Velocity field control of robot manipulators by using only position measurements

Operational space trajectory tracking control of robot manipulators endowed with a primary controller of synthetic joint velocity

“…On the other hand, the results of the implementation of the new joint velocity controller (57)-(58), filter (15)- (16), and kinematic controllers (17)- (18), are shown in Fig. 6, that depicts the Cartesian robot path, and Fig.…”

“…In fact, if we computeω d from (18) and remove the terms associated with the signalsẏ andq, thenω ⋆ d is obtained. The proposed control method is summarized as follows: the primary control loop is given by the controller (12)-(13) and the filter (15)- (16), while the operational space secondary controller is defined by Eqs. (17) and (18).…”

“…To prove that the controller (12)-(13), (15)- (16) and (17)-(18) guarantees the control objective (8), we show that there exists ϵ * > 0 such that the state-space origin of the closed-loop system (30)-(32) is locally exponentially stable with ϵ * > ϵ > 0. Such a proof is obtained by verifying the conditions of Theorem 1 in Appendix, which will be set down in the following four items:…”

“…where K ′ i and K ′ p are 2 × 2 diagonal positive definite matrices, ϑ is the output of the filter (15)- (16), and ω d andω ⋆ d are defined in (17) and (18), respectively. In analogous form, the only information required to implement the new velocity controller (57) is the numerical values of the parameters θ 1 , .…”

“…The most common secondary loop is designed with the aim of satisfying either the motion or the force control objective. The papers [11][12][13][14][15][16][17][18][19], show designs of robot controllers based on a primary joint velocity and secondary task-based loops.…”