Safe Path Planning for Polynomial Shape Obstacles via Control Barrier Functions and Logistic Regression

TL;DR

This paper introduces a novel control barrier function-based RRT* algorithm that uses logistic regression to model complex polynomial-shaped obstacles, enabling safe and feasible path planning for bipedal robots in intricate environments.

Contribution

It presents a new method combining logistic regression and control barrier functions to handle irregular-shaped obstacles in path planning for bipedal robots.

Findings

Successfully validated in simulation with a differential drive model.

Experimentally tested on a 3D humanoid robot, Digit, in a lab environment.

Achieved collision-free, dynamically feasible paths in complex obstacle scenarios.

Abstract

Safe path planning is critical for bipedal robots to operate in safety-critical environments. Common path planning algorithms, such as RRT or RRT*, typically use geometric or kinematic collision check algorithms to ensure collision-free paths toward the target position. However, such approaches may generate non-smooth paths that do not comply with the dynamics constraints of walking robots. It has been shown that the control barrier function (CBF) can be integrated with RRT/RRT* to synthesize dynamically feasible collision-free paths. Yet, existing work has been limited to simple circular or elliptical shape obstacles due to the challenging nature of constructing appropriate barrier functions to represent irregular-shaped obstacles. In this paper, we present a CBF-based RRT* algorithm for bipedal robots to generate a collision-free path through complex space with polynomial-shaped obstacles. In particular, we used logistic regression to construct polynomial barrier functions from a grid map of the environment to represent arbitrarily shaped obstacles. Moreover, we developed a multi-step CBF steering controller to ensure the efficiency of free space exploration. The proposed approach was first validated in simulation for a differential drive model, and then experimentally evaluated with a 3D humanoid robot, Digit, in a lab setting with randomly placed obstacles.