Minimum-Time Trajectory Generation for Wheeled Mobile Systems Using Bézier Curves with Constraints on Velocity, Acceleration and Jerk

This paper considers the problem of minimum-time smooth trajectory planning for wheeled mobile robots. The smooth path is defined by several Bézier curves and the calculated velocity profiles on individual segments are minimum-time with continuous velocity and acceleration in the joints. We describe a novel solution for the construction of a 5th order Bézier curve that enables a simple and intuitive parameterization. The proposed trajectory optimization considers environment space constraints and constraints on the velocity, acceleration, and jerk. The operation of the trajectory planning algorithm has been demonstrated in two simulations: on a racetrack and in a warehouse environment. Therefore, we have shown that the proposed path construction and trajectory generation algorithm can be applied to a constrained environment and can also be used in real-world driving scenarios.

Path planning and collision avoidance methods for distributed multi-robot systems in complex dynamic environments

Multi-robot systems are experiencing increasing popularity in joint rescue, intelligent transportation, and other fields. However, path planning and navigation obstacle avoidance among multiple robots, as well as dynamic environments, raise significant challenges. We propose a distributed multi-mobile robot navigation and obstacle avoidance method in unknown environments. First, we propose a bidirectional alternating jump point search A* algorithm (BAJPSA*) to obtain the robot's global path in the prior environment and further improve the heuristic function to enhance efficiency. We construct a robot kinematic model based on the dynamic window approach (DWA), present an adaptive navigation strategy, and introduce a new path tracking evaluation function that improves path tracking accuracy and optimality. To strengthen the security of obstacle avoidance, we modify the decision rules and obstacle avoidance rules of the single robot and further improve the decision avoidance capability of multi-robot systems. Moreover, the mainstream prioritization method is used to coordinate the local dynamic path planning of our multi-robot systems to resolve collision conflicts, reducing the difficulty of obstacle avoidance and simplifying the algorithm. Experimental results show that this distributed multi-mobile robot motion planning method can provide better navigation and obstacle avoidance strategies in complex dynamic environments, which provides a technical reference in practical situations.

A Smooth Jump Point Search Algorithm for Mobile Robots Path Planning Based on a Two-Dimensional Grid Model

To address the problems of the traditional A ${}^{\ast }$ algorithm in solving paths with many expansion nodes, high memory overhead, low operation efficiency, and many path corners, this paper improved the traditional A ${}^{\ast }$ algorithm by combining jump point search strategy and adaptive arc optimization strategy. Firstly, to improve the safety of our paths, the risk area of the obstacles was expanded. Then, the A ${}^{\ast }$ algorithm was combined with the jump point search strategy to achieve the subnode jump search, reducing the calculation scale and memory overhead, and improving search efficiency. Considering the influence of the density of obstacles on search efficiency, the heuristic function was enhanced according to the special effects of the density of obstacles. Finally, the redundant jump point and adaptive arc optimization strategies were used to shorten the path length further and enhance the initial path’s smoothness. Simulation results showed that our algorithm outperforms traditional A $\ast$ and literature algorithms in path length, security, and smoothness, and then was further validated and applied in large-scale marine environments and realistic settings.

Effective Parametrization of Low Order Bézier Motion Primitives for Continuous-Curvature Path-Planning Applications

We propose a new parametrization of motion primitives based on Bézier curves that suits perfectly path-planning applications (and environment exploration) of wheeled mobile robots. The individual motion primitives can simply be calculated taking into account the requirements of path planning and the constraints of a vehicle, given in the form of the starting and ending orientations, velocities, turning rates, and curvatures. The proposed parametrization provides a natural geometric interpretation of the curve. The solution of the problem does not require optimization and is obtained by solving a system of simple polynomial equations. The resulting planar path composed of the primitives is guaranteed to be C2 continuous (the curvature is therefore continuous). The proposed primitives feature low order Bézier (third order polynomial) curves. This not only provides the final path with minimal required turns or unwanted oscillations that typically appear when using higher-order polynomial primitives due to Runge’s phenomenon but also makes the approach extremely computationally efficient. When used in path planning optimizers, the proposed primitives enable better convergence and conditionality of the optimization problem due to a low number of required parameters and a low order of the polynomials. The main contribution of the paper therefore lies in the analytic solution for the third-order Bézier motion primitive under given boundary conditions that guarantee continuous curvature of the composed spline path. The proposed approach is illustrated on some typical scenarios of path planning for wheeled mobile robots.