LiDAR-based Humanoid Navigation in Dynamic, Non-Convex Environments via Spatio-Temporal Safe Corridors

Humanoid locomotion in highly confined environments requires navigating dense environmental obstacles and complex self-collision bounds while maintaining multi-contact dynamic feasibility. Traditional trajectory optimizers frequently struggle in these restricted spaces, as navigating the large collision space with splines on particle abstractions is insufficient and leads to poor local minima. To address this, we propose a three-stage whole-body planning framework that formulates kinematic path planning directly over kinematically reachable rigid-body volumes. By integrating differentiable collision avoidance into a reachability-constrained formulation, our framework synthesizes volume-informed guides that reliably guide a full-order trajectory optimizer over long horizons. We show that these optimized plans serve as high-quality references to train a residual reinforcement learning policy for robust online execution. We validate our approach on the Unitree G1 humanoid across three benchmark testbeds exceeding NIST emergency response standards, achieving restricted confinement ratios ($C_r < 1.5$). Our framework generates feasible trajectories across 12-to-18-second tasks with complex foot and hand contacts where standard baselines fail, while the learned policy successfully tracks these plans under extensive domain randomization in physics simulation.

Autonomous robot navigation requires rapid construction of obstacle-points-separated convex regions for trajectory planning. When obstacles are represented as point clouds from LiDAR or depth cameras, these regions must be constructed directly from finite obstacle samples while providing suitable constraints for downstream optimization. However, existing corridor-generation methods often struggle to meet real-time, sensor-rate computational requirements. To address this bottleneck, we introduce RISP, a randomized algorithm that constructs convex polytopes from finite point-cloud data, and PathCover, which chains these polytopes along a reference path to form an overlapping corridor. We prove finite termination, sequential intersection, and complete path coverage with respect to the supplied finite point set. Under a probabilistic elimination condition, the sampling-and-elimination stage of RISP has expected O(n) time and unconditional worst-case O(n^2) time. Extensive benchmarks on synthetic and real-world LiDAR datasets demonstrate an order-of-magnitude speedup over state-of-the-art methods in both corridor generation as well as trajectory optimization, while closed-loop quadrotor simulation and a physical quadruped traversal demonstrate integration with downstream motion planners. These results establish corridor separation from the supplied point-cloud representation and practical implementation feasibility. Source code of the entire pipeline is available at https://github.com/kunalnk123690/PathCover.

Humanoid local navigation in cluttered environments must jointly resolve obstacle avoidance, sparse-goal recovery, and stable whole-body locomotion under short-range and partially observable sensing. Explicit planner-control decompositions introduce latency and can mismatch agile humanoid command-tracking limits, while purely reactive controllers may lose the goal after obstacle occlusion. We present LP-NavOA, a limited-perception navigation and obstacle-avoidance framework for humanoid robots. A raycast-conditioned perception-action proximal policy optimization (PPO) locomotion backbone is first trained with a robot-centered circular heading-speed command and a shared command-side safety filter. With this backbone frozen, A-star and waypoint teachers generate rollouts for distilling a recurrent local planner that overwrites only the heading command at deployment, leaving the whole-body policy intact. At runtime, LP-NavOA uses proprioception, short-range local range sensing, and a body-frame goal direction, requiring no global map, waypoint stream, or external planner. In MuJoCo open-wall and indoor layouts, the distilled planner produces obstacle bypassing and post-avoidance goal recovery, raising teacher-calibrated on-time arrival from 38--40% to 85--97% and reducing brush/contact-heavy progress relative to a backbone-only controller. Ablations show that dynamic route shaping, teacher-active data collection, and the circular command interface are important for navigation efficiency and for training the 3.0,m/s backbone. A Unitree G1 deployment analysis demonstrates hardware executability without continuous joystick steering.