Control of Constrained Robot Manipulators based on Fractional Order Error Manifolds

There exists a large class of physical systems modeled by differential equations subject to holonomic constraints, called DAE (Differential Algebraic Equations) systems, such as constrained robots. Several schemes have been successfully implemented by using integer order error manifolds, however no studies have been reported on fractional order manifolds that fully addresses their benefits or limitations. In this paper, a model-free force-position controller is proposed based on a novel design of fractional order manifolds of velocity and force errors. The salient features of our proposal are threefold: i) a model-free controller that guarantees robustness to bounded disturbances and parametric uncertainties; ii) a generalized-order design of orthogonalized force-velocity error manifolds, which includes as a particular case the integer order design; and iii) an intuitive tuning procedure of the closed-loop frequency response accordingly to task specifications. Such features are quite useful to deal with rigid contacts, including the analysis on the frequency performance. The viability of this proposal is exemplified and discussed in a representative simulation study.