Cooperative Curve-Based Synchronized Control of a Fleet of Autonomous Robots

This article introduces the Pythagorean hodograph (PH) curve-based state-space (PHoCS) method, a framework for synchronized collaborative control of autonomous robot fleets. The approach employs PH parametric curves with predefined lengths to structure coordinated robot movements. Each robot is represented as a control point projected onto these PH curves, ensuring precise kinematic modeling. Matrix transformations, derived from the Lagrange method, are applied to map control point motions onto the PH curves, enabling accurate curve shape modeling and control. A collaborative synchronized control strategy is then developed, operating directly on the control points of the PH curve. By treating the PH curve and its control points as a state-space dynamic system, the strategy effectively manages interrobot interactions while optimizing the PH curve’s shape for dynamic coordination. The first and last robots reach their designated initial and final states within finite time, while intermediate robots continuously track the evolving PH curve. Numerical simulations confirm the effectiveness of the PHoCS control strategy across multiple degrees of complexity. In addition, real-world experiments with a fleet of four autonomous robots validate its practical implementation and performance. This work provides a promising approach for advancing coordinated autonomous robotic systems in dynamic environments.