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Page 90 Li et al. Intell Robot 2022;2(1):89–104 I http://dx.doi.org/10.20517/ir.2022.02

Figure 1. The prototype of the 4-dof parallel robot.

dedicated to pick-and-place operations (PPOs) with high dynamic movements. For instance, Figure 1 depicts
a four-degree-of-freedom (4-dof) robot of this family suitable for PPO. Accordingly, the design of a control
system for the robot under study is the focus of this work, since precise control is of importance, in particular
for such a robot working with highly frequent switching of joint motions.

In the control design, classical model-free controller techniques, such as PID and PD controls, have been ex-
tensively adopted by industrial robots due to their simplicity and ease of implementation. However, these
[2]
controllers are not applicable to parallel robots due to the highly nonlinear coupled characteristics . In this
[3]
[4]
light, some control methods, such as torque feedforward control , computed torque control , sliding mode
control [5,6] , etc, have been proposed to improve the control quality for parallel robots. Although those meth-
[6]
ods overcome some problems, such as trajectory tracking accuracy , other problems (i.e, increased compu-
tational burden and requirement of an accurate dynamic model) arise. Taking the characteristics of repetitive
tasks for most parallel robots into consideration, it turns out that iterative learning control (ILC) is suitable
for controlling the parallel robots, as ILC can benefit robot control from the system repeatability, wherein ILC
makes use of the last output motion of the robot end-effector to obtain control inputs that can track the desired
trajectory repeatedly.

[7]
ILC was first proposed in 1978 , but it did not attract the attention of researchers until 1984 because of
[8]
language restrictions . Over several decades, ILC has been developed and improved with numerous variants.
One example is the ILC with a P-type switching surface using a proportional structure, which can effectively
[9]
cope with external disturbances . Compared with the sliding mode surface, this controller is able to remove
the chattering in the control process. It has been used for mobile robots to improve the robustness of path
tracking against the presence of initial shifts, but it introduced a large trajectory tracking error and had a
poor convergence effect [10] . The D-type ILC is proposed with an initial condition algorithm [11] to specify
the initial state value in each iteration automatically. However, a lot of jittering occurs in the control torque,
leading to damage to the actuator and some other robotic components. Sequentially, a modified D-type ILC
was designed [12] to effectively avoid the jitter and glitch for enhanced convergence accuracy, compared to
the conventional D-type one. By means of the filter, another D-type ILC method with a unit-gain derivative is
proposed tocompensatefortheunexpected high gainoftheconventionalderivativeathigh frequency, wherein
the desired phase compensation can be realized within a designated frequency band.

Despite the advantages of the above-mentioned ILC methods, neither P- nor D-type learning laws can make
full use of system information. In the control law, P- and D-type gains not only play a role in learning gain
but also take the task of accomplishment of the feedback in the control system [13,14] . However, it is difficult to
achieve the compatibility between feedback stability and learning convergence. Alternatively, PD-type ILCs