Iterative adaptive control of a strongly underactuated mechanical system with limited possibilities for state observation

Efficient control of strongly underactuated mechanical systems in which no practical means exist for developing observers to reveal the internal dynamic state of the system under control is a challenging task. In many practical cases it is even hopeless to develop an at least formally complete system model. For instance deformable robot arms may have infinitely many “degree of freedom” that -under special boundary conditions- may become at least countable. In such cases the controllers have to do with observing and manipulating the behavior only of the modeled and directly actuated axles while the lack of at least a formal model anticipates the use of some adaptive technique without tuning any model parameter. The Robust Fixed Point Transformations (RFPT)-based technique using appropriate adaptive input deformation seems to be a natural possibility for this purpose. In this paper a deformable single robot arm is modeled by six rigid arm-segments connected by deformable joints without internal actuation. Only the first section´s axle is actuated and the position of the end-point of the last segment is assumed to be optically observable. The excitation of the internal axles is “observed” only trough their effect of the torque fluctuation of the controller. Simulation results substantiate the assumption that the RFPT-base adaptive controller can efficiently solve such tasks.