The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the agent are present, no prior algorithm guarantees convergence to an optimal MT-TSP solution. Therefore, we introduce the Iterated Random Generalized (IRG) TSP framework. The idea behind IRG is to alternate between randomly sampling a set of agent configuration-time points, corresponding to interceptions of targets, and finding a sequence of interception points by solving a generalized TSP (GTSP). This alternation asymptotically converges to the optimum. We introduce two parallel algorithms within the IRG framework. The first algorithm, IRG-PGLNS, solves GTSPs using PGLNS, our parallelized extension of state-of-the-art solver GLNS. The second algorithm, Parallel Communicating GTSPs (PCG), solves GTSPs for several sets of points simultaneously. We present numerical results for three MT-TSP variants: one where intercepting a target only requires coming within a particular distance, another where the agent is a variable-speed Dubins car, and a third where the agent is a robot arm. We show that IRG-PGLNS and PCG converge faster than a baseline based on prior work. We further validate our framework with physical robot experiments.

The moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting position. Each target moves with a constant velocity within its time windows, and the agent has a speed limit no smaller than any target's speed. We present FMC*-TSP, the first complete and bounded-suboptimal algorithm for the MT-TSP-O, and results for an agent whose configuration space is$\mathbb{R}^{3}$. Our algorithm interleaves a high-level search and a lowlevel search, where the high-level search solves a generalized traveling salesman problem with time windows (GTSP-TW) to find a sequence of targets and corresponding time windows for the agent to visit. Given such a sequence, the low-level search then finds an associated agent trajectory. To solve the low-level planning problem, we develop a new algorithm called FMC*, which finds a shortest path on a graph of convex sets (GCS) via implicit graph search and pruning techniques specialized for problems with moving targets. We test FMC*-TSP on 280 problem instances with up to 40 targets and demonstrate its smaller median runtime than a baseline based on prior work.