Implications of Motion Planning: Optimality and k-survivability

We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the existence of optimal trajectories is guaranteed, and design an algorithm to find approximately optimal trajectories for a kinematic planar robot within this model. We also design an algorithm to build data structures to represent the configuration space, supporting optimal trajectory queries for any given pair of configurations in an obstructed environment. We are also interested in planning paths for expendable robots moving in a threat environment. Since robots are expendable, our goal is to ensure a certain number of robots reaching the goal. We consider a new motion planning problem, maximum k-survivability: given two points in a stochastic threat environment, find n paths connecting two given points while maximizing the probability that at least k paths reach the goal. Intuitively, a good solution should be diverse to avoid several paths being blocked simultaneously, and paths should be short so that robots can quickly pass through dangerous areas. Finding sets of paths with maximum k-survivability is NP-hard. We design two algorithms: an algorithm that is guaranteed to find an optimal list of paths, and a set of heuristic methods that finds paths with high k-survivability

Mission and Motion Planning for Multi-robot Systems in Constrained Environments

abstract: As robots become mechanically more capable, they are going to be more and more integrated into our daily lives. Over time, human’s expectation of what the robot capabilities are is getting higher. Therefore, it can be conjectured that often robots will not act as human commanders intended them to do. That is, the users of the robots may have a different point of view from the one the robots do. The first part of this dissertation covers methods that resolve some instances of this mismatch when the mission requirements are expressed in Linear Temporal Logic (LTL) for handling coverage, sequencing, conditions and avoidance. That is, the following general questions are addressed: * What cause of the given mission is unrealizable? * Is there any other feasible mission that is close to the given one? In order to answer these questions, the LTL Revision Problem is applied and it is formulated as a graph search problem. It is shown that in general the problem is NP-Complete. Hence, it is proved that the heuristic algorihtm has 2-approximation bound in some cases. This problem, then, is extended to two different versions: one is for the weighted transition system and another is for the specification under quantitative preference. Next, a follow up question is addressed: * How can an LTL specified mission be scaled up to multiple robots operating in confined environments? The Cooperative Multi-agent Planning Problem is addressed by borrowing a technique from cooperative pathfinding problems in discrete grid environments. Since centralized planning for multi-robot systems is computationally challenging and easily results in state space explosion, a distributed planning approach is provided through agent coupling and de-coupling. In addition, in order to make such robot missions work in the real world, robots should take actions in the continuous physical world. Hence, in the second part of this thesis, the resulting motion planning problems is addressed for non-holonomic robots. That is, it is devoted to autonomous vehicles’ motion planning in challenging environments such as rural, semi-structured roads. This planning problem is solved with an on-the-fly hierarchical approach, using a pre-computed lattice planner. It is also proved that the proposed algorithm guarantees resolution-completeness in such demanding environments. Finally, possible extensions are discussed.Dissertation/ThesisDoctoral Dissertation Computer Science 201