Results indicate that the proposed formulation can generate safe, feasible, and smooth USV trajectories in representative complex environments.
Abstract
Autonomous trajectory planning for unmanned surface vehicles (USVs) in complex environments must ensure collision safety, kinematic feasibility, and smooth motion. This paper presents an optimal-control trajectory optimization method implemented in CasADi and solved with the IPOPT interior-point algorithm. The USV is represented by a simplified planar kinematic model with position, heading, and surge speed as states. Longitudinal acceleration and yaw rate are used as the control variables. Obstacle avoidance is modeled through squared-distance inequality constraints for circular obstacles inflated by safety radii. The planning problem is formulated as a finite-horizon nonlinear program with objectives for terminal accuracy, control effort, control smoothness, and path compactness. By optimizing path generation and kinematic feasibility in a single problem, the formulation avoids the decoupling common in staged planning pipelines. Simulations in five scenarios, including single static, multiple static, narrow-corridor, single dynamic, and multi-dynamic obstacle cases, validate the method. Across all scenarios, the optimizer achieved sub-millimeter terminal errors while maintaining positive obstacle clearances. Parameter sensitivity analysis shows a predictable trade-off between safety margin and path length, and ablation experiments quantify each objective term’s contribution. These results indicate that the proposed formulation can generate safe, feasible, and smooth USV trajectories in representative complex environments.
This paper presents a guide path-free multimodal trajectory planning framework for autonomous surface vehicles operating in dynamic environments. The proposed method integrates model predictive control (MPC) with a turning circle-based control barrier function (TC-CBF). Unlike conventional Euclidean distance-based CBFs (ED-CBFs), which evaluate safety solely based on proximity, the TC-CBF accounts for the nonholonomic motion and finite turning capability of a surface vehicle. Its geometric formulation identifies feasible avoidance regions according to the vehicle's turning circles and generates distinct left- and right-turning avoidance modes. These modes allow the optimization solver to explore and select topologically different trajectories without relying on globally planned guide paths, as required by many conventional multimodal planning approaches. By embedding the avoidance direction directly into the safety constraint, the proposed framework alleviates the local-minimum and deadlock problems of single-mode MPC while maintaining computational efficiency. Extensive simulations involving multiple moving vessels demonstrate that the proposed method achieves higher success rates, fewer safety violations, and smaller residual violations than single-mode baselines across all tested traffic densities.
A hybrid real-time CPP framework that integrates an offline coverage strategy with an online optimisation and control scheme and achieves improved tracking consistency and smoother trajectories, while maintaining real-time feasibility is presented.
Mohammad Khaneghaei, Benyamin Ebrahimi, D. Asadi et al.· Aerospace· 0 citations
Simulation results for a three-UAV swarm in a cluttered environment demonstrate that the proposed distributed NMPC-based trajectory planning method can generate dynamically feasible and collision-free trajectories, while enabling the swarm to reach the assigned target positions and preserve the desired formation within a certain formation error.
Ying-Ting Cui, Tong-Xin Zeng, Bin Li· Drones· 0 citations
To address the difficulty of simultaneously satisfying heading continuity, minimum turning-radius constraints, and safe obstacle avoidance in trajectory planning for fixed-wing aircraft operating in static no-fly zone (NFZ) environments, a horizontal trajectory planning model is formulated by incorporating position, heading, curvature constraints, and safety margins around NFZs. A planning method combining weighted kinematic A* with Dubins terminal connection is then proposed. The method jointly represents planar position and heading angle as the search state and expands nodes using constant-curvature motion primitives that satisfy the prescribed curvature constraints. A weighted Dubins distance is employed to guide the search toward the target, while a Dubins curve is used within the target neighborhood to connect the current state to the desired terminal state. Simulation results demonstrate that, in scenarios involving multiple circular NFZs, the proposed method can generate continuous collision-free trajectories that satisfy the prescribed initial and terminal headings, safety-clearance requirements, and minimum turning-radius constraints. The resulting trajectory length increases only moderately relative to the straight-line distance, while the explored nodes are primarily concentrated near feasible passages. These results validate the effectiveness of the proposed method for trajectory planning of fixed-wing aircraft in static NFZ environments.
Cheng-Yi Zhang, Yang Guo, Jia Liu et al.· World Journal of Engineering...· 0 citations
Addressing the challenges of obstacle avoidance for autonomous vehicles in complex dynamic environments, traditional Artificial Potential Field (APF) methods often suffer from delayed responses to dynamic obstacles and generate paths that violate vehicle kinematic constraints. To overcome these limitations, this paper proposes an improved path planning algorithm, the Relative Velocity Potential Field (RVPF), which fuses relative velocity information with kinematic constraints. First, a relative velocity sensitivity factor is introduced to construct a dynamic potential field. By dynamically reshaping the repulsive field distribution based on the relative velocity vector, this approach endows the algorithm with a predictive capability regarding collision risks, facilitating a transition from passive reaction to active defense. Second, a vehicle kinematic model is established incorporating Ackermann steering geometry. A virtual tangential force strategy is employed to map the resultant potential forces into control variables that adhere to wheelbase and steering angle limits, thereby ensuring the generation of smooth and feasible trajectories. Simulation results demonstrate the superior performance of the proposed algorithm in scenarios involving high-speed oncoming traffic, overtaking, and lateral crossing. Notably, in the lateral crossing scenario—where traditional APF failed due to collisions—the RVPF algorithm achieved collision-free passage by actively decelerating and yielding, increasing the minimum safety distance to 5.02 m. These results confirm that the proposed algorithm significantly enhances the safety and stability of autonomous vehicles across diverse traffic situations.
