  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.
