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

Jake Gonzales; Arturo Flores Alvarez; Yu-Ming Chen; Aaron D. Ames; Lillian J. Ratliff; Manikantan Nambi

cs.ROSep 18, 2026

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

Authors: Jake Gonzales, Arturo Flores Alvarez, Yu-Ming Chen, Aaron D. Ames, Lillian J. Ratliff, Manikantan Nambi

Organizations: Amazon · University of Washington, Seattle · University of California, Los Angeles · California Institute of Technology

Abstract

Safe whole-body control requires coordinating collision avoidance and balance under high-dimensional, nonlinear dynamics--making safety certificates difficult to design and reuse across behaviors. We present LIMBO, a framework for synthesizing a state-action control barrier function and distilling its safety structure into a task policy. LIMBO learns the safety certificate from black-box transitions and a state-based failure specification over residual actions around a frozen base controller, making Q-CBF synthesis tractable in the full control dimension while placing the certificate in the task policy's control space. During synthesis, the learned safety value drives risk-guided sampling near the estimated boundary of recoverability; during task learning, it serves as a teacher that provides action-level safety feedback, yielding a robust task policy and alleviating the need for an online safety filter at deployment. We demonstrate LIMBO on a 29-degree-of-freedom humanoid performing dodgeball avoidance and locomotion beneath low obstacles. Beyond scaling learned Q-CBFs to whole-body control, we show that risk-guided boundary sampling provides a theoretically grounded way to explore the edge of recoverability. Under the same safety specification, ceteris paribus, varying the sampling concentration produces strategies ranging from crouching to a novel backward-leaning limbo maneuver. In both settings, the learned policies transfer to hardware without online safety filtering, showing that learned safety synthesis scales to agile whole-body control.

Figures & tables

Panel of Figure 1 — Figure 1: Safety synthesized and distilled into agile behavior. The deployed $29$ -DoF humanoid performs backward-leaning limbo (top) and dodgeball evasion (bottom) using policies trained from an automatically synthesized Q-CBF and subsequent safe policy distillation.

Figure 2: LIMBO Overview. Stage I : Q-CBF synthesis via black-box transitions using the residual formulation and risk-guided boundary replay. Stage II : learned Q-CBF is a safety teacher , shaping task-policy rewards via constraint violations and corrections. Deployment : compose task policy with the frozen base controller, with optional filtering. Hardware demonstrations operate without online filtering, relying on the safety behavior internalized during Stage II.

Figure 3: Dodgeball training distribution. Training throws span a $\pm 25^{\circ}$ frontal cone and target the head and shoulders, with $15\%$ sampled misses.

Figure 4: Barrier value & hit rate. (left) Cumulative distributions of launch-time safety values; hits tend to originate from states with lower safety value. (right) $\Pr_{\pi}(\mathrm{hit}\,|\,V_{\phi}(X)\in[v_{k},v_{k+1}))$ in ten bins, with 95% intervals; points placed at each bin’s mean. Higher launch-time $V_{\phi}$ corresponds to lower hit rates, and the distilled policy has lower hit rates.

Figure 5: Simulated dodgeball. (a) Hit rate, (b) fall rate, and (c) torque-saturation; lower is better. QCBF-PD is hit less than half as often as CBF-RL on in distribution throws, and never falls, while CBF-RL falls on 4.08%/1.6% of in/out of distribution throws; both policies differ from the frozen base at $p$ below precision. QCBF-PD torque saturates its actuators roughly half as much as CBF-RL , while the base barely actuates, and absorbs the hits.

Figure 6: Hardware with human throws. Throw locations and outcomes.

Figure 7: Hardware dodgeball. Top, (a) : Hit rates are statistically indistinguishable: 10.2% on synthetic throws (exact McNemar on paired throws, $p=1.0$ ) and 23.1% vs. 30.8% on human throws (Fisher exact, $p=0.76$ ). Top, (b/c) : While both policies are equally likely to be hit, QCBF-PD evades with more agile motion. For QCBF-PD vs. CBF-RL , drift is 0.16 m vs. 0.94 m (Wilcoxon, $p=7\mathrm{e}^{-10}$ ) on synthetic and 0.14 m vs. 0.90 m (Mann–Whitney, $p=2.1\mathrm{e}^{-6}$ ) on human throws, with peak tilt 14.9 ∘ vs. 32.4 ∘ (Wilcoxon, $p=2.4\mathrm{e}^{-11}$ ) and 18.2 ∘ vs. 30.7 ∘ (Mann–Whitney, $p=4.6\mathrm{e}^{-4}$ ).

Figure 8: Value concentration sets avoidance behavior. (a) : pelvis drop and torso lean vs. $\beta$ ; the shaded band marks where the dominant mechanism flips. (b) : per-wall pelvis drop against torso lean, one point per scored wall, large markers the per- $\beta$ medians. (c) : the highest point on the robot lands in the same $0.909$ – $0.948$ m band at every $\beta$ , and clear rate stays flat.

Figure 9: Clearance outcomes & sampling distribution. (a) : Duck and limbo clear comparably; limbo’s

8.3\%

abort rate is all lane exits (topple rate

=0\%

). (b) : replay selected mass over signed safety value

\hat{V}

given replay distribution

p_{\beta}\propto\exp(-\beta b_{\phi})+\bar{p}

, for

b_{\phi}=|g|

|\hat{V}|

. (c) : Dotted line marks standing head height (

1.234

m): the base policy falls off here; duck and limbo hold

88

–

99\%

, with headroom at all rungs.

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Safety-critical control is essential for humanoid robots operating in complex human-centered environments, where physical safety constraints such as joint limits, self-collision avoidance, obstacle avoidance, and workspace boundaries must be satisfied during real-robot operation. However, existing approaches remain limited because kinematic safety guarantees can be degraded in the presence of unknown disturbances, such as model uncertainties, trajectory-tracking errors, and external perturbations. This paper presents a hierarchical safety-critical whole-body control framework for humanoid robots based on input-to-state safe control barrier functions (ISSf-CBFs). The proposed architecture integrates a kinematic-level whole-body controller (KinWBC), an ISSf-CBF safety filter, and a dynamic-level whole-body controller (DynWBC). KinWBC generates nominal joint-motion references from prioritized tasks; the ISSf-CBF filter minimally modifies these references to satisfy kinematic safety constraints under bounded disturbances; and DynWBC tracks the filtered references while enforcing full-body dynamic feasibility and contact stability. Safety constraints are imposed on a whole-body kinematic model, and the ISSf-CBF parameters are conservatively tuned so that the resulting kinematic safety guarantees can be transferred to full-order humanoid dynamics under unknown disturbances. Simulation and real-robot experiments demonstrate that the proposed framework improves safety margins under model mismatch and reliably enforces multiple safety constraints in real time during locomotion, teleoperation, and single-leg balancing with hand control. Project website: https://kwlee365.github.io/SafeWBC-Website/

Abstract

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