Enhanced $A^{*}$ Algorithm for Mobile Robot Path Planning with Non-Holonomic Constraints

TL;DR

This work tackles mobile robot path planning under non-holonomic constraints and finite dimensions by integrating these constraints directly into the planning layer using two instantiations of $A^{*}$: the non-holonomic $A^{*}$ and the geometric $A^{*}$. The methods derive neighbor sets from either a kinematic model, with dynamics $\dot{x}=v\cos\theta$, $\dot{y}=v\sin\theta$, $\dot{\theta}=\frac{v}{l}\tan\delta$, or from a geometric model based on a minimum turn radius $r$, and use a cost function $g(n+1)=g(n)+\operatorname{dist}(n+1,n)+c(\delta)+c(v)$ along with a heading-aware heuristic $h(n)=\sqrt{(x_n-x_g)^2+(y_n-y_g)^2+(\theta_n-\theta_g)^2}$. Collision avoidance is enforced via a rectangular convex hull for the robot, checked at each expansion, enabling safe operation in cluttered environments. The authors validate the approach through multiple simulations, including varying initial headings, reverse-maneuver penalties, U-turns, narrow corridors, and a rasterized road-map test, demonstrating improved feasibility and safety over conventional single-layer planning. Overall, the work presents a practical path-planning framework that respects non-holonomic dynamics and dimensions, with implications for autonomous navigation in real-world, constrained settings.

Abstract

In this paper, a novel method for path planning of mobile robots is proposed, taking into account the non-holonomic turn radius constraints and finite dimensions of the robot. The approach involves rasterizing the environment to generate a 2D map and utilizes an enhanced version of the $A^{*}$ algorithm that incorporates non-holonomic constraints while ensuring collision avoidance. Two new instantiations of the $A^{*}$ algorithm are introduced and tested across various scenarios and environments, with results demonstrating the effectiveness of the proposed method.

Figures (8)

• Figure 1: Kinematic model
• Figure 2: Geometric model
• Figure 3: Enhanced A* subject to different initial heading
• Figure 4: Controlling reverse manuever by cost selection
• Figure 5: Navigation under U-turn scenarios for small (length =1) and big (length = 2) vehicles