Path planning algorithm for a car-like robot based on cell decomposition method

This project proposes an obstacle avoiding path planning algorithm based on cell decomposition method for a car-like robot. Dijkstra’s algorithm is applied in order to find the shortest path. Using cell decomposition, the free space of the robot is exactly partitioned into cells. Then, the connectivity graph is created followed by calculating the shortest path by Dijkstra’s algorithm. This project also concerns the robot kinematic constraints such as minimum turning radius. Thus, kinematic modeling and Bezier curve have been used to obtain a feasible path. The algorithm is able to obtain a curvature bounded path with sub-optimal curve length while taking cell decomposition as reference skeleton. The C-space concept has been applied in this situation. The obstacles on the map are expanded according to the size of car-like robot, so that the robot could be treated as points on this map and the coordinates of the map is corresponding to these points. The simulation and experimental result shows the algorithm can obtain the collision free path which satisfies the curvature constraint and approaches the minimal curve length for a car-like robot

Collision-free motions of round robots on metric graphs

In this thesis, we study the path-connectivity problem of configuration spaces of two robots that move without collisions on a connected metric graph. The robots are modelled as metric balls of positive radii. In other words, we wish to find the number of path-connected components of such a configuration space. Finding a solution to this problem will help us to understand which configurations can be reached from any chosen configuration. In order to solve the above problem, we show that any collision-free motion of two robots can be replaced by a finite sequence of elementary motions. As a corollary, we reduce the path-connectivity problem for a 2-dimensional configuration space to the same problem for a simple 1-dimensional subgraph (the configuration skeleton) of the space

A space decomposition method for path planning of loop linkages

This paper introduces box approximations as a new tool for path planning of closed-loop linkages. Box approximations are finite collections of rectangloids that tightly envelop the robot's free space at a desired resolution. They play a similar role to that of approximate cell decompositions for open-chain robots - they capture the free-space connectivity in a multi-resolutive fashion and yield rectangloid channels enclosing collision-free paths - but have the additional property of enforcing the satisfaction of loop closure constraints frequently arising in articulated linkages. We present an efficient technique to compute such approximations and show how resolution-complete path planners can be devised using them. To the authors' knowledge, this is the first space-decomposition approach to closed-loop linkage path planning proposed in the literature.Peer Reviewe

A space decomposition method for path planning of loop linkages

This paper introduces box approximations as a new tool for path planning of closed-loop linkages. Box approximations are finite collections of rectangloids that tightly envelop the robot's free space at a desired resolution. They play a similar role to that of approximate cell decompositions for open-chain robots - they capture the free-space connectivity in a multi-resolutive fashion and yield rectangloid channels enclosing collision-free paths - but have the additional property of enforcing the satisfaction of loop closure constraints frequently arising in articulated linkages. We present an efficient technique to compute such approximations and show how resolution-complete path planners can be devised using them. To the authors' knowledge, this is the first space-decomposition approach to closed-loop linkage path planning proposed in the literature.This work has been partially supported by the Spanish Ministryof Education and Science through the contract DPI2004-07358, by the“Comunitat de Treball dels Pirineus” under contract 2006ITT-10004, andby Ram ́on y Cajal and I3 programme funds.Peer ReviewedPostprint (author's final draft

Neural Informed RRT* with Point-based Network Guidance for Optimal Sampling-based Path Planning

Sampling-based planning algorithms like Rapidly-exploring Random Tree (RRT) are versatile in solving path planning problems. RRT* offers asymptotical optimality but requires growing the tree uniformly over the free space, which leaves room for efficiency improvement. To accelerate convergence, informed approaches sample states in an ellipsoidal subset of the search space determined by current path cost during iteration. Learning-based alternatives model the topology of the search space and infer the states close to the optimal path to guide planning. We combine the strengths from both sides and propose Neural Informed RRT* with Point-based Network Guidance. We introduce Point-based Network to infer the guidance states, and integrate the network into Informed RRT* for guidance state refinement. We use Neural Connect to build connectivity of the guidance state set and further boost performance in challenging planning problems. Our method surpasses previous works in path planning benchmarks while preserving probabilistic completeness and asymptotical optimality. We demonstrate the deployment of our method on mobile robot navigation in the real world.Comment: 7 pages, 6 figure

Disk-Graph Probabilistic Roadmap: Biased Distance Sampling for Path Planning in a Partially Unknown Environment

International audienceIn this paper, we propose a new sampling-based path planning approach, focusing on the challenges linked to autonomous exploration. Our method relies on the definition of a disk graph of free-space bubbles, from which we derive a biased sampling function that expands the graph towards known free space for maximal navigability and frontiers discovery. The proposed method demonstrates an exploratory behavior similar to Rapidly-exploring Random Trees, while retaining the connectivity and flexibility of a graph-based planner. We demonstrate the interest of our method by first comparing its path planning capabilities against state-of-theart approaches, before discussing exploration-specific aspects, namely replanning capabilities and incremental construction of the graph. A simple frontiers-driven exploration controller derived from our planning method is also demonstrated using the Pioneer platform

The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies

Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and connectivity of the solution space. Motivated by this work, we study structural and connectivity-related properties of the space of solutions of Boolean satisfiability problems and establish various dichotomies in Schaefer's framework. On the structural side, we obtain dichotomies for the kinds of subgraphs of the hypercube that can be induced by the solutions of Boolean formulas, as well as for the diameter of the connected components of the solution space. On the computational side, we establish dichotomy theorems for the complexity of the connectivity and st-connectivity questions for the graph of solutions of Boolean formulas. Our results assert that the intractable side of the computational dichotomies is PSPACE-complete, while the tractable side - which includes but is not limited to all problems with polynomial time algorithms for satisfiability - is in P for the st-connectivity question, and in coNP for the connectivity question. The diameter of components can be exponential for the PSPACE-complete cases, whereas in all other cases it is linear; thus, small diameter and tractability of the connectivity problems are remarkably aligned. The crux of our results is an expressibility theorem showing that in the tractable cases, the subgraphs induced by the solution space possess certain good structural properties, whereas in the intractable cases, the subgraphs can be arbitrary

Balancing Global Exploration and Local-connectivity Exploitation with Rapidly-exploring Random disjointed-Trees

Sampling efficiency in a highly constrained environment has long been a major challenge for sampling-based planners. In this work, we propose Rapidly-exploring Random disjointed-Trees* (RRdT*), an incremental optimal multi-query planner. RRdT* uses multiple disjointed-trees to exploit local-connectivity of spaces via Markov Chain random sampling, which utilises neighbourhood information derived from previous successful and failed samples. To balance local exploitation, RRdT* actively explore unseen global spaces when local-connectivity exploitation is unsuccessful. The active trade-off between local exploitation and global exploration is formulated as a multi-armed bandit problem. We argue that the active balancing of global exploration and local exploitation is the key to improving sample efficient in sampling-based motion planners. We provide rigorous proofs of completeness and optimal convergence for this novel approach. Furthermore, we demonstrate experimentally the effectiveness of RRdT*'s locally exploring trees in granting improved visibility for planning. Consequently, RRdT* outperforms existing state-of-the-art incremental planners, especially in highly constrained environments.Comment: Submitted to IEEE International Conference on Robotics and Automation (ICRA) 201