of achieving diverse and high-fidelity 3D content creation.

-- Efficient real-time trajectory planning and control for fixed-wing unmanned aerial vehicles is challenging due to their non-holonomic nature, complex dynamics, and the additional uncertainties introduced by unknown aerodynamic effects. In this paper, we present a fast and efficient real-time trajectory planning and control approach for fixed-wing unmanned aerial vehicles, leveraging the differential flatness property of fixed-wing aircraft in coordinated flight conditions to generate dynamically feasible trajectories. The approach provides the ability to continuously replan trajectories, which we show is useful to dynamically account for the curvature constraint as the aircraft advances along its path. In recent years, the deployment of small Fixed-Wing Unmanned Aerial V ehicles (FW-UA Vs) has significantly increased across various applications, including environmental monitoring [1], low-altitude surveillance [2], and support for first responders in search and rescue operations [3]. Their popularity is primarily due to their superior endurance, extended operational range, and lower energy consumption compared to traditional V ertical Take-Off and Landing (VTOL) platforms like quadrotors. Since FW-UA Vs cannot hover in place or execute sharp turns and must maintain continuous motion to remain airborne, accurate trajectory planning and precise tracking are essential for their safe operations.

Path planning for wheeled mobile robots is a critical component in the field of automation and intelligent transportation systems. Car-like vehicles, which have non-holonomic constraints on their movement capability impose additional requirements on the planned paths. Traditional path planning algorithms, such as A* , are widely used due to their simplicity and effectiveness in finding optimal paths in complex environments. However, these algorithms often do not consider vehicle dynamics, resulting in paths that are infeasible or impractical for actual driving. Specifically, a path that minimizes the number of grid cells may still be too curvy or sharp for a car-like vehicle to navigate smoothly. This paper addresses the need for a path planning solution that not only finds a feasible path but also ensures that the path is smooth and drivable. By adapting the A* algorithm for a curvature constraint and incorporating a cost function that considers the smoothness of possible paths, we aim to bridge the gap between grid based path planning and smooth paths that are drivable by car-like vehicles. The proposed method leverages motion primitives, pre-computed using a ribbon based path planner that produces smooth paths of minimum curvature. The motion primitives guide the A* algorithm in finding paths of minimal length and curvature. With the proposed modification on the A* algorithm, the planned paths can be constraint to have a minimum turning radius much larger than the grid size. We demonstrate the effectiveness of the proposed algorithm in different unstructured environments. In a two-stage planning approach, first the modified A* algorithm finds a grid-based path and the ribbon based path planner creates a smooth path within the area of grid cells. The resulting paths are smooth with small curvatures independent of the orientation of the grid axes and even in presence of sharp obstacles.

Effective path planning is a pivotal challenge across various domains, from robotics to logistics and beyond. This research is centred on the development and evaluation of the Dynamic Curvature-Constrained Path Planning Algorithm (DCCPPA) within two dimensional space. DCCPPA is designed to navigate constrained environments, optimising path solutions while accommodating curvature constraints.The study goes beyond algorithm development and conducts a comparative analysis with two established path planning methodologies: Rapidly Exploring Random Trees (RRT) and Probabilistic Roadmaps (PRM). These comparisons provide insights into the performance and adaptability of path planning algorithms across a range of applications.This research underscores the versatility of DCCPPA as a path planning algorithm tailored for 2D space, demonstrating its potential for addressing real-world path planning challenges across various domains. Index Terms Path Planning, PRM, RRT, Optimal Path, 2D Path Planning.

