Dynamics and trajectory tracking control of a two-link robot manipulator

Operational problems with robot manipulators in space relate to several factors, most importantly, structural flexibility and subsequent difficulties with their position control. In this paper we present control methods for endpoint tracking of a 12.6 x 12.6 m(2) trajectory by a two-link robot manipulator. Initially, a manipulator with rigid links is modeled using inverse dynamics, a linear quadratic regulator and fuzzy logic schemes actuated by a Jacobian transpose control law computed using dominant cantilever and pinned-pinned assumed mode frequencies. The inverse dynamics model is pursued further to study a manipulator with flexible links where nonlinear rigid-link dynamics are coupled with dominant assumed modes for cantilever and pinned-pinned beams. A time delay in the feedback control loop represents elastic wave travel time along the links to generate non-minimum phase response. A time delay acting on control commands ameliorates non-minimum phase response. Finally, a fuzzy logic system outputs a variable to adapt the control law in response to elastic deformation inputs. Results show greater endpoint position control accuracy using a flexible inverse dynamics robot model combined with a fuzzy logic adapted control law and time delays than could be obtained for the rigid dynamics models.