InPTC: Integrated Planning and Tube-Following Control for Prescribed-Time Collision-Free Navigation of Wheeled Mobile Robots

TL;DR

The paper tackles prescribed-time, collision-free navigation of nonholonomic wheeled mobile robots in convex workspaces cluttered with static obstacles. It introduces InPTC, a two-stage framework consisting of a tangent-cone-based prescribed-time planner that produces a collision-free reference trajectory converging to the goal at a preassigned time, and a tube-following controller that enforces tracking within a safe tube using barrier-based, prescribed-time gains. Theoretical results guarantee forward invariance of the safe space, almost-global convergence to the goal, and prescribed-time tracking within a residual set despite disturbances. Empirical validation through simulations and Mona-robot experiments demonstrates precise task completion at prescribed times (e.g., 250 s) with millimeter-to-submillimeter tracking accuracy, highlighting practical viability for time-critical navigation in cluttered environments.

Abstract

In this article, we propose a novel approach, called InPTC (Integrated Planning and Tube-Following Control), for prescribed-time collision-free navigation of wheeled mobile robots in a compact convex workspace cluttered with static, sufficiently separated, and convex obstacles. A path planner with prescribed-time convergence is presented based upon Bouligand's tangent cones and time scale transformation (TST) techniques, yielding a continuous vector field that can guide the robot from almost all initial positions in the free space to the designated goal at a prescribed time, while avoiding entering the obstacle regions augmented with safety margin. By leveraging barrier functions and TST, we further derive a tube-following controller to achieve robot trajectory tracking within a prescribed time less than the planner's settling time. This controller ensures the robot moves inside a predefined ``safe tube'' around the reference trajectory, where the tube radius is set to be less than the safety margin. Consequently, the robot will reach the goal location within a prescribed time while avoiding collision with any obstacles along the way. The proposed InPTC is implemented on a Mona robot operating in an arena cluttered with obstacles of various shapes. Experimental results demonstrate that InPTC not only generates smooth collision-free reference trajectories that converge to the goal location at the preassigned time of $250\,\rm s$ (i.e., the required task completion time), but also achieves tube-following trajectory tracking with tracking accuracy higher than $0.01\rm m$ after the preassigned time of $150\,\rm s$. This enables the robot to accomplish the navigation task within the required time of $250\,\rm s$.

Figures (13)

• Figure 1: Sketch of the wheeled mobile robot.
• Figure 2: Schematic diagram of the operating environment, where the dark gray balls denote the actual obstacles $\mathcal{O}_{i}^{\ast}$, the light gray regions denote the augmented obstacle regions $\mathcal{O}_{i}$, and the light blue regions denote the safety margin. In addition, the dashed circles are the influence regions of obstacles, whereas the pink and yellow lines denote the discontinuous trajectory and its continuous counterpart, respectively.
• Figure 3: Block diagram of the proposed InPTC scheme.
• Figure 4: Augmented regions of convex polygonal obstacles.
• Figure 5: Illustration of the predefined safe tube.

Theorems & Definitions (11)

• Remark 1
• Definition 1: Bouligand's tangent cone bouligand1932introduction
• Theorem 1: Nagumo 1942 nagumo1942lage
• Definition 2: Time scale transformation function, TSTF tran2020finite
• Theorem 2
• Theorem 3
• Remark 2
• Remark 3
• Remark 4
• Theorem 4