Control of a 3RRR planar parallel robot based on a dynamic model and a kinematic estimator

Abstract

Redundant coordinates are often used to establish the dynamics equations of parallel
robots because that makes the problem simpler in comparison to the case of using
minimal coordinates. The obtained results are a set of differential algebraic equations
(DAEs). After that, these equations are transformed to the form of minimal coordinates
to design a feedback controller. This controller requires feedbacks of all the redundant
coordinates and their derivatives. In practice, to have all feedback variables for the
controller, a robot needs more sensors than its degree of freedom. These sensors
measure not only the actuated joint variables, but also the auxiliary variables and
position and velocity of the moving platform. However, some coordinates can not be
easily measured by sensors like encoder. In this paper, a novel method is introduced to
estimate dependently generalized coordinates and motion of the moving platform. A
kinematic error feedback technique is exploited to ensure the estimated motion
converge to the actual motion of the robot. Numerical simulation results are performed
to confirm the reliability and efficiency of the proposed method.