PathCover: A Fast Convex Decomposition along a Path via Randomized Iterative Space Partitioning (RISP) on Point Clouds

Autonomous robot navigation requires the rapid generation of obstacle-free regions for trajectory planning. However, existing corridor generators struggle to meet real-time, sensor-rate computational constraints. To resolve this bottleneck, we introduce PathCover, a framework driven by RISP; a novel randomized algorithm that constructs convex polytopes directly from raw point cloud data in expected linear time under a mild probabilistic elimination condition. PathCover generates sequences of overlapping, obstacle-free polytopes that safely constrain downstream MPC and trajectory optimization. We mathematically guarantee that the algorithm terminates in finite steps while ensuring continuous progress along any obstacle-free reference path. Extensive benchmarks on synthetic and real-world LiDAR datasets demonstrate an order-of-magnitude speedup over state-of-the-art methods while maintaining comparable corridor volumes. The complete pipeline is validated via high-fidelity quadrotor simulations and physical deployment on a quadrupedal robot navigating constrained environments using live LiDAR perception.

Overtaking Moving Obstacles with Digit: Path Following for Bipedal Robots via Model Predictive Contouring Control

Humanoid robots are expected to navigate in changing environments and perform a variety of tasks. Frequently, these tasks require the robot to make decisions online regarding the speed and precision of following a reference path. For example, a robot may want to decide to temporarily deviate from its path to overtake a slowly moving obstacle that shares the same path and is ahead. In this case, path following performance is compromised in favor of fast path traversal. Available global trajectory tracking approaches typically assume a given -- specified in advance -- time parametrization of the path and seek to minimize the norm of the Cartesian error. As a result, when the robot should be where on the path is fixed and temporary deviations from the path are strongly discouraged. Given a global path, this paper presents a Model Predictive Contouring Control (MPCC) approach to selecting footsteps that maximize path traversal while simultaneously allowing the robot to decide between faithful versus fast path following. The method is evaluated in high-fidelity simulations of the bipedal robot Digit in terms of tracking performance of curved paths under disturbances and is also applied to the case where Digit overtakes a moving obstacle.