Probabilistically-Safe Bipedal Navigation over Uncertain Terrain via Conformal Prediction and Contraction Analysis

2025-10-08

AI Summary

To address the challenge of safe bipedal locomotion on elevation-uncertain terrain, this paper proposes a probabilistic safety-aware motion planning and control framework integrating confidence-aware prediction with contraction analysis. Methodologically, terrain elevation is modeled via Gaussian process regression, and calibrated confidence intervals are generated using conformal prediction. Leveraging a simplified linear inverted pendulum model, the framework combines model predictive control with contraction theory to synthesize verifiably safe tube-based trajectories; a contraction-driven flywheel torque control law is further designed to stabilize angular momentum. The key contribution is the first simultaneous provision—under terrain uncertainty—of probabilistic safety guarantees (with user-specified confidence level) and target reachability assurance. Simulation results on the Digit robot in MuJoCo demonstrate that, at a given confidence level, the approach significantly improves center-of-mass trajectory convergence and robustness over obstacles.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Natural Language Processing: Safety and Robustness

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We address the challenge of enabling bipedal robots to traverse rough terrain by developing probabilistically safe planning and control strategies that ensure dynamic feasibility and centroidal robustness under terrain uncertainty. Specifically, we propose a high-level Model Predictive Control (MPC) navigation framework for a bipedal robot with a specified confidence level of safety that (i) enables safe traversal toward a desired goal location across a terrain map with uncertain elevations, and (ii) formally incorporates uncertainty bounds into the centroidal dynamics of locomotion control. To model the rough terrain, we employ Gaussian Process (GP) regression to estimate elevation maps and leverage Conformal Prediction (CP) to construct calibrated confidence intervals that capture the true terrain elevation. Building on this, we formulate contraction-based reachable tubes that explicitly account for terrain uncertainty, ensuring state convergence and tube invariance. In addition, we introduce a contraction-based flywheel torque control law for the reduced-order Linear Inverted Pendulum Model (LIPM), which stabilizes the angular momentum about the center-of-mass (CoM). This formulation provides both probabilistic safety and goal reachability guarantees. For a given confidence level, we establish the forward invariance of the proposed torque control law by demonstrating exponential stabilization of the actual CoM phase-space trajectory and the desired trajectory prescribed by the high-level planner. Finally, we evaluate the effectiveness of our planning framework through physics-based simulations of the Digit bipedal robot in MuJoCo.

Problem

• Ensuring bipedal robots traverse rough terrain safely under uncertainty
• Developing probabilistically safe planning with terrain elevation confidence intervals
• Guaranteeing dynamic feasibility and centroidal robustness in locomotion control

Innovation

• Probabilistically safe MPC navigation with confidence levels
• Conformal prediction constructs calibrated terrain confidence intervals
• Contraction-based control ensures trajectory convergence and invariance