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
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.
Figures & tables
θ−ik={θj}j=i
Algorithm 1 Altruistic Fictitious Play
Fig. 1 : Representative simulated exploration trajectories for (a) the selfish baseline (i.e., Γ=I ) and (b) the altruistic utility with relationships defined by ( 13 ), where λblue=λorange=40 and λred=λgreen=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.
Hierarchical multi-robot exploration commonly decouples frontier allocation from local navigation, which can make the system brittle in dense and dynamic environments. Because the allocator lacks direct awareness of execution difficulty, robots may cluster at bottlenecks, trigger oscillatory replanning, and generate redundant coverage. We propose VORL-EXPLORE, a hybrid learning and planning framework that addresses this limitation through execution fidelity, a shared estimate of local navigability that couples task allocation with motion execution. This fidelity signal is incorporated into a fidelity-coupled Voronoi objective with inter-robot repulsion to reduce contention before it emerges. It also drives a risk-aware adaptive arbitration mechanism between global A* guidance and a reactive reinforcement learning policy, balancing long-range efficiency with safe interaction in confined spaces. The framework further supports online self-supervised recalibration of the fidelity model using pseudo-labels derived from recent progress and safety outcomes, enabling adaptation to non-stationary obstacles without manual risk tuning. We evaluate this capability separately in a dedicated severe-traffic ablation. Extensive experiments in randomized grids and a Gazebo factory scenario show high success rates, shorter path length, lower overlap, and robust collision avoidance. The source code will be made publicly available upon acceptance.
Ning Liu, Sen Shen, Zheng Li +4
The University of Western Australia · The Chinese University of Hong Kong · Karlsruhe Institute of Technology +1
Efficient robotic extraterrestrial exploration requires robots with diverse capabilities, ranging from scientific measurement tools to advanced locomotion. A robotic team enables the distribution of tasks over multiple specialized subsystems, each providing specific expertise to complete the mission. The central challenge lies in efficiently coordinating the team to maximize utilization and the extraction of scientific value. Classical planning algorithms scale poorly with problem size, leading to long planning cycles and high inference costs due to the combinatorial growth of possible robot-target allocations and possible trajectories. Learning-based methods are a viable alternative that move the scaling concern from runtime to training time, setting a critical step towards achieving real-time planning. In this work, we present a collaborative planning strategy based on Multi-Agent Proximal Policy Optimization (MAPPO) to coordinate a team of heterogeneous robots to solve a complex target allocation and scheduling problem. We benchmark our approach against single-objective optimal solutions obtained through exhaustive search and evaluate its ability to perform online replanning in the context of a planetary exploration scenario.
Matthias Rubio, Julia Richter, Hendrik Kolvenbach +1
Robotic Systems Lab (RSL), ETH Zürich, Zürich, Switzerland
This paper studies heterogeneous multi-team collaboration through dynamic robot allocation, where robots are treated as transferable resources. Leveraging Hamilton's rule from ecology as an altruistic decision-making mechanism, we propose a multi-team collaborative resource allocation framework with heterogeneous capabilities, transfer costs, and capability-dependent contributions. The resulting allocation problem is combinatorial and is shown to be NP-hard. To address scalability, we develop a graph neural network policy under centralized training and decentralized execution that approximates the altruistic allocations based on Hamilton's rule. The model operates over the team interaction graph and predicts robot-level transfer decisions and next robot-to-team assignments. The proposed approach is validated in a firefighting scenario through simulations and experiments, demonstrating that the learned policy achieves near-optimal performance while scaling to larger systems.
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Samueli School of Engineering, University of California, Irvine, Irvine, CA, 92697, USA · University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA