Singularity-Free Task-Space Formation Control for Manipulators with Joint Constraints Using Relative Bearing-Only Feedback

In many industrial robotics applications, multiple robots must form a desired formation in task space to complete specified collaborative tasks, often under safety constraints due to physical and environmental limitations. Most of the existing robotic cooperative control algorithms focus on joint-space coordination under joint constraints, limiting their practical applicability. In this work, we address the task-space formation control problem of networked robotic manipulators with dynamic uncertainties using relative bearing-only feedback. We present a distributed formation controller for manipulators under full joint constraints, employing a unified barrier function to achieve constraint objectives with an auxiliary controller that does not interfere with the main formation task. The selection of feasible joint constraint functions is discussed to prevent infeasible constraints from hindering task completion. In addition, we propose a distributed formation controller with singularity avoidance by leveraging the specific structural properties of the Jacobian matrix of planar manipulators. These bearing-based solutions reduce the cost of sensing measurements and eliminate the need for costly agent-to-agent communication. Simulation studies involving a group of three-degree-of-freedom planar robotic manipulators validate the efficiency of the theoretical results.