cs.ROAug 28, 2026

Cooperative Risk-Aware Exploration in Heterogeneous Multi-Robot Systems Using Algorithmic Altruism

Authors: Brooks A. Butler, Jair Certório, João P. Hespanha, Magnus Egerstedt

Organizations: School of Electrical and Computer Engineering at Oklahoma State University, Stillwater, OK, 74074, USA · Systems Engineering Division, Instituto Tecnológico de Aeronáutica, Fortaleza, CE, 60415-513, Brazil · Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, 93106, USA · Department of Computer Science at the University of North Carolina, Chapel Hill, NC, 27599, USA

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Abstract

Multi-robot systems are well-positioned for exploration in hazardous environments, but effective deployment requires deciding not only where robots should gather information, but also how risk should be distributed across heterogeneous team members. This paper develops a game-theoretic framework for cooperative risk-aware exploration based on ecologically inspired altruistic behavior. Each robot selects a finite-horizon trajectory to maximize information gain while penalizing redundant exploration and expected hazard exposure. Heterogeneity is introduced through agent-specific value parameters for encoding altruistic coupling, which is modeled through relatedness weights inspired by Hamilton's rule. We introduce a game-theoretic structure for trajectory planning that defines a Social Nash Equilibrium, which modifies the utility of agent actions according to agent relatedness. This utility shaping causes agents to internalize the effect of their trajectory choices on teammates, encouraging lower-valued robots to accept risk when doing so benefits higher-valued agents and improves team performance. We define an exploration utility for agents that rewards area coverage and uncertainty reduction, while also penalizing redundancy and risk, enabling projected gradient-based waypoint optimization in a receding-horizon planner. Simulations show that altruistic planning reduces redundant exploration, improves inter-robot separation, and reallocates risk according to agent value while maintaining comparable map coverage. We further demonstrate the approach in hardware experiments, where planned waypoints are tracked by wheeled robots using single-integrator controllers and barrier certificates.

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 θ−ik={θj}j≠i\theta_{-i}^{k}=\{\theta_{j}\}_{j\neq i} 
Algorithm 1 Altruistic Fictitious Play
Fig. 1 : Representative simulated exploration trajectories for (a) the selfish baseline (i.e., Γ=I\Gamma=I ) and (b) the altruistic utility with relationships defined by ( 13 ), where λblue=λorange=40\lambda_{\text{blue}}=\lambda_{\text{orange}}=40 and λred=λgreen=15\lambda_{\text{red}}=\lambda_{\text{green}}=15 . The filled background shows final map uncertainty, with darker regions corresponding to lower remaining uncertainty. Red contours denote the known hazard field. While both methods explore the domain, the altruistic planner produces more spatially separated trajectories and allocates hazardous exploration according to agent value, allowing lower-valued agents to absorb risk that would otherwise be borne by higher-valued teammates.
Fig. 2 : Aggregate simulation performance over 50 trials for selected value configurations. Bars show sample means and error bars show standard error. The altruistic planner maintains comparable uncertainty reduction to the selfish baseline, while generally increasing minimum pairwise distance and reducing redundant exploration. In heterogeneous and high-value configurations, altruism also lowers value-weighted risk, indicating that the relatedness-weighted utility reallocates risk away from more valuable agents.
Fig. 3 : Robotarium execution of the altruistic risk-aware exploration planner. The projected visualization shows the online uncertainty estimate together with contour lines for the known hazard field. At each replanning round, the high-level planner produces waypoint trajectories, which are tracked by Robotarium single-integrator controllers with boundary-aware barrier certificates. Over time, the robots reduce uncertainty across the arena while maintaining safe separation and respecting workspace boundaries.
Figure 5
 Jair Certório (Member, IEEE) is an Assistant Professor in the Systems Engineering Division at Instituto Tecnológico de Aeronáutica, Fortaleza, CE, Brazil. He received his B.S. degree in Electrical Engineering from the Universidade Estadual de Maringá, PR, Brazil, in 2018, and his Ph.D. degree in Electrical Engineering from the University of Maryland, College Park, MD, USA, in 2025. Between 2025 and 2026, he was a Postdoctoral Scholar in the Department of Electrical and Computer Engineering at the University of California, Santa Barbara.
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