Planning Tours of Robotic Arms among Partitioned Goals

Abstract

In this paper we consider a motion planning problem that occurs in tasks such as spot welding, car painting, inspection, and measurement, where the end-effector of a robotic arm must reach successive goal placements given as inputs. The problem is to compute a nearoptimal path of the arm so that the end-effector visits each goal once. It combines two notoriously hard subproblems: the collisionfree shortest-path and the traveling-salesman problems. It is further complicated by the fact that each goal placement of the end-effector may be achieved by several configurations of the arm (distinct solutions of the arm's inverse kinematics). This leads to considering a set of goal configurations of the robot that are partitioned into groups. The planner must compute a robot path that visits one configuration in each group and is near optimal over all configurations in every goal group and over all group orderings. The algorithm described in this paper operates under the assumption that finding a good tour in a graph with edges of given costs takes much less time than computing good paths between all pairs of goal configurations from different groups. So, the algorithm balances the time spent in computing paths between goal configurations and the time spent in computing tours. Although the algorithm still computes a quadratic number of such paths in the worst case, experimental results show that it is much faster in practice.

Sampling-based sweep planning to exploit local planarity in the inspection of complex 3D structures

“…This property originated in the context of point-to-point path planning [18], but we offer a definition in the context of sweep paths. We analyze probabilistic completeness with respect to a local set system, (Q k , S k ), that applies to a specific segment k. We define the property of probabilistic completeness for a CSP algorithm as follows.…”

Multi-goal feasible path planning using ant colony optimization

“…This algorithm is based on the lazy-GMGP algorithm of [6], which approximates the optimal TSP solution using the MST heuristic. Similar to the Christofides heuristic, the MST heuristic yields a tour within a factor of two of optimality by doubling the edges of the MST and traversing every edge, visiting every goal node in the process.…”

“…In our application, every goal is mandatory, and a regular MST can be used in lieu of the Steiner tree solution procedure of [6]. The computation time required by this method can be described as N * (O(n 2 )+C * O(n)), where N is the number of iterations in which the lazy MST is computed, the O(n 2 ) term captures the complexity of computing the MST over a complete graph (since all goal-to-goal pairings are considered as candidate edges), and the O(n) term captures the worst-case number of RRT calls required per iteration.…”

“…Surveillance applications are also solved by mapping mission goals to graph nodes and modeling the multi-goal planning problem as some variant of the traveling salesman problem (TSP) [4], [5]. Multigoal problems in industrial manufacturing applications have also been solved using the TSP, including spot welding [6], [7] and measuring fabricated parts to ensure tolerances have been met [8]. Additionally, TSP solutions have been developed for robotic systems with kinodynamic constraints [9], [10].…”

“…In Section II the first comparison algorithm is introduced, an exhaustive all-pairs search for feasible paths, followed by the use of the best-known heuristic upper bound on the TSP [8]. In Section III the second comparison algorithm is introduced, a fast algorithm designed to require as little collision checking as possible by iteratively computing and checking the minimum spanning tree (MST) [6]. Section IV presents ACO for feasible multi-goal planning, and Section V presents results comparing all three algorithms using a two-dimensional robot test case.…”