SAGE: Safety-Aligned Gradient Enforcement for Human--Robot Collaboration

Yisen Li; Hao Zhang; Ruize Geng; Yves Tseng; Ding Zhao; H. Eric Tseng

cs.ROSep 17, 2026

SAGE: Safety-Aligned Gradient Enforcement for Human--Robot Collaboration

Authors: Yisen Li, Hao Zhang, Ruize Geng, Yves Tseng, Ding Zhao, H. Eric Tseng

Organizations: University of Texas at Arlington · Carnegie Mellon University

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%.

Figures & tables

Fig. 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.

Fig. 2: Training and deployment structure of SAGE, where 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, while SAIL, exploration, the critic, and TALO are removed at deployment, leaving only the learned hard-tree actors and the exact joint CBF-QP.

Category	Scenario	HAPPO		HAPPO+CBF		TALO+CBF		SAIL+CBF		SAGE+CBF
Category	Scenario	SR $\uparrow$	Col./1k $\downarrow$	SR $\uparrow$	Col./1k $\downarrow$	SR $\uparrow$	Col./1k $\downarrow$	SR $\uparrow$	Col./1k $\downarrow$	SR $\uparrow$ Col./1k $\downarrow$
LCP	Narrow Gate	76.7	156.7	73.0	0.2	74.0	0.4	74.0	0.4	76.0	0.1
	Needle Gate	68.7	42.2	48.1	0.6	48.3	1.8	54.6	0.1	58.3	0.1
	Tilt Gate	68.3	235.4	55.7	1.1	78.7	0.1	74.8	1.3	77.7	0.6
	LCP Mean	71.2	144.8	58.9	0.6	67.0	0.8	67.8	0.6	70.7	0.3
STR	Double Gate	66.3	147.7	64.3	0.3	67.0	0.6	70.6	0.2	69.7	0.3

TABLE I: Performance and safety across the LCP, STR, and CCN cooperative-transport task families, with SR reported in % and Col./1k in collision steps per thousand environment steps.

Fig. 3: 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.

Fig. 4: Suite-level performance across LCP, STR, and CCN, with success rate (SR,

\uparrow

) above and collision steps per thousand environment steps (Col./1k,

\downarrow

) below; the broken lower axis accommodates the much larger collision rate of unshielded HAPPO, and error bars denote standard deviation across evaluation runs.

Fig. 5: 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.

Representation	Purity $\uparrow$	Shuffle $z$ $\uparrow$	NMI $\uparrow$
Individual leaf	0.580	97.9	0.52
Joint tuple $(\ell_{1},\ell_{2},\ell_{3})$	0.845	95.2	0.78

TABLE II: Association of individual and joint leaf states with route progress in the Isaac Lab Maze.

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

Fig. 7: SAIL and TALO mechanism dynamics showing (a) proposal violation rate of the raw hard-tree nominal action

a_{\mathrm{ST}}

, (b) proposal–execution correction, (c) update-consistency gap

W_{\mathrm{gap}}

, and (d) cosine alignment between

g_{\mathrm{ind}}

and

g_{\mathrm{team}}

Fig. 8: Execution-level comparison across the five methods in (a) payload-tilt-induced vertical deviation, (b) mean step-wise heading error

|\mathrm{yaw}-\mathrm{yaw}_{\mathrm{goal}}|

, (c) payload height error, and (d) task completion time, with error bars indicating variability across runs.

Panel of Figure 11 — Fig. 9: 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.

Fig. 10: 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, and $1$ – $3$ denote tuple order.

Formation	Time (s)	Height Std. (cm)	Tilt P95 (deg)	Yaw RMS (deg/s)	Min. Clearance (cm)
Outbound	122	1.0	1.30	7.9	9.6
Return	119	1.3	2.12	7.3	9.1

TABLE III: Transport quality metrics for the real-world deployment.

Fig. 11: Representative snapshots from five real-world human–robot cooperative-transport trials showing temporal progression across five task configurations, including transport of an octagonal table.

Fig. 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.

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Multi-Robot Motion Planning Multi-Agent Trajectory Prediction Social Robot Navigation Robot Safety

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Safe and socially compliant navigation in open human-robot environments requires robots to reason about heterogeneous participants with different dynamics, autonomy levels, and social roles. Existing trajectory prediction and planning methods often rely on homogeneous interaction assumptions or enforce only geometric collision constraints, making it difficult to jointly model asymmetric interactions, coupled prediction-planning, and soft social norms. This paper proposes SAGE, a socially-aware generative engine for heterogeneous multi-agent navigation. SAGE represents robots and surrounding entities as a directed heterogeneous graph and employs a Heterogeneous Graph Transformer (HGT) to encode type-specific asymmetric interactions. Conditioned on the resulting context, a diffusion-based generative module jointly models future entity trajectories and robot trajectory plans. During inference, a training-free safety-social energy guidance mechanism refines sampled robot trajectories using differentiable collision, kinematic, task-progress, and role-conditioned social-compliance terms. Extensive experiments on real-world (ETH/UCY and SDD) and synthetic datasets verify the effectiveness of SAGE in improving safety and social compliance while maintaining task performance. The proposed guidance mechanism consistently reduces collision and social-violation rates, scales to teams of up to 20 robots, and enables explicit control of the safety-accuracy-task trade-off without retraining. These findings demonstrate the potential of SAGE as a scalable framework for socially-aware multi-agent navigation in complex environments.

Abstract

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