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

Mobile robotic network deployment for intruder detection and tracking

This thesis investigates the problem of intruder detection and tracking using mobile robotic networks. In the first part of the thesis, we consider the problem of seeking an electromagnetic source using a team of robots that measure the local intensity of the emitted signal. We propose a planner for a team of robots based on Particle Swarm Optimization (PSO) which is a population based stochastic optimization technique. An equivalence is established between particles generated in the traditional PSO technique, and the mobile agents in the swarm. Since the positions of the robots are updated using the PSO algorithm, modifications are required to implement the PSO algorithm on real robots to incorporate collision avoidance strategies. The modifications necessary to implement PSO on mobile robots, and strategies to adapt to real environments are presented in this thesis. Our results are also validated on an experimental testbed. In the second part, we present a game theoretic framework for visibility-based target tracking in multi-robot teams. A team of observers (pursuers) and a team of targets (evaders) are present in an environment with obstacles. The objective of the team of observers is to track the team of targets for the maximum possible time. While the objective of the team of targets is to escape (break line-of-sight) in the minimum time. We decompose the problem into two layers. At the upper level, each pursuer is allocated to an evader through a minimum cost allocation strategy based on the risk of each evader, thereby, decomposing the agents into multiple single pursuer-single evader pairs. Two decentralized allocation strategies are proposed and implemented in this thesis. At the lower level, each pursuer computes its strategy based on the results of the single pursuer-single evader target-tracking problem. We initially address this problem in an environment containing a semi-infinite obstacle with one corner. The pursuer\u27s optimal tracking strategy is obtained regardless of the evader\u27s strategy using techniques from optimal control theory and differential games. Next, we extend the result to an environment containing multiple polygonal obstacles. We construct a pursuit field to provide a guiding vector for the pursuer which is a weighted sum of several component vectors. The performance of different combinations of component vectors is investigated. Finally, we extend our work to address the case when the obstacles are not polygonal, and the observers have constraints in motion

Path Planning and Real-Time Collision Avoidance Based on the Essential Visibility Graph

This paper deals with a novel procedure to generate optimum flight paths for multiple unmanned aircraft in the presence of obstacles and/or no-fly zones. A real-time collision avoidance algorithm solving the optimization problem as a minimum cost piecewise linear path search within the so-called Essential Visibility Graph (EVG) is first developed. Then, a re-planning procedure updating the EVG over a selected prediction time interval is proposed, accounting for the presence of multiple flying vehicles or movable obstacles. The use of Dubins curves allows obtaining smooth paths, compliant with flight mechanics constraints. In view of possible future applications in hybrid scenarios where both manned and unmanned aircraft share the airspace, visual flight rules compliant with International Civil Aviation Organization (ICAO) Annex II Right of Way were implemented. An extensive campaign of numerical simulations was carried out to test the effectiveness of the proposed technique by setting different operational scenarios of increasing complexity. Results show that the algorithm is always able to identify trajectories compliant with ICAO rules for avoiding collisions and assuring a minimum safety distance as well. Furthermore, the low computational burden suggests that the proposed procedure can be considered a promising approach for real-time applications

Multi-query Path Planning for an Unmanned Fixed-Wing Aircraft

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106491/1/AIAA2013-4791.pd

Shortest Dubins Path to a Circle

The Dubins path problem had enormous applications in path planning for autonomous vehicles. In this paper, we consider a generalization of the Dubins path planning problem, which is to find a shortest Dubins path that starts from a given initial position and heading, and ends on a given target circle with the heading in the tangential direction. This problem has direct applications in Dubins neighborhood traveling salesman problem, obstacle avoidance Dubins path planning problem etc. We characterize the length of the four CSC paths as a function of angular position on the target circle, and derive the conditions which to find the shortest Dubins path to the target circle

Motion Planning for a Tethered Mobile Robot

Recently there has been surge of research in motion planning for tethered robots. In this problem a planar robot is connected via a cable of limited length to a fixed point in R2. The configuration space in this problem is more complicated than the one of a classic motion planning problem as existence of the cable causes additional constraints on the motion of the robot. In this thesis we are interested in finding a concise representation of the configuration space that results in a straightforward planning algorithm. To achieve such a representation we observe that configuration space manifold has a discrete structure that conveniently can be separated from its continuous aspect when it is represented as an atlas of charts. We provide a method for generating either the complete atlas or a subset of its charts based on special cable events. Generating parts of the configuration space on-the-fly enables the following improvements over the state-of-the-art. a) We decompose the environment into cells as needed rather than an off-line global discretization, obtaining competitive time and space complexity for our planner. b) We are able to exploit topological structure to represent robot-cable configurations concisely leading us towards solutions to the more complex problems of interest. To underscore the potential of this representation, we take further steps to generalize it to two more complicated instances of the tethered robot planning problem that has been widely disregarded in the literature. We will first consider a simplified model of cable-to-cable contacts, giving the robot the option to perform knot-like tying motions. Next, we will address the planning problem for a tethered robot whose cable has a constraint on its curvature. This adds to the realism of the model since most practical cables have some degree of stiffness which limits curvature. In this case we provide a novel technique to relate Dubins' theory of curves with work on planning with topological constraints. Our results show the efficiency of the method and indicate further promise for procedures that represent manifolds via an amalgamation of implicit discrete topological structure and explicit Euclidean cells