Contact-Implicit Whole-Body Trajectory Optimization for Dynamic Humanoid Locomotion on Parameterizable Uneven Terrain

Bipedal robots are challenging to control because they operate close to instability, where small variations in foot-terrain contact can rapidly destabilize locomotion. On rigid terrain, bipedal robots mitigate this fragility by using well-established contact mechanics and control strategies. On flowable surfaces such as granular slopes, foot contact can induce large surface deformations and solid-fluid-like transitions, coupling terrain effects with robot dynamics, leading to underperformance or failure. This is partly due to the lack of reliable methods to represent the dynamics of flowable terrain, making it difficult to account for terrain effects in locomotion design. Here, we investigate how controlling terrain response can improve bipedal locomotion on granular slopes by studying the terradynamics of cleated feet, thin plates emanating from the foot soles. Systematic studies of a small-scale (1.4 kg) robophysical biped reveal that cleats with sparse and dense spacing lead to excessive terrain yielding and resistance, respectively, degrading performance and leading to failure. An intermediate cleat spacing distributes interaction forces to maintain substrate stresses near (or below) the yield threshold, enabling walking on granular slopes up to 30 degrees. Guided by these principles, we design a foot that actively adjusts cleat depth and accommodates both rigid and granular terrain. We also demonstrate that the principles of effective foot-terrain interaction translate to a larger (15 kg) autonomous biped. Our study presents an alternative to conventional body-centric robot control approaches, which regulate terrain-induced effects through body motion, by instead regulating terrain interactions through limb-centric approach.

Advancing bipedal robots to navigate diverse terrains remains a significant challenge in robotics. Traditional locomotion controllers excel on specific surfaces but struggle across varied environments, limiting their practical applications. Given the unpredictable nature of real-world environments, a single controller capable of handling multiple terrains is ideal, eliminating the need for multiple specialized controllers. We propose a multi-terrain controller to enhance the versatility and robustness of bipedal locomotion. Building on previous work with a stance ankle motor for stability on inclined and rough surfaces, this paper extends capabilities to steep wet uneven grassy slopes, and compliant terrains such as sand, gravel, rocks, and constrained terrains like staircases. To address the unique demands of these terrains, we introduce a new impact map that is essential for maintaining performance and robustness against unseen terrains. We also discuss in detail the control structure for real-time deployment on the robot. We validate our controller on the 20 degree-of-freedom Cassie bipedal robot.

Walking over disconnected footholds requires selecting landing regions while adapting step timing to the robot's motion. We present a perceptive model predictive planner that combines discrete region selection, foot placement, and current-step duration in a mixed-integer quadratic program using step-to-step Divergent Component of Motion (DCM) dynamics. Onboard depth data are fused into a probabilistic heightmap in the stance foot frame. Convex steppable regions are extracted and shrunk by margins that increase with estimated height uncertainty. Linear constraints impose capturability-based bounds on DCM evolution and limit swing-foot retargeting using the remaining commanded swing time. Within-step replanning updates the initial DCM from measurements to respond to model mismatch and disturbances. We evaluate the framework on Digit in simulation over randomized footholds and on hardware over separated plates, with mean planner solve times of 11.4ms and 4.0ms, respectively.