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Page 2 of 16 Wang et al. Intell Robot 2023;3(3):479-94 I http://dx.doi.org/10.20517/ir.2023.26

manoid robots require complex mechanical control systems, environmental awareness, and motion planning
capabilities, which are widely used in service entertainment, disaster rescue, rehabilitation medicine, and so
on [1–3] . Specially, flexible and robust walking is the most basic guarantee for various tasks. However, uncer-
tain disturbances are inevitable in biped walking, which can affect walking stability or even periodic motion.
Hence, it is of great significance to explore advanced high-performance robot control systems, break through
the application bottleneck for fieldwork robots, and promote the development of humanoid robots.

Stabilityanalysisisaconvincingdemonstrationofrobustwalking. Byanalyzingtheconditionsfortheexistence
of stable equilibrium points, the stability analysis will transform into a mathematical problem for the existence
of limit cycles. Various stability criteria have been proposed. Early scholars proposed the zero moment point
(ZMP) stability criterion, which means that the robot is considered stable when the ZMP falls within the
[4]
support area. Goswamiti designed a sole flipping indicator . Huang further discussed the determination
[5]
of the stable region , and then a large number of 3D bipedal solid robots were manufactured based on this
criterion. However, a series of problems arose subsequently, such as stiff movement and poor anti-interference
ability. Considering stable bipedal walking exhibits periodic motion, the restricted Poincare Return Map can
be used to analyze the stability of the system, which transforms the target of stable biped walking into the
problem of stabilization of periodic orbits. The main purpose of using the Poincare return map is to analyze
the stability of periodic orbits in low dimensions. Besides, it is not constrained by motion speed and, thus,
is suitable for various foot structures. Tedrake analyzed the walking stability of a partially passive robot with
[6]
drive only at the ankle joint . Grizzle et al. developed new jumping and running postures for point-legged
[7]
robots .

Compared to the walking ability of humans, biped robots still have a long way to go. They can be regarded
as multi-variable, variable structure, and strong coupling nonlinear systems, possessing the characteristics of
strong environmental adaptability, complex structure, and difficult motion control [8–11] . Recent years have
witnessed the rapid development of robust control of dynamic biped walking. The traditional quasi-static
walking control based on ZMP has practicability; however, it is required that ZMP always falls in the support
polygon, which is inconsistent with human walking [12–14] . For the dynamic walking of biped robots under
external forces, Ames [14] proposed a hybrid zero dynamics control method and gave the analytical conditions
for stable dynamic walking. Since SMC is insensitive to parameter changes and disturbances and has a fast
response, it has become a research focus for robot control. Active force control is achieved by adding sensors
to detect the external forces on the robot and designing corresponding force control algorithms to achieve the
robot’s active compliance with external forces. The classical force control usually includes impedance control
and hybrid position and force control. Yadukumar et al. achieved the robot AMBER walking by collecting and
analyzing human gait data and combining it with hybrid zero dynamics [15] . The classic force control strategy
is applicable to static environments in which environmental information is determined. The foundation of
force control is the perception of external forces. There are generally two ways to measure external forces: one
is to directly obtain the interaction force with the environment through external sensors; Another approach
is to use the dynamic model of the robot to obtain external forces. Dai et al. took the ground as an external
disturbance, quantified the robustness of the robot to ground disturbances through gain L2, and realized the
robot’s walking based on robust control [16] .

Inthereferences [17–20] , thecontrolmethodofasecond-orderslidingmodeisintroducedsystematically,includ-
ing a twisting algorithm, sub-optimal algorithm, and terminal sliding mode algorithm. Then, a motion/force
hybrid control method based on recurrent neural networks (RNNs) was proposed afterward. Spong et al. pro-
posed a continuous controller design method for dynamic walking on the uneven road [21] . However, it is
difficult to adjust control parameter items. Ravichandran et al. proposed a neural network control method
withtheinvertedpendulummodel [22] . Inviewofthestrongapproximationability ofneuralnetworks, they are
usuallyutilizedtoapproximatecomplexnonlinearsystems. Particularly, combiningwiththeself-adaptivetech-