Shortest Path Planning for a Tethered Robot or an Anchored Cable

We consider the problem of planning shortest paths for a tethered robot with a finite length tether in a 2D environment with polygonal obstacles. We present an algorithm that runs in time O((k{sub 1} + 1){sup 2}n{sup 4}) and finds the shortest path or correctly determines that none exists that obeys the constraints; here n is the number obstacle vertices, and k{sub 1} is the number loops in the initial configuration of the tether. The robot may cross its tether but nothing can cross obstacles, which cause the tether to bend. The algorithm applies as well for planning a shortest path for the free end of an anchored cable

A Topological Approach to Workspace and Motion Planning for a Cable-controlled Robot in Cluttered Environments

There is a rising demand for multiple-cable controlled robots in stadiums or warehouses due to its low cost, longer operation time, and higher safety standards. In a cluttered environment the cables can wrap around obstacles. Careful choice needs to be made for the initial cable congurations to ensure that the workspace of the robot is optimized. The presence of cables makes it imperative to consider the homotopy classes of the cables both in the design and motion planning problems. In this thesis we study the problem of workspace planning for multiple-cable controlled robots in an environment with polygonal obstacles. This goal of this thesis is to establish a relationship between the workspace\u27s boundary and cable congurations of such robots, and solve related optimization and motion planning problems. We rst analyze the conditions under which a conguration of a cable-controlled robot can be considered valid, then discuss the relationship between cable conguration, the robot\u27s workspace and its motion state, and finally use graph search based motion planning in h-augmented graph to perform workspace optimization and to compute optimal paths for the robot. We demonstrated corresponding algorithms in simulations

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

Solving the Non-Crossing MAPF with CP

We introduce a new Multi-Agent Path Finding (MAPF) problem which is motivated by an industrial application. Given a fleet of robots that move on a workspace that may contain static obstacles, we must find paths from their current positions to a set of destinations, and the goal is to minimise the length of the longest path. The originality of our problem comes from the fact that each robot is attached with a cable to an anchor point, and that robots are not able to cross these cables. We formally define the Non-Crossing MAPF (NC-MAPF) problem and show how to compute lower and upper bounds by solving well known assignment problems. We introduce a Variable Neighbourhood Search (VNS) approach for improving the upper bound, and a Constraint Programming (CP) model for solving the problem to optimality. We experimentally evaluate these approaches on randomly generated instances

Exploration of Unknown Environments Using a Tethered Mobile Robot

Exploration with mobile robots is a well known field of research, but current solutions cannot be directly applied for tethered robots. In some applications, tethers may be very important to provide power or allow communication with the robot. This thesis presents an exploration algorithm that guarantees complete exploration of arbitrary environments within the length constraint of the tether, while keeping the tether tangle-free at all times. While a generalized algorithm that can be used with several exploration strategies is also proposed, the presented implementation uses a modified frontier-based exploration approach, where the robot chooses its next goal in the frontier between explored and unexplored regions of the environment. The main modification from standard frontier-based method is the use of a cost function to sort multiple goals in one iteration and pick the cheapest one to go to, minimizing global path length in the process. The cost is calculated in terms of path length with tether constraints accounted for. The basic idea of the algorithm is to keep an estimate of the tether configuration, including length and homotopy, and decide the next robot path based on the length difference between the current tether length and the shortest tether length at the next goal position. The length difference is then used to determine whether it is safe for the robot to take the shortest path to the goal, or whether the robot has to take a different path to the goal in the way that would put the tether back into the most optimal configuration. The maximum length difference that would still guarantee global tangle-free paths has been shown to be the circumference of the smallest expected obstacle in the environment. The presented algorithm is provable correct and was tested and evaluated using both simulations and real-world experiments. Navigation of a planar robot is done with the aid of a Simultaneous Localization and Mapping (SLAM) system, with the data being provided by the on-board LiDAR scanner. The results from conducted experiments have demonstrated that the proposed algorithm results in the total path length increase of anywhere from 30% up to to 80% compared to untethered frontier-based approach, with the exact percentage increase dependent on the complexity of the environment. It is also approximately 6 times shorter than the total path length in a conservative approach of backtracking to the base to avoid tangling

Tangle-Free Exploration with a Tethered Mobile Robot

Exploration and remote sensing with mobile robots is a well known field of research, but current solutions cannot be directly applied for tethered robots. In some applications, tethers may be very important to provide power or allow communication with the robot. This paper presents an exploration algorithm that guarantees complete exploration of arbitrary environments within the length constraint of the tether, while keeping the tether tangle-free at all times. While we also propose a generalized algorithm that can be used with several exploration strategies, our implementation uses a modified frontier-based exploration approach, where the robot chooses its next goal in the frontier between explored and unexplored regions of the environment. The basic idea of the algorithm is to keep an estimate of the tether configuration, including length and homotopy, and decide the next robot path based on the difference between the current tether length and the shortest tether length at the next goal position. Our algorithm is provable correct and was tested and evaluated using both simulations and real-world experiments

