Motion control design for functionally related systems

When a complex task has to be performed by multiple systems, it imposes functional dependencies between the states and outputs of the systems. These functional dependencies create a system of 'virtually' interconnected subsystems, even though they may be physically separated. The component subsystems within the overall system we call 'functionally related systems', since nature of the task of the system is defining functional relations between the system components. This dissertation deals with motion control design for functionally related systems. The design is based on identifying functions to be executed within a task and design of control to make these functions follow their references. The main goal is to obtain unit control distribution matrix in the function space and enforce a desired dynamics for each of the identified functions. However, the decoupling is not based on physical separation, but rather on the functions. By transforming the configuration space dynamics of the controlled system to the function space, it is shown that by properly selected transformation one can obtain the desired structure of the dynamics in the function space which has identity control distribution matrix. This was done by projecting the configuration space velocities to the function space by the function Jacobian matrix, and having transformation of the control signals from the function space back to the configuration space by a right pseudoinverse of the function Jacobian matrix. In the presented approach, any right pseudoinverse of the function Jacobian matrix can be used. A weighted pseudoinverse is proposed in this dissertation; thus, a weighting matrix can arbitrarily be selected. While any appropriate control method can be used for control input synthesis in the function space, three control methods were employed in this dissertation. These are disturbance-observer-based control, sliding mode control, and control based on the equivalent control estimation. All these methods provide stable and robust control in the function space. The proposed approach for control design is tested in experiments and simulations. Experimental results on a piezoelectric walker showed that nanometric precision positioning can be achieved. In experiments for tasks including two pantograph manipulators, results validated the presented approach allowing simultaneous grasping force and motion control. Simulation results for different tasks including different robotic manipulators and for the formation control of mobile robots showed the potential of our proposed methods in some other interesting scenarios as well.