3D Hopping in Discontinuous Terrain Using Impulse Planning With Mixed-Integer Strategies

As quadruped controllers approach greater maturity for locomotion on level ground, a next challenge relates to enabling these systems to carefully choose contacts in cluttered or discontinuous terrain. In pursuit of this goal, this letter proposes an approach to motion generation for dynamic hopping in clutter. Due to fundamental scalability limitations of mixed-integer programming (MIP) formulations, it is common to adopt simplified models, most often focused on the center of mass (COM) or the centroidal dynamics, to generate a motion sketch for subsequent whole-body planning. This letter considers a MIP formulation on a single-rigid-body model, but simplifies the locomotion planning problem by considering each stance phase as impulsive. We show that this reduction enables our MIP formulation to address locomotion in discontinuous and cluttered environments, while including 3D orientation evolution and actuator limitations, and keeping the computational demands manageable for real-time deployment. Once contacts are fixed, the resulting motion sketch can be readily post-processed by existing optimization tools to remove the impulse assumption and smooth the desired COM trajectory. The work is validated in experiments with the MIT Mini Cheetah executing multiple consecutive hops between surfaces while avoiding obstacle regions.