Task and Motion Informed Trees (TMIT*): Almost-Surely Asymptotically Optimal Integrated Task and Motion Planning

Abstract

High-level autonomy requires discrete and continuous reasoning to decide both what actions to take and how to execute them. Integrated Task and Motion Planning (TMP) algorithms solve these hybrid problems jointly to consider constraints between the discrete symbolic actions (i.e., the task plan) and their continuous geometric realization (i.e., motion plans). This joint approach solves more difficult problems than approaches that address the task and motion subproblems independently.TMP algorithms combine and extend results from both task and motion planning. TMP has mainly focused on computational performance and completeness and less on solution optimality. Optimal TMP is difficult because the independent optima of the subproblems may not be the optimal integrated solution, which can only be found by jointly optimizing both plans.This paper presents Task and Motion Informed Trees (TMIT*), an optimal TMP algorithm that combines results from makespanoptimal task planning and almost-surely asymptotically optimal motion planning. TMIT* interleaves asymmetric forward and reverse searches to delay computationally expensive operations until necessary and perform an efficient informed search directly in the problem's hybrid state space. This allows it to solve problems quickly and then converge towards the optimal solution with additional computational time, as demonstrated on the evaluated robotic-manipulation benchmark problems.

On Optimal Integrated Task and Motion Planning with Applications to Tractor-Trailers

“…Recently, there has been an increased interest in optimal task and motion planning [16,40,60,63], where the objective is to find a solution that is not only feasible but that optimizes some performance measure as well. This is the focus of this thesis.…”

“…In [60] an almost-surely asymptotically optimal planner is presented. The proposed planner integrates a symbolic planner based on Satisfiability Modulo Theories with sampling-based motion planning.…”

PROTAMP-RRT: A Probabilistic Integrated Task and Motion Planner Based on RRT

“…These methods can make additional assumptions, such as heuristics based on regions [20], and removal of objects to reduce constraints [21]. While our work aims at finding the first geometrically feasible solution, other works [22] [23] [24] focus on finding an optimal trajectory, e.g. in terms of robot execution time, by applying complex optimization approaches.…”

Failure is an option: Task and Motion Planning with Failing Executions

“…The input to the algorithm is the task planning domain, the initial state, the goal described as some symbolic expression, and the model of the world for motion planning. An SMT-solver as the task planner supports the incrementalsolving feature, leveraged by many existing planners [1], [49], [50]. A candidate task plan is a sequence of symbolic actions (Alg.…”