Online Terrain-Aware Bipedal Gait Generation via Manifold Projection and Optimization-Guided Motion Libraries

Online terrain-adaptive gait generation for humanoid robots presents a fundamental conflict between motion optimality and real-time computational efficiency. To address this, we propose a framework based on a projection–optimization–reconstruction paradigm. A step-adaptive virtual sagittal plane (VSP) projection maps 3-D dynamics and complex terrain geometry onto a task-aligned low-dimensional manifold. Within this manifold, a swing foot trajectory optimization (SFTO), integrated with a tightened discrete-time control barrier function, generates optimized, safety-guaranteed swing templates, which are encoded into a hash-based library for expected O(1) retrieval. At runtime, an adaptive trajectory synthesizer (ATS) performs efficient retrieval and full-dimensional reconstruction to synthesize consistent swing motions. Integrated with a model-based centroidal motion planner, it generates feasible, terrain-aware, and physically consistent bipedal gaits. Comparative studies and quantitative evaluations verify the effectiveness of the VSP projection and the superior performance of both SFTO and ATS. Extensive experiments on the BHR8-2 humanoid robot validate the framework, demonstrating agile omnidirectional locomotion across irregular hybrid terrains, including stairs, slopes, ditches, and obstacles, and online adaptation to emergent terrain changes.