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Safe path planning is critical for bipedal robots to operate insafety-critical environments. Common path planning algorithms, such as RRT orRRT*, typically use geometric or kinematic collision check algorithms to ensurecollision-free paths toward the target position. However, such approaches maygenerate non-smooth paths that do not comply with the dynamics constraints ofwalking robots. It has been shown that the control barrier function (CBF) canbe integrated with RRT/RRT* to synthesize dynamically feasible collision-freepaths. Yet, existing work has been limited to simple circular or ellipticalshape obstacles due to the challenging nature of constructing appropriatebarrier functions to represent irregular-shaped obstacles. In this paper, wepresent a CBF-based RRT* algorithm for bipedal robots to generate acollision-free path through complex space with polynomial-shaped obstacles. Inparticular, we used logistic regression to construct polynomial barrierfunctions from a grid map of the environment to represent arbitrarily shapedobstacles. Moreover, we developed a multi-step CBF steering controller toensure the efficiency of free space exploration. The proposed approach wasfirst validated in simulation for a differential drive model, and thenexperimentally evaluated with a 3D humanoid robot, Digit, in a lab setting withrandomly placed obstacles.

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