Optimal Path Planning in Distinct Topo-Geometric Classes using Neighborhood-augmented Graph and its Application to Path Planning for a Tethered Robot in 3D

Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables, multi-robot topological exploration & coverage, and, congestion reduction for mobile robots navigation without inter-robot coordination. Existing paradigm is to use topological path planning methods that can provide optimal paths from distinct topological classes available in the underlying configuration space. However, these methods usually require non-trivial and non-universal geometrical constructions, which are prohibitively complex or expensive in 3 or higher dimensional configuration spaces with complex topology. Furthermore, topological methods are unable to distinguish between locally optimal paths that belong to the same topological class but are distinct because of genus-zero obstacles in 3D or due to high-cost or high-curvature regions. In this paper we propose an universal and generalized approach to multi-class path planning using the concept of a novel neighborhood-augmented graph, search-based planning in which can compute paths in distinct topo-geometric classes. This approach can find desired number of locally optimal paths in a wider variety of configuration spaces without requiring any complex pre-processing or geometric constructions. Unlike the existing topological methods, resulting optimal paths are not restricted to distinct topological classes, thus making the algorithm applicable to many other problems where locally optimal and geometrically distinct paths are of interest. For the demonstration of an application of the proposed approach, we implement our algorithm to planning for shortest traversible paths for a tethered robot with cable-length constraint navigating in 3D and validate it in simulations & experiments.Comment: 18 pages, 17 figure

Coordination-free Multi-robot Path Planning for Congestion Reduction Using Topological Reasoning

We consider the problem of multi-robot path planning in a complex, cluttered environment with the aim of reducing overall congestion in the environment, while avoiding any inter-robot communication or coordination. Such limitations may exist due to lack of communication or due to privacy restrictions (for example, autonomous vehicles may not want to share their locations or intents with other vehicles or even to a central server). The key insight that allows us to solve this problem is to stochastically distribute the robots across different routes in the environment by assigning them paths in different topologically distinct classes, so as to lower congestion and the overall travel time for all robots in the environment. We outline the computation of topologically distinct paths in a spatio-temporal configuration space and propose methods for the stochastic assignment of paths to the robots. A fast replanning algorithm and a potential field based controller allow robots to avoid collision with nearby agents while following the assigned path. Our simulation and experiment results show a significant advantage over shortest path following under such a coordination-free setup.Comment: 30 pages, 9 figure

A Scalable Strategy for Open Loop Magnetic Control of Microrobots Using Critical Points

A novel scalable strategy for open loop control of ferromagnetic microrobots on a plane using a scalable array of electromagnets is presented. Instead of controlling the microrobot directly, we create equilibrium points in the magnetic force field that are stable and attractive on the plane in which the microrobot is to be controlled. The microrobot moves into these equilibrium points rapidly in presence of low viscous forces, and thus controlling the equilibrium points let us control the microrobot precisely. An unit/cell in the array of electromagnets allows precise control of the microrobot in the unit/cell’s domain. Motion synthesis across multiple overlapping domains allows control of the microrobot in large regions across the array. We perform numerical analysis and demonstrate the control of the ferromagnetic microrobot using the proposed method through simulations