Resumen
This study introduces a reduced-order leg dynamic model to simplify the controller design and enhance robustness. The proposed multi-loop control scheme tackles tracking control issues in legged robots, including joint angle and contact-force regulation, disturbance suppression, measurement delay, and motor saturation avoidance. Firstly, model predictive control (MPC) and sliding mode control (SMC) schemes are developed using a simplified model, and their stability is analyzed using the Lyapunov method. Numerical simulations under two disturbances validate the superior tracking performance of the SMC scheme. Secondly, an Nth-order linear active disturbance rejection control (LADRC) is designed based on a simplified model and optimization problems. The second-order LADRC-SMC scheme reduces the contact-force control error in the SMC scheme by ten times. Finally, a fourth-order LADRC-SMC with a Smith Predictor (LADRC-SMC-SP) scheme is formulated, employing each loop controller independently. This scheme simplifies the design and enhances performance. Compared to numerical simulations of the above and existing schemes, the LADRC-SMC-SP scheme eliminates delay oscillations, shortens convergence time, and demonstrates fast force-position tracking responses, minimal overshoot, and strong disturbance rejection. The peak contact-force error in the LADRC-SMC-SP scheme was ten times smaller than that in the LADRC-SMC scheme. The integral square error (ISE) values for the tracking errors of joint angles ??1
?
1
and ??2
?
2
, and contact force ??
f
, are 1.6636×10-28 rad2·s
1.6636
×
1
0
-
28
r
a
d
2
·
s
, 1.7983×10-28 rad2·s
1.7983
×
1
0
-
28
r
a
d
2
·
s
, and 1.8062×10-30 N2·s
1.8062
×
1
0
-
30
N
2
·
s
, respectively. These significant improvements in control performance address the challenges in single-leg dynamic systems, effectively handling disturbances, delays, and motor saturation.