B-spline-based trajectory optimization is widely used for robot navigation due to its computational efficiency and convex-hull property (ensures dynamic feasibility), especially as quadrotors, which have circular body shapes (enable efficient movement) and freedom to move each axis (enables convex-hull property utilization). However, using the B-spline curve for trajectory optimization is challenging for autonomous vehicles (AVs) because of their vehicle kinodynamics (rectangular body shapes and constraints to move each axis). In this study, we propose a novel trajectory optimization approach for AVs to circumvent this difficulty using an incremental path flattening (IPF), a disc type swept volume (SV) estimation method, and kinodynamic feasibility constraints. IPF is a new method that can find a collision-free path for AVs by flattening path and reducing SV using iteratively increasing curvature penalty around vehicle collision points. Additionally, we develop a disc type SV estimation method to reduce SV over-approximation and enable AVs to pass through a narrow corridor efficiently. Furthermore, a clamped B-spline curvature constraint, which simplifies a B-spline curvature constraint, is added to dynamical feasibility constraints (e.g., velocity and acceleration) for obtaining the kinodynamic feasibility constraints. Our experimental results demonstrate that our method outperforms state-of-the-art baselines in various simulated environments. We also conducted a real-world experiment using an AV, and our results validate the simulated tracking performance of the proposed approach.

Rapidly exploring random trees (RRTs) have proven effective in quickly finding feasible solutions to complex motion planning problems. RRT* is an extension of the RRT algorithm that provides probabilistic asymptotic optimality guarantees when using straight-line motion primitives. This work provides extensions to RRT and RRT* that employ fillets as motion primitives, allowing path curvature constraints to be considered when planning. Two fillets are developed, an arc-based fillet that uses circular arcs to generate paths that respect maximum curvature constraints and a spline-based fillet that uses Bezier curves to additionally respect curvature continuity requirements. Planning with these fillets is shown to far exceed the performance of RRT* using Dubin's path motion primitives, approaching the performance of planning with straight-line path primitives. Path sampling heuristics are also introduced to accelerate convergence for nonholonomic motion planning. Comparisons to established RRT* approaches are made using the Open Motion Planning Library (OMPL).

Due to nonholonomic dynamics, the motion planning of nonholonomic robots is always a difficult problem. This letter presents a Discrete States-based Trajectory Planning(DSTP) algorithm for autonomous nonholonomic robots. The proposed algorithm represents the trajectory as x and y positions, orientation angle, longitude velocity and acceleration, angular velocity, and time intervals. More variables make the expression of optimization and constraints simpler, reduce the error caused by too many approximations, and also handle the gear shifting situation. L-BFGS-B is used to deal with the optimization of many variables and box constraints, thus speeding up the problem solving. Various simulation experiments compared with prior works have validated that our algorithm has an order-of-magnitude efficiency advantage and can generate a smoother trajectory with a high speed and low control effort. Besides, real-world experiments are also conducted to verify the feasibility of our algorithm in real scenes. We will release our codes as ros packages.

Abstract-- This paper demonstrates how an efficient representation of the planned path using B-splines, and a construction procedure that takes advantage of the neural network's inductive bias, speed up both the inference and training of a DNN-based motion planner. We build upon our recent work on learning local car maneuvers from past experience using a DNN architecture, introducing a novel B-spline path construction method, making it possible to generate local maneuvers in almost constant time of about 11 ms, respecting a number of constraints imposed by the environment map and the kinematics of a car-like vehicle. I. INTRODUCTION Although autonomous vehicles are researched intensively, Learning through the interaction seems to carry out the most research on motion planning for these vehicles focuses important information to improve the performance of the mostly on managing traffic scenarios and rules [1], [2], paying trained system [7], while it does not impose any upperbounds less attention to the local maneuvers that are necessary on it, unlike supervised learning, which performance to park a car in a crowded city center, to enter a shopping is bounded by the quality of the reference trajectories or mall's garage, or to avoid a collision with another car that human demonstrations. Human drivers perform Although our previously introduced DNN [5] keeps the such local maneuvers intuitively, leveraging the experience path computation time below 50 ms, some emergency maneuvers from similar situations they have encountered in the past. Therefore, we contribute in this seconds) avoiding collisions in dangerous situations, and paper a novel path parametrization and procedure of its satisfying the constraints of a car-like vehicle. A car is nonholonomic, construction, which enables our method to compute yet has a limited steering angle and some physical better paths in an even shorter time in comparison to dimensions, while the planned path should allow control [5] Although these requirements planning function, breaks up with the Markov Decision call for a solution that is rather a reactive behavior than Process formalism used in [5], instead plans the whole a classic planning algorithm, reactive methods [3] rarely maneuver at once.