Perceptive Mixed-Integer Footstep Control for Underactuated Bipedal Walking on Rough Terrain

Abstract--Traversing rough terrain requires dynamic bipeds to stabilize themselves through foot placement without stepping in unsafe areas. Planning these footsteps online is challenging given non-convexity of the safe terrain, and imperfect perception and state estimation. First, we develop model-predictive footstep control (MPFC), a single mixed-integer quadratic program which assumes a convex polygon terrain decomposition to optimize over discrete foothold choice, footstep position, ankle torque, template dynamics, and footstep timing at over 100 Hz. We then propose a novel approach for generating convex polygon terrain decompositions online. Our perception stack decouples safe-terrain classification from fitting planar polygons, generating a temporally consistent terrain segmentation in real time using a single CPU thread. We demonstrate the performance of our perception and control stack through outdoor experiments with the underactuated biped Cassie, achieving state of the art perceptive bipedal walking on discontinuous terrain. Figure 1: The bipedal robot Cassie walks up and down brick I. However, dynamic bipedal walking over rough terrain remains challenging for today's perception and control algorithms. This is a highly over the discrete choice of stepping surface and the robot's coupled problem where online terrain estimation is used to dynamics in real time Despite the existence and its precursor [9] represent the first deployment of such a of mature techniques for both underactuated walking, and footstep controller on hardware.