TSP-Bot: Robotic TSP Pen Art using High-DoF Manipulators

TL;DR

Translating digital TSP art into physical pen drawings on planar canvases, the paper presents TSP-Bot, a multi-color robotic system that converts raster images into color-split stippled point sets, solves per-channel TSP tours, and renders smooth Bezier paths under curvature constraints. The pipeline uses CMYK color processing, stippling, and a combination of a TSP solver with heuristic smoothing, followed by path-wise inverse kinematics to drive high-DoF manipulators. A novel pen-holding tool enables robust color changes, demonstrated on dual-arm and mobile configurations, showing diverse and aesthetically compelling results. This work advances autonomous robotic drawing by combining color-aware stippling, efficient TSP path generation, and practical tooling to produce high-quality TSP pen art at scale.

Abstract

TSP art is an art form for drawing an image using piecewise-continuous line segments. We present TSP-Bot, a robotic pen drawing system capable of creating complicated TSP pen art on a planar surface using multiple colors. The system begins by converting a colored raster image into a set of points that represent the image's tone, which can be controlled by adjusting the point density. Next, the system finds a piecewise-continuous linear path that visits each point exactly once, which is equivalent to solving a Traveling Salesman Problem (TSP). The path is simplified with fewer points using bounded approximation and smoothed and optimized using Bezier spline curves with bounded curvature. Our robotic drawing system consisting of single or dual manipulators with fingered grippers and a mobile platform performs the drawing task by following the resulting complex and sophisticated path composed of thousands of TSP sites. As a result, our system can draw complicated and visually pleasing TSP pen art.

Figures (9)

• Figure 1: TSP-Bot system drawing TSP pen arts using a dual arm setup (top) and a mobile manipulator setup (bottom).
• Figure 2: System overview. Given an original digital image, it is split into predefined color channels. A set of points is generated from each color channel using a stippling technique. We find a path that visits every point for each channel by solving a TSP on the generated points as TSP sites. The generated piecewise linear path is then smoothed and optimized with Bézier spline curves that ensure bounded curvature. We plan the robot's joint configurations so that the pen-holding end-effector follows the path for the drawing.
• Figure 3: Interpolating cubic Bézier curve. $\mathbf{p}_i$'s represent the control points for the first Bézier spline that interpolates $\mathbf{p}_0$, $\mathbf{p}_3$.
• Figure 4: Reachability of the manipulators. Green or blue spheres in (a) and (b) represent the points that are reachable by each manipulator with a fixed end-effector orientation. Red spheres in (a) represent the region that is reachable by both manipulators.
• Figure 5: Pen tool picking sequences using a 3-finger gripper in five stages: from left to right, ready pose, approach, half grasp, vertical lift, and full grasp. Placing the tool back to the docking structure is in reverse.