Non Normalized Shared-Constraint Dynamic Games for Human-Robot Collaboration with Asymmetric Responsibility

TL;DR

The paper introduces a dynamic-game approach for cooperative human-robot navigation with shared safety constraints, modeling asymmetric responsibility through a non-normalized generalized Nash equilibrium (GNE) parameterized by α and embedded in a receding-horizon MPC solved as a mixed complementarity problem. This framework allows the human and robot to contribute different levels of effort toward enforcing safety constraints such as inter-player distance and obstacle avoidance. Simulation results across scenarios demonstrate that adjusting α yields intuitive leader–follower behaviors, smoother trajectories with obstacles, and improved robustness under human motion uncertainty. The approach offers a principled mechanism to allocate enforcement burden in human–robot collaboration with potential applications in safe shared autonomy and cooperative manipulation.

Abstract

This paper proposes a dynamic game formulation for cooperative human-robot navigation in shared workspaces with obstacles, where the human and robot jointly satisfy shared safety constraints while pursuing a common task. A key contribution is the introduction of a non-normalized equilibrium structure for the shared constraints. This structure allows the two agents to contribute different levels of effort towards enforcing safety requirements such as collision avoidance and inter-players spacing. We embed this non-normalized equilibrium into a receding-horizon optimal control scheme.

Figures (3)

• Figure 1: Scenario 1 Trajectories
• Figure 2: Scenario 2 — Trajectories of both players for different values of $\alpha$.
• Figure 3: Scenario 3 Monte-Carlo sample Trajectories

Theorems & Definitions (1)

• Theorem 1