Motional stabilization of the elastic manipulator
The problem addressed is the joint space trajectory tracking in a manipulation robot having some kind of flexibility. This flexibility is modeled by introducing into the manipulator a suitable number of artificial, non-actuated joints. It is assumed that the elastic forces exerted at these joints depend on the joints' positions and velocities, and are described as \[ M_i=-k_i \psi_i-l_i \dot\psi_i \] \((\psi_i\) denote positions of the non-actuated joints) for some positive gain coefficients \(k_i,l_i\). Under such an assumption the main result of this paper establishes that a control law of the form \[ u_j=-H_j \text{sign}(s_k), \quad s_i=\dot e_j+\lambda_je_j,\;e_j= \varphi_j- \varphi^*_j, \] where \(\varphi_j\) stand for positions of actuated joints, \(\varphi^*_j\) denote desirable actuated joint trajectory, \(\lambda_t>0\), renders the closed loop system exponentially stable provided that the gain coefficients \(l_i\) of non-actuated joints are sufficiently large.
scientific article; zbMATH DE number 1263131