An Evenly Partition Approach to the Modeling and Constraint-Following Control for the Spatial Cooperative Dual-Robot-System

Abstract

Abstract Due to the breadth and complexity of spatial motion, and the nonlinear coupling caused by multiple degree-of-freedom, the control difficulties of spatial cooperative multirobot system are two mainly aspects, the modeling method and the dispose of uncertainty. For modeling, the process of directly using ordinary methods such as Lagrange mechanics are very complex. For control, the external disturbances and imperceptible errors will lead to the instability of dynamic system, these factors are collectively referred to as uncertainty. In this paper, a universal modeling method based on spatial cooperative multirobot system was proposed, and an adaptive robust controller was designed to solve the control problems. Simplify the connection link into a load and divide the system into two symmetrical subsystems by disconnecting the load center. The inherent physical position and given trajectories were unified as constraints. The constraints applied on system are creatively converted into consistent standard form through the Udwadia–Kalaba (U–K) method, and the corresponding constraints can be generated easily from the Udwadia–Kalaba basic equations. In addition, a nominal term to stable the system and an adaptive term was added to the controller. The adaptive term works through an adaptive parameter, the parameter estimates the uncertainty bound, thus, only the boundedness of uncertainty should be known, and more accurate control input can be gained. Eventually, the correctness of the model and controller has been confirmed through numerical simulation.