A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R^2 x S^1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning

Efficient mobile robot path planning by Voronoi-based heuristic

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A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R^2 x S^1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning

A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles

We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the ambient geometry by assuming the car is a point mass. We present a Hamilton-Jacobi formulation of the problem that resolves time-optimal paths and considers the geometry of the vehicle

Obround trees: Sparsity enhanced feedback motion planning of differential drive robotic systems

© 2021 Turkiye Klinikleri. All rights reserved.Robot motion planning & control is one of the most critical and prevalent problems in the robotics community. Even though original motion planning algorithms had relied on "open-loop" strategies and policies, researchers and engineers have been focusing on feedback motion planning and control algorithms due to the uncertainties, such as process and sensor noise of autonomous robotic applications. Recently, several studies proposed some robust feedback motion planning strategies based on sparsely connected safe zones. In this class of planning and control policies, local control policy inside a single zone computes and feeds the control actions that can drive the robot to a different connected region while guaranteeing that the robot never exceeds the boundaries of the active area until convergence. While most of these studies apply only to holonomic robotic models, a recent motion planning method (RCT) can solve the motion planning and navigation problems for unicycle like robotic systems based on a randomly connected circular region tree. In this paper, we propose a new/updated feedback motion planning algorithm that substantially enhances the sparsity, computational feasibility, and input effort compared to their methodology. The new algorithm generates a sparse neighborhood tree as a set of connected obround zones. Obround regions cover larger areas inside the environment, thus leads to a more sparse tree structure. During navigation, we modify the nonlinear control policy adopted in RCT method to handle the obround shaped zones. The feedback control policy navigates the robot model from one obround zone to the adjacent area in the tree structure, ensuring it stays inside the active region's boundaries and asymptotically reaches the connected obround. We demonstrate the effectiveness and validity of the algorithm on simulation studies. Our Monte Carlo simulations show that our enhancement to the original algorithm probabilistically improves the sparsity, and produces smoother trajectories compared to two motion planning algorithms that rely on sampling based neighborhood structures