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Source: own elaboration. Table 4. Estimation error (%) of 2-DOF robotic manipulator parameters for cases 1 and 2.

Table 4 Source: own elaboration. Table 4. Estimation error (%) of 2-DOF robotic manipulator parameters for cases 1 and 2.

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This paper presents the way in which the algebraic identification method wa: used to estimate the parameters and the payload of a robotic manipulator (see figure 1). The dynamic equation of the manipulator is given by (Lin, 2007):
This paper presents the way in which the algebraic identification method wa: used to estimate the parameters and the payload of a robotic manipulator (see figure 1). The dynamic equation of the manipulator is given by (Lin, 2007):
Source: own elaboration. Table 1. Replacement of parameters by constants for the first stage. Considering equation (1), it is convenient to include an identifier for each .quation in order to estimate all the parameters of the manipulator. Considering equation (1), it is convenient to include an identifier for each quation in order to estimate all the parameters of the manipulator. Table 1 shows replacements of parameter sets by constants, considering ma- nipulator equations without load (m, = 0). They are useful to facilitate the handling of the equations.
Source: own elaboration. Table 1. Replacement of parameters by constants for the first stage. Considering equation (1), it is convenient to include an identifier for each .quation in order to estimate all the parameters of the manipulator. Considering equation (1), it is convenient to include an identifier for each quation in order to estimate all the parameters of the manipulator. Table 1 shows replacements of parameter sets by constants, considering ma- nipulator equations without load (m, = 0). They are useful to facilitate the handling of the equations.
Paez-Garcia, J., Vargas-Tenjo, L.C., Charry-Belén, R. A., y Coral-Enriquez, H. (2023). https://doi.org/10.21789/22561498.1975 Since there are six terms to be estimated (k, + k3, k,, k3, kg, ky, kz), the last equation is integrated five times in order to obtain a 6 X 6 linear system. There- fore, the linear equation is expressed as P. (t, 01, 92, 0;, 02) Xy = Gr (t, 71), in which P.. (t, 0,, 95, 0,, 8,), dy (t, T,) and x,. are given by:
Paez-Garcia, J., Vargas-Tenjo, L.C., Charry-Belén, R. A., y Coral-Enriquez, H. (2023). https://doi.org/10.21789/22561498.1975 Since there are six terms to be estimated (k, + k3, k,, k3, kg, ky, kz), the last equation is integrated five times in order to obtain a 6 X 6 linear system. There- fore, the linear equation is expressed as P. (t, 01, 92, 0;, 02) Xy = Gr (t, 71), in which P.. (t, 0,, 95, 0,, 8,), dy (t, T,) and x,. are given by:
Finally, the constant k, was estimated by solving equation 4 (4) for the sin- e unknown term after having elapsed ty + €, where € = 0.2s, resulting as follows:
Finally, the constant k, was estimated by solving equation 4 (4) for the sin- e unknown term after having elapsed ty + €, where € = 0.2s, resulting as follows:
Equation (2) was also used to estimate the payload mass with the same iden- tification process as in the first identifier. However, it is necessary to consider here that the parameters that are shown in Table 1 have already been identified, so the only unknown parameter is the tip-payload. A table of substitution of parameters by constants is proposed again considering the payload as the only unknown term (see Table 2).
Equation (2) was also used to estimate the payload mass with the same iden- tification process as in the first identifier. However, it is necessary to consider here that the parameters that are shown in Table 1 have already been identified, so the only unknown parameter is the tip-payload. A table of substitution of parameters by constants is proposed again considering the payload as the only unknown term (see Table 2).
Table 2. Replacement of parameters by constants for the second stage. Paez-Garcia, J., Vargas-Tenjo, L.C., Charry-Belén, R. A., y Coral-Enriquez, H. (2023). https://doi.org/10.21789/22561498.1978 Equation 2(2) also reveals that that either of the two equations that comprise t allowed us to estimate the constants that are shown in Table 2. Thus,
Table 2. Replacement of parameters by constants for the second stage. Paez-Garcia, J., Vargas-Tenjo, L.C., Charry-Belén, R. A., y Coral-Enriquez, H. (2023). https://doi.org/10.21789/22561498.1978 Equation 2(2) also reveals that that either of the two equations that comprise t allowed us to estimate the constants that are shown in Table 2. Thus,
Table 3. 2-DOF robotic manipulator parameters for cases 1 and 2. Both cases were simulated using the MATLAB-Simulink software and the .unge-Kutta solver to guarantee a good sampling of the signals obtained in the simu- ations. A sampling time of 0.0015 was selected. Figure 2 shows the results of the arameter convergence.
Table 3. 2-DOF robotic manipulator parameters for cases 1 and 2. Both cases were simulated using the MATLAB-Simulink software and the .unge-Kutta solver to guarantee a good sampling of the signals obtained in the simu- ations. A sampling time of 0.0015 was selected. Figure 2 shows the results of the arameter convergence.
Paez-Garcia, J., Vargas-Tenjo, L.C., Charry-Belén, R. A., y Coral-Enriquez, H. (2023). https://doi.org/10.21789/22561498.1978 CONCLUSIONS
Paez-Garcia, J., Vargas-Tenjo, L.C., Charry-Belén, R. A., y Coral-Enriquez, H. (2023). https://doi.org/10.21789/22561498.1978 CONCLUSIONS
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