Path planning algorithms for single and multiple mobile robot systems

Abstract

Mobile robots have become ubiquitous today and are used widely in sensor networks. Their use in applications involving long-term operations, remote sensing and complex environments is a widely studied area of research due to their high precision capabilities over extended periods of time and low cost operation. This thesis develops methods for path planning of mobile robot systems for use in novel applications under various application and system specific constraints. First, path planning algorithms for visual surveillance applications are developed. The problems addressed therein relate to long-term autonomy, visual monitoring on terrains, cooperative operations and large-scale coverage. The proposed solutions consider environment and robot limitations such as visibility obstructions, terrain restrictions and refueling considerations. Second, path planning for robots with a curvature-constrained motion model is considered. This motion model is widely used to model mobile robot kinematics and poses computationally hard problems in path planning. This thesis addresses two interesting problems in this space. The results focus on practical considerations and implementability of the solution approach. Cooperative Air-Ground Route Planning for Large-Scale Coverage Applications This problem considers the use of an aerial robot for large-scale visual coverage in two dimensional planar environments. The use of aerial robots for surveillance is limited by their fuel capacity. The approach discussed in this work uses a ground-based mobile refueling vehicle, constrained to travel on the road, to increase operational range of the aerial robot in both space and time. The planning algorithm determines paths for both aerial and ground robots for visual coverage and coordinated rendezvous visits to refuel the aerial robot. The solution techniques include a branch-and-cut based exact method; and a construction heuristic for computationally efficient solutions. The techniques are validated in field demonstrations using real robots. Persistent Monitoring of Piece-Wise Linear Features on Terrains using Multiple Aerial and Ground Robots. Persistent monitoring on terrains using multiple mobile robotic sensors requires coordinated planning. Terrain features add visibility obstacles and limited fuel capacity of aerial robots leads to range restrictions, that make the problem challenging. This work addresses the visual-monitoring problem on piece-wise linear features within a terrain using multiple mobile robots for persistent operations. The planner must account for visual coverage, refueling aerial robots during the mission and placement of refueling depots while also utilizing the available sensor diversity to minimize overall costs for the monitoring mission. Building on existing literature on visibility in specific classes of polygons and fuel-constrained routing, this thesis develops a discrete representation of the problem that allows the design and application of discrete optimization techniques to find optimal solutions. It develops a Mixed Integer Linear Programming formulation and a branch-and-cut implementation to speed-up computation. It also includes the design of a construction heuristic based on competitive construction of robot paths using a step-increment strategy. The thesis reports results from computational simulations and illustrates proof-of-concept using experiments on real robots. Multi-Point Visual Monitoring on a Terrain using an Aerial Robot The multi-point monitoring problem on terrains using an aerial robot extends the results of visual monitoring on planar environments and 1.5 D terrains. The points-of-interest may be located anywhere within the terrain. A solution strategy to the problem involves addressing the visibility constraints due to topographical features and camera field-of-view limitations. This work develops a visibility computation strategy based on existing techniques on terrain visibility, to compute visibility regions fully contained in the flight plane. The route planning problem is posed as an instance of TSP with neighbourhoods (TSPN). A constant-factor approximation algorithm is designed and construction of the proof for the approximation bounds is discussed in detail. The bounds on solution are computed based on properties of the visibility regions and the terrain. The problem is further reduced to an instance of generalized TSP (GTSP) and a practically useful approach that uses a standard GTSP solver to solve the reduced problem is developed. A branch-and-cut method based on a new ILP formulation is also developed to solve and benchmark the solutions found using the GTSP solver. Proof-of-concept experiments were performed using an aerial robot for paths computed by the planner. Curvature Constrained Trajectory Planning for a Mobile Robot through a sequence of points: A Perturbation - based Approach Curvature constrained motion modeling is a popular modeling technique for a majority of wheeled ground mobile robots as also altitude-constrained flight operations of fixed-wing aerial robots. In this work, Dubins’ model for a forward moving car-like vehicle is used to account for the curvature constraint. Path planning for the model is challenging for any sequence of more than two points and is known to be NP-hard. Hence, one cannot expect to design polynomial time exact algorithmic solutions. This thesis develops a perturbation-based method to design approximate paths through a sequence of points. The problem extends Dubins’ original results on optimal paths between two locations, to a sequence of n locations. It is shown that bounded perturbations of the location coordinates at precisely computed parameter values that correspond to discontinuity in the path length function, lead to computationally efficient solutions with path length close to known lower bounds. Path Planning for a UAV with Kinematic Constraints in the Presence of Polygonal Obstacles Building on the work on path planning through a sequence of points, this work develops a path planner for a curvature constrained vehicle in the presence of polygonal obstacles. It uses a visibility graph representation for the environment and develops a modified Dijkstra’s shortest path algorithm as a first step in the two-step path planning approach. The second step performs a reverse search on the graph to find feasible paths and uses results of the first step as priors to speed up the search. Simulation results are used to substantiate the claims. In summary, this thesis develops novel path planning algorithms for mobile robots that account for application and system-level constraints. Optimal planning algorithms and efficient heuristics are developed for airground robots operating individually and in cooperation, to perform visual coverage and persistent monitoring. The methods developed in the thesis are validated through computational simulations and field demonstrations. Further, practically useful path planners are developed for robots with a curvature constrained motion model for visiting a sequence of points and in the presence of obstacles.