Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints

Legged robots rely on accurate ground interaction awareness to traverse variable terrains, such as slippery surfaces. Existing slip detection methods often rely on kinematics and proprioception, which lack the sensitivity to detect early-stage slips that occur prior to catastrophic instability. Thus, this paper presents SlipSense, a novel framework for online force-based slip detection using a custom lightweight sensorized foot for quadrupeds to detect slip. The framework integrates a multimodal sensor design with a LSTM-based model to infer ground reaction forces and detect slip-indicative anomalies during locomotion. The proposed framework is deployed on a Unitree Go1 quadruped to demonstrate blind online slip detection over a slippery terrain. Our method detects early-stage slips down to an average displacement of 24.1 +/-6.4mm with an overall accuracy of 85.9%. This represents a 3.3-fold finer detection resolution and a 24% relative accuracy improvement over a standard kinematic baseline that uses foot velocity inferred through state estimation. The work in this paper serves as a foundation for force-aware gait adaptation in legged robotic locomotion, allowing future controllers to estimate terrain friction and adjust constraints, thus improving the overall stability of the system.

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.

In this letter, we present a hierarchical control framework that enables wheeled bipedal robots to perform planar object sliding tasks with their wheeled legs. The proposed approach formulates a nonlinear model predictive controller (NMPC) based on a reduced-order three rigid bodies (TRB) dynamical model that explicitly accounts for the hip roll degree of freedom and multiple wheel-environment contact modes, which is essential for lateral stepping and pedipulation tasks. Within this framework, the NMPC simultaneously regulates robot locomotion and interaction forces, allowing the robot to stably execute both rolling and object manipulation behaviors. A trajectory-optimization-based robot-object motion planner is developed to generate reference motions that incorporate stick-slip transitions in ground-object contact. Two representative pedipulation motions, namely scooting and lateral sliding, are validated through real-world hardware experiments, in which the robot successfully retrieves a 1 kg object from under a desk and slides a 4 kg object over a distance of 0.228 m via scooting.