Safe Optimal Control Framework for Cooperative Manipulation of Objects in Human-Robot Teams.

This article introduces a distributed deep neural network (NN)-based adaptive control framework for cooperative object manipulation in human-robot teams with unknown agent dynamics by using three distinct multilayer NN observers (MNNOs). The first observer, termed the reference point estimator, enables each robotic agent to estimate the object's reference center using consensus-based learning, even without direct access to global reference trajectories. The second observer, referred to as the human force-to-trajectory estimator, uses human-applied forces to infer the intended position, velocity, and acceleration of the object, enabling real-time estimation of human intent. Together, these two observers allow distributed estimation of human-intended motion. In addition, a third observer, the distributed NN dynamics observer, is integrated into the control layer to simultaneously estimate the agent's own state and unknown system dynamics while incorporating the state vector of all other agents. Weight update laws for the multilayer NN observers are developed using singular value decomposition (SVD), enabling stable and efficient parameter tuning in multiagent settings. The framework combines the observer estimates with a distributed online multilayer actor-critic NN controller to compute Pareto game theoretic optimal effort that coordinates robot actions while considering neighborhood interactions. Safety is enforced via barrier Lyapunov functions (BLFs) formulated using Karush-Kuhn-Tucker (KKT) conditions, which dynamically adjust safety constraints based on both the agent's own state and its neighbor state vector. Simulation results demonstrate that the proposed approach achieves accurate intent estimation, robust control, and a 60% reduction in total cost compared to baseline methods.