Online Coverage by a Tethered Autonomous Mobile Robot in Planar Unknown Environments

Abstract—This paper is concerned with online tethered coverage, in which a mobile robot of size D is attached to a fixed point S by a cable of finite length L. Starting at S, the robot has to cover an unknown planar environment containing obstacles, and return to S with the cable fully retracted. The paper first establishes an optimal off-line tethered coverage methodology, then introduces the TC (Tethered Coverage) algorithm that performs online tethered coverage using position and local obstacle detection sensors. The performance of the TC algorithm is measured by its competitiveness, determined by measuring its total online path length, l, relative to the optimal off-line solution lopt. The paper establishes that the TC algorithm has a competitive performance of l ≤ 2 L lopt. Execution example and experiments with a D tethered recoiling mechanism illustrate the usefulness of the TC algorithm. I

Path planning for a tethered robot using Multi-Heuristic A* with topology-based heuristics

Abstract — In this paper, we solve the path planning problem for a tethered mobile robot, which is connected to a fixed base by a cable of length L. The reachable space of the robot is restricted by the length of the cable and obstacles. The reachable space of the tethered robot can be computed by considering the topology class of the cable. However, it is computationally too expensive to compute this space a-priori. Instead, in this paper, we show how we can plan using a recently-developed variant of A * search, called Multi-Heuristic A*. Normally, the Multi-Heuristic A * algorithm takes in a fixed set of heuristic functions. In our problem, however, the heuristics represent length of paths to the goal along different topology classes, and there can be too many of them and not all the topology classes are useful. To deal with this, we adapt Multi-Heuristic A * to work with a dynamically generated set of heuristic functions. It starts out as a normal weighted A*. Whenever the search gets trapped in a local minimum, we find the proper topology class of the path to escape from it and add the corresponding new heuristic function into the set of heuristic functions considered by the search. We present experimental analysis comparing our approach with weighted A * on planning for a tethered robot in simulation. I

Tethered Motion Planning for a Rappelling Robot

The Jet Propulsion Laboratory and Caltech developed the Axel rover to investigate and demonstrate the potential for tethered extreme terrain mobility, such as allowing access to science targets on the steep crater walls of other planets. Tether management is a key issue for Axel and other rappelling rovers. Avoiding tether entanglement constrains the robot's valid motions to the set of outgoing and returning path pairs that are homotopic to each other. In the case of a robot on a steep slope, a motion planner must additionally ensure that this ascent-descent path pair is feasible, based on the climbing forces provided by the tether. This feasibility check relies on the taut tether configuration, which is the shortest path in the homotopy class of the ascent-descent path pair. This dissertation presents a novel algorithm for tethered motion planning in extreme terrains, produced by combining shortest-homotopic-path algorithms from the topology and computational geometry communities with traditional graph search methods. The resulting tethered motion planning algorithm searches for this shortest path, checks for feasibility, and then generates waypoints for an ascent-descent path pair in the same homotopy class. I demonstrate the implementation of this algorithm on a Martian crater data set such as might be seen for a typical mission. By searching only for the shortest path, and ordering that search according to a heuristic, this algorithm proceeds more efficiently than previous tethered path-planning algorithms for extreme terrain. Frictional tether-terrain interaction may cause dangerously intermittent and unstable tether obstacles, which can be categorized based on their stability. Force-balance equations from the rope physics literature provide a set of tether and terrain conditions for static equilibrium, which can be used to determine if a given tether configuration will stick to a given surface based on tether tension. By estimating the tension of Axel's tether when driving, I divide potential tether tension obstacles into the following categories: acting as obstacles, acting as non-obstacles, and hazardous intermittent obstacles where it is uncertain whether the tether would slip or stick under normal driving tension variance. This dissertation describes how to modify the obstacle map as the categorization of obstacles fluctuates, and how to alter a motion plan around the dangerous tether friction obstacles. Together, these algorithms and methods form a framework for tethered motion planning on extreme terrain.</p

Axel: A Minimalist Tethered Rover for Exploration of Extreme Planetary Terrains

Recent scientific findings suggest that some of the most interesting sites for future exploration of planetary surfaces lie in terrains that are currently inaccessible to conventional robotic rovers. To provide robust and flexible access to these terrains, we have been developing Axel, the robotic rover. Axel is a lightweight two-wheeled vehicle that can access steep terrains and negotiate relatively large obstacles because of its actively managed tether and novel wheel design. This article reviews the Axel system and focuses on those system components that affect Axel's steep terrain mobility. Experimental demonstrations of Axel on sloped and rocky terrains are presented