VectorTSP: A Traveling Salesperson Problem with Racetrack-like acceleration constraints

by   Arnaud Casteigts, et al.

We study a new version of the Euclidean TSP called VectorTSP (VTSP for short) where a mobile entity is allowed to move according to a set of physical constraints inspired from the pen-and-pencil game Racetrack (also known as Vector Racer ). In contrast to other versions of TSP accounting for physical constraints, such as Dubins TSP, the spirit of this model is that (1) no speed limitations apply, and (2) inertia depends on the current velocity. As such, this model is closer to typical models considered in path planning problems, although applied here to the visit of n cities in a non-predetermined order. We motivate and introduce the VectorTSP problem, discussing fundamental differences with previous versions of TSP. In particular, an optimal visit order for ETSP may not be optimal for VTSP. We show that VectorTSP is NP-hard, and in the other direction, that VectorTSP reduces to GroupTSP in polynomial time (although with a significant blow-up in size). On the algorithmic side, we formulate the search for a solution as an interactive scheme between a high-level algorithm and a trajectory oracle, the former being responsible for computing the visit order and the latter for computing the cost (or the trajectory) for a given visit order. We present algorithms for both, and we demonstrate and quantify through experiments that this approach frequently finds a better solution than the optimal trajectory realizing an optimal ETSP tour, which legitimates the problem itself and (we hope) motivates further algorithmic developments.


page 1

page 2

page 3

page 4


MGA trajectory planning with an ACO-inspired algorithm

Given a set of celestial bodies, the problem of finding an optimal seque...

Pivot Rules for Circuit-Augmentation Algorithms in Linear Optimization

Circuit-augmentation algorithms are a generalization of the Simplex meth...

Robot navigation and target capturing using nature-inspired approaches in a dynamic environment

Path Planning and target searching in a three-dimensional environment is...

What to Do When You Can't Do It All: Temporal Logic Planning with Soft Temporal Logic Constraints

In this paper, we consider a temporal logic planning problem in which th...

Jerk-limited Real-time Trajectory Generation with Arbitrary Target States

We present Ruckig, an algorithm for Online Trajectory Generation (OTG) r...

Pandora's Box Problem with Order Constraints

The Pandora's Box Problem, originally formalized by Weitzman in 1979, mo...

Planning and Formulations in Pursuit-Evasion: Keep-away Games and Their Strategies

We study a pursuit-evasion problem which can be viewed as an extension o...

Please sign up or login with your details

Forgot password? Click here to reset