Stochastic Traveling Salesperson Problem with Neighborhoods for Object Detection

TL;DR

The paper tackles planning the shortest tour to detect a set of objects by modeling detection regions as diameter-bounded, potentially non-convex 3D neighborhoods defined via an entropy-based viewing score. It formulates a 3D stochastic TSPN and develops a center-visit method that achieves provable approximation factors for disjoint neighborhoods ($O\left(\frac{D_{max}}{D_{min}}\right)$) and a finite detour for non-disjoint neighborhoods ($O\left(\frac{D_{max}^2}{D_{min}^2}\right)$). The approach covers offline and online settings, extends to both disjoint and non-disjoint cases, and is validated through photo-realistic simulations showing efficient trajectories and successful detections (e.g., cars and license plates) using YOLO and ALPR networks. This work provides a theoretically grounded, practical framework for perception-aware trajectory planning with uncertainty, applicable to robotics, inspection, and autonomous systems.

Abstract

We introduce a new route-finding problem which considers perception and travel costs simultaneously. Specifically, we consider the problem of finding the shortest tour such that all objects of interest can be detected successfully. To represent a viable detection region for each object, we propose to use an entropy-based viewing score that generates a diameter-bounded region as a viewing neighborhood. We formulate the detection-based trajectory planning problem as a stochastic traveling salesperson problem with neighborhoods and propose a center-visit method that obtains an approximation ratio of O(DmaxDmin) for disjoint regions. For non-disjoint regions, our method -provides a novel finite detour in 3D, which utilizes the region's minimum curvature property. Finally, we show that our method can generate efficient trajectories compared to a baseline method in a photo-realistic simulation environment.

Figures (6)

• Figure 1: The trajectory of an aerial vehicle for observing a set of cars in the Unreal Engine simulator unrealengine. Images are captured along the trajectory toward the objects of interest. Detection results using yolo-v3 yolov3 network are shown here.
• Figure 2: (a) In 2D, a detour (spike) can visit all neighborhood disks that touch the region surface. (b) In 3D, a detour (red curves) can visit all neighborhoods that touch the region surface. The spikes are line segments with distance $D_{min}$ that are parallel to the surface normal.
• Figure 3: $(a)$ Given 3 spheres of the same radius $r$, we can intersect a plane through their spherical centers. $(b)$ The resulting intersection between the spheres and the plane are 3 disks of the same radius. The shortest path through those spheres is $0.4876 r$tekdas2012efficient.
• Figure 4: Omnidirectional view of a car and their corresponding scores. We applied a threshold to limit the views. The rest views formed a diameter-bounded region. The object orientations are shown in the center of the viewing scores. (High entropy to low entropy corresponds blue to yellow view points.)
• Figure 5: Comparison between yolo detection and our viewing scores. $(a)$ Scores for images with the same elevation angle and azimuth angle ranging from $-\pi$ to $\pi$. $(b)$ Scores for images of the same elevation and azimuth angle with increasing viewing distance to the center of the car.

Theorems & Definitions (12)

• Theorem IV.1
• Lemma IV.2
• proof
• Lemma IV.3
• proof
• proof
• Theorem IV.4
• Lemma IV.5
• proof
• proof