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Wang et al. Intell Robot 2023;3(3):479-94 I http://dx.doi.org/10.20517/ir.2023.26 Page 3 of 16

Figure 1. The nine-link model of biped robots.

nology, network weight coefficient identification and updating learning factors can be realized. It has a good
generalization ability and can approach any nonlinear function with the required accuracy, which is suitable
for real-time and online control of signal processing and robot control [23–26] . Although there are numerous
advanced results on biped dynamic walking [27,28] , there are still some unresolved issues worth studying, such
as the robustness of walking and mobility flexibility. In this paper, we concentrate on adaptive robust control
for bipedal robots under uncertain external forces.

Themaincontentofthearticleisarrangedasfollows. Section2describesthedynamicmodelofthebipedrobot.
It is modeled as a nonlinear impulsive system. An adaptive sliding-mode controller is proposed in Section 3.
In Section 4, a primary RNN with self-stabilizing ability is utilized to deal with the complicated optimization
problem. The hybrid robust control is then proposed to approximate unknown dynamic functions, and the
network weights are adaptive. The simulation results are shown in Section 5, and Section 6 further proposes
future work.

2. DYNAMIC MODELS
The biped robot model discussed in this paper is depicted in Figure 1, which includes a torso and two legs

with revolute knees. = [ 1 , 2 , 3 , 4 , 5 , 6 ] represents the angle of each joint. According to geometrical
constraints on the biped robot joint coordinates, the constraints in the double-support phase are holonomic.

Assumption 2.1. The swinging foot and the ground are completely elastic collisions.

Assumption 2.2. The joint angle remains the same, while the angular velocity changes immediately since the
impact occurs instantaneously.