SAGE: Safety-Aligned Gradient Enforcement for Human

Multi-robot cooperative transport with auditable hard-tree policies and exact CBF-QP safety filtering.

Abstract

Multi-party human–robot collaboration poses a dual challenge: robot decisions should remain interpretable and auditable, while executed actions must satisfy safety constraints during physical interaction. Combining explainable decision-tree policies with control-barrier-function (CBF) filtering provides a promising architecture but creates two learning mismatches in multi-agent reinforcement learning. Safety projection changes the action applied to the environment, while the coupled proposal graph can misalign independently optimized actor updates with a team-level update. We present safety-aligned gradient enforcement (SAGE) to address both mismatches. Its shield-annealed internalization layer (SAIL) uses a differentiable finite-penalty proposal map while retaining the exact CBF quadratic program for execution, preserving constraint-normal sensitivity to internalize repeatedly active safety constraints. Team-averaged Lyapunov policy optimization (TALO) constructs a team-aware update reference and applies a Lyapunov half-space correction to regulate independent actor updates. Physical experiments with two humanoid robots and a human partner demonstrate deployment feasibility. Across nine simulation scenarios, SAGE achieves a 71.0% success rate with 0.5 collision steps per thousand environment steps. Ablations show that direct CBF filtering reduces collision frequency by 98.5% but decreases success from 67.3% to 59.3%. SAIL reduces proposal violation by 48.8% and proposal–execution correction by 85.2%, while TALO reduces the update-consistency gap by 50.8%.

Figure 1: Architecture of SAGE integrating auditable hard-tree nominal policies, SAIL-based proposal learning, exact joint CBF-QP execution, and TALO-based multi-actor policy optimization.

SAGE Training & Deployment Framework

Figure 2: Training and deployment structure of SAGE. Hard-tree actors generate auditable nominal actions, SAIL forms differentiable proposal centers for safety-aware proposal learning, the exact joint CBF-QP maps sampled proposals to constraint-satisfying executed actions, and TALO uses executed-transition returns and a team-aware update reference to regulate independent actor updates. SAIL, exploration, the critic, and TALO are removed at deployment, leaving only the learned hard-tree actors and the exact joint CBF-QP.

Real-World Human–Humanoid Transport

Scenario 1: Three-carrier physical collaboration — two Unitree G1 humanoids + one human partner

Scenario 2: Spatially confined transport — octagonal table and human-partner variation

Scenario 3: Simulation — three-carrier cooperative transport in the Isaac Lab Maze

Scenario 4: Diverse payloads — tire, ladder, and long-board transport with different human partners

Figure 3: Human–humanoid transport with two Unitree G1s and a human partner in outbound (human on the long edge, G1s at the short ends) and return (human at one short end, G1s at the opposite short end and long edge) formations, showing (a) multi-exposure trial views, (b) top-view and (c) 3-D Vicon trajectories over four trials (Exp. A–D), and (d) board-corner velocity components versus normalized carry progress.

Figure 4: Representative snapshots from five real-world human–robot cooperative-transport trials showing temporal progression across five task configurations, including transport of an octagonal table.

Simulation Benchmark

Figure 5: Nine multi-carrier cooperative-transport scenarios grouped by row into LCP (Narrow Gate, Needle Gate, Tilt Gate), STR (Double Gate, Chicane, S-Shaped Corridor), and CCN (L-Corridor, U-Shaped Corridor, Maze), with overlaid payload poses indicating representative trajectory configurations.

Figure 6: Illustrative multi-robot cooperative-transport scenarios across indoor environments and payload geometries.

Quantitative Analysis & Ablations

Figure 7: Suite-level performance across LCP, STR, and CCN, with success rate (↑) above and collision steps per thousand environment steps (↓) below; the broken lower axis accommodates the much larger collision rate of unshielded HAPPO, and error bars denote standard deviation across evaluation runs.

Figure 8: Training dynamics of the five methods showing (a) cumulative reward and (b) payload drop rate, with solid curves denoting the mean and shaded regions the variability across runs.

Figure 9: SAIL and TALO mechanism dynamics showing (a) proposal violation rate of the raw hard-tree nominal action, (b) proposal–execution correction, (c) update-consistency gap, and (d) cosine alignment between the independent and team-aware gradients.

Figure 10: Execution-level comparison across the five methods in (a) payload-tilt-induced vertical deviation, (b) mean step-wise heading error, (c) payload height error, and (d) task completion time, with error bars indicating variability across runs.

Figure 11: Joint-leaf-tuple audit in the Isaac Lab Maze showing (a) occupancy over path progress across 30 evaluation episodes and (b) the highlighted episode colored by the 12 most frequent tuples, with remaining tuples grouped as other; the black square and red star mark the start and goal.

Figure 12: Representative decision traces through a deployed hard-tree policy in the Isaac Lab Maze, with green and purple branches marking two complete root-to-leaf predicate sequences and their affine leaf commands; unselected sibling branches are collapsed for readability.

BibTeX

@article{li2026sage,
  title={SAGE: Safety-Aligned Gradient Enforcement for Human-Robot Collaboration},
  author={Li, Yisen and Zhang, Hao and Geng, Ruize and Tseng, Yves and Zhao, Ding and Tseng, H. Eric},
  journal={arXiv preprint arXiv:2609.21130},
  year={2026}
}