IEEE Robotics & Automation Magazine - September 2022 - 100

closed-loop system acted like a prespecified reference model
using the fuzzy learning mechanism.
In [137], an inverse dynamics analysis of the FAST was
derived using the Lagrangian method. Random wind forces
acting on the cabin (MP) were simulated, and a PD fuzzy
controller was implemented to handle the vibrations induced
by the wind. In [138], passivity-based control of a planar 2-1
CRPM using a modified input torque and output tip rate for
establishing a passive input-output mapping was presented. A
lumped-mass method was used to model the dynamics considering
the changing stiffness and mass of the cable wrapped
around a winch.
Controllers Considering the Elasticity of Cables
Different approaches are employed to control the effect of
elasticity and vibration of CDPRs. One approach is to separate
the fast and slow motion of the system. In [71], dynamic
equations of a spatial IRPM were rewritten to the standard
form of the singular perturbation approach. A corrective
term was added to the rigid part of the controller to guarantee
the asymptotic stability of the fast dynamics. The Tikhonov
theorem was used to separate slow and fast variables
for stability analysis. In [139], a composite robust adaptive
method was presented for a 4-3 planar CRPM. A fast control
term, (),KL L
dinal vibrations, where L1
v 12 was added to compensate for the longituand
L2
oosioned
and free cable lengths, respectively, and Kv
are the vectors of the tenis
a
diagonal matrix. In [140], the MP's undesired vibration was
separated from its desired equation of motion by neglecting
the second- and higher-order terms of the motion errors to
form a linear parametric variable dynamic system. A robust
vibration compensator was designed using the H3
method
to control the system.
In [23] and [141], PD, PID, and fuzzy PID controllers
were used for a 7-6 spatial CRPM and a 4-3 planar CRPM.
The fuzzy method was used to tune the gains of the PID controller,
and an online dynamic minimum torque estimation
was used to ensure positive tensions in the cables. System
responses showed that the fuzzy PID controller is more
robust than the PID controller when encountering disturbances
from the elastic cables. IMUs and encoders were used
to detect the fast and slow dynamic movements of the MP in
[73]. Their feedback was used in the FL controller to estimate
the precise position and orientation of the MP, and a Kalman
filter was used to smooth the noises in the process.
In [72], the MP vibration was considered as a process
noise. To achieve a tradeoff between the control input and the
tracking error, the FL gains were obtained using the linear
quadratic Gaussian method. A Lyapunov analysis demonstrated
that a system with damping less than a specified minimum
value could be stable with this approach. In [142], a
mechanical reaction-based stabilizer was used for nonmodelbased
vibration control of CDPRs. The stabilizer was composed
of three actuators attached to a pendulum in a
perpendicular arrangement mounted on the MP. The stabilizer
needed only the actuators' directly measurable position and
100 * IEEE ROBOTICS & AUTOMATION MAGAZINE * SEPTEMBER 2022
velocity to form its closed-loop control feedback signals. In
[143], a linear decoupled model of an 8-6 suspended RRPM
with elastic cables was derived using modal analysis. The
model is projected in the modal space yielding six decoupled
second-order transfer functions for six DoFs of the robot,
which can be easily controlled with standard single-input, single-output
techniques.
Conclusion and Outlook
In this review, different design configurations and applications
of planar and spatial CDPRs have been presented.
Along with reviewing new and emerging research aspects of
CDPRs with massless inelastic cables, the effects of considering
the mass and elasticity of cables on the kinematics,
dynamics, and control were emphasized. Achieving configuration
optimization by changing motor and cable placements
or adding additional elements for having a larger
workspace and collision-free trajectory planning were
addressed. Moreover, robust and adaptive controllers for
compensating uncertainties in the robot's parameters and
disturbances were reported.
This review reveals some outstanding research aspects
concerning the CDPRs, listed as follows.
1) In terms of considering the mass and elasticity of the
cables, most of the literature considers linear behavior for
the cables. The kinematics and dynamics considering the
nonlinear elastic behavior of the thin cables still require
investigation. Moreover, a framework for carrying out the
comprehensive formulation for the kinematics and
dynamics considering mass, nonlinear elasticity, and
environmental effects, such as temperature and wind, still
needs to be developed. Furthermore, only a few research
works [69], [88], [102] have reported the effect of mass
and elasticity of the cables on the workspace and trajectory
planning.
2) While several investigations of CDPRs have been reported,
the combination of traditional serial and parallel
robots with CDPRs for constructing hybrid manipulators
is still in its infancy. CDPRs can be integrated into traditional
manipulators to cover some DoF of the system.
However, kinematics, dynamics, workspace, trajectory
planning, and control will require further investigation in
such configurations.
3) The application of CDPRs for underwater applications or
fluid environments has been little studied in the literature.
However, a large workspace and lightweight structure can
enable a CDPR to be suitable for such applications. This
type of implementation requires considering the effect of
fluid forces such as buoyancy and drag force on the MP
and cables during dynamics analysis and control implementation.
Efficient control algorithms need to be developed
for such CDPR applications to handle the nonlinear
dynamics arising from fluid forces.
4) CDPRs have several advantages over other robotic solutions
in terms of easier modularity, scalability, and
reconfigurability, which can be further enhanced by
IEEE Robotics & Automation Magazine - September 2022

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