Analysis of robot dynamics and compensation using classical and computed torque techniques

In memory of Professor José António Tenreiro Machado (1957–2021)

“…Later, he continued pursuing these control goals by embedding the concepts of fractional calculus (FC) with VSCs [ 3 , 4 ]. Nevertheless, the contributions of Professor Tenreiro Machado to the area of control went beyond those already mentioned and included the development of other control techniques, such as computed torque [ 5 ] and fractional PID controllers [ 6 ]. In particular, the hybrid force–torque control interested Professor Tenreiro Machado for long, with emphasis in the 1990s.…”

Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method

“…We verified that: (i) for each robot link, Expression (16) has two zeros or two zeros and one pole, for α > 0 or α < 0, respectively; (ii) the dynamics of the manipulator, from torque to position, presents two poles; (iii) coupling phenomena can be regarded as perturbations, p k (see Figure 1). The location of the robot poles varies considerably [69], and the VSC adapts the gain to guaranty that the system's global dynamics follows the desired reference. Figure 2 sketches the root locus of the unit-feedback VSC-controlled robot links for various values of α [70,71].…”

Dynamics of theN-link pendulum: a fractional perspective

“…The inverse model (15) may be used within certain feedforward control schemes (Machado & de Carvalho, 1989;Machado, de Carvalho, & Galhano, 1993), while the direct model, represented in Figure 2 as a block diagram, is required for simulation (Lewis, Dawson, & Abdallah, 2004;Slotine, 1985;Spong & Vidyasagar, 2008). Model (15) can be calculated in analytic form, for an arbitrary number of links, by symbolic computational software packages (Char, Fee, Geddes, Gonnet, & Monagan, 1986;Moore, 2014;Wolfram, 2000).…”