LIMBO: Learning and Internalizing Model-Free Barrier Objectives for Agile and Safe Whole-Body Control

LIMBO introduces a method for safe, agile whole-body control that first learns a state–action safety certificate, or Q-CBF, from black-box transitions and a state-based failure specification, then distills that certificate into a task policy. Its residual formulation learns safety in the same 29-dimensional control space used by the task policy, while a frozen base controller preserves nominal balance or locomotion. Risk-guided replay concentrates training near the estimated boundary of recoverability, allowing the same safety specification to produce either crouching or a backward-leaning limbo maneuver. During PPO training, the learned Q-CBF acts as a counterfactual teacher, supplying violation penalties and minimum-deviation action corrections; the deployed policy therefore needs no online safety filter. Experiments used a Unitree G1 humanoid, 4096 parallel MuJoCo environments, 50 Hz control, AMP motion priors, and Kimodo-generated reference motions. In simulated dodgeball, LIMBO’s QCBF-PD policy achieved a 1.48% in-distribution hit rate versus 3.58% for analytical CBF-RL, and 38.11% versus 59.50% on out-of-distribution targets, with zero falls in both settings. On hardware, it transferred directly from simulation without adaptation or filtering; synthetic throws produced 0.162 m median drift versus 0.944 m for CBF-RL. For locomotion beneath a 1.234 m obstacle, boundary sampling shifted the strategy from pelvis dropping to torso leaning, while clearance remained 85.7% to 91.2%, demonstrating behavior discovery through learned safety rather than hand-designed motion targets.