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Transactions on Mechatronics
IEEE TRANSACTIONS ON MECHATRONICS: FOCUSED SECTION ON DESIGN AND CONTROL OF HYDRAULIC ROBOTS 3
(a) (b) (c)
Fig. 1. Hydraulically actuated robotic serial manipulators: (a) Schilling
ORION for underwater manipulation, (b) Cybernetix’s MAESTRO for nuclear
decommissioning and (c) HIAB031 for academic research purposes.
robot, the proposed control method demonstrated highly ac-
curate joint pressure-based force and position tracking.
Koivumäki and Mattila [43] proposed a VDC-based con-
troller for a two-DOF heavy-duty hydraulic manipulator. In
[45], they demonstrated in three-DOF that by using VDC,
more “subsystems” can be added to the original system
without control performance deterioration and significant con-
troller redesign. Both these stability-guaranteed NMBC studies
demonstrated a position tracking performance improvement
(using a performance indicator ρ) in relation to [19] and [38];
see Section II-A3.
2) Hydraulic Parallel Manipulators (HPMs): The Stewart-
Gough platform (SGP) in Fig.2a is the most widely used
parallel manipulator [53]. Fig.2b and Fig.2c show other ex-
amples of HPMs. HPMs inherit challenging features from
both parallel manipulators and hydraulic actuators. On one
hand, the main advantage of the closed-chain kinematics of
the robot is that it distributes force among the limbs and can
provide higher stiffness and acceleration. On the other hand, it
makes all of the actuator motions constrained by the motion of
the end-effector and have a limited workspace [54]. It is also
well known that forward kinematics of parallel manipulators
are challenging compared with the inverse kinematics of serial
manipulators [55]. These issues are addressed in various con-
troller topologies for different types of parallel robots where
the dynamics of the actuator implies specific restrictions to the
robot controller [56], [57]. Actuator redundancy, which is suit-
able for dexterity improvement, affects force distribution and
kinematic structure; see the shoulder mechanism in Fig.2(b),
which has three DOF and four actuators [55].
This section focuses on recent research in experimentally
verified and stability-guaranteed NMBC design for the hy-
draulic SGP. A number of experimentally verified control
strategies for HPMs, albeit without rigorous stability proof,
also exist in the literature, e.g., [58]–[61]. For a review of
parallel manipulators from their early days to the year 2000,
the interested reader is referred to the work of Dasgupta and
Mruthyunjaya [53].
Kim et al. [62] proposed one of the first studies on stability-
guaranteed Lyapunov-based methods for a hydraulic SGP. In
their robust tracking control design, stability of rigid body dy-
namics was proven, however, stability analysis of the actuator
dynamics was neglected.
Sirouspour and Salcudean [64] tackled the above problem
and proposed for the first time stability-guaranteed NMBC
considering both rigid body dynamics and actuator dynamics.
Adaptation laws were incorporated into the controller to com-
pensate for parametric uncertainties in rigid body parameters
(a) (b) (c)
Fig. 2. Hydraulically actuated parallel manipulators: (a) IHA’s six-DOF SGP,
(b) Concept of a redundant shoulder [55] and (c) A miniature three-DOF SGP
as a part of an endoscope [63].
and hydraulic parameters. Acceleration feedback was avoided
by using two adaptive and robust sliding-type observers.
Tracking errors were rigorously proven to converge to zero
asymptotically using Lyapunov analysis. Very advanced con-
trol performance was demonstrated in experiments.
In [65], Pi and Wang proposed an observer-based cascade
control. A cascade control algorithm was used to separate the
hydraulics dynamics (inner-loop control) from the mechanical
part (outer-loop control). Feedback linearization was used for
the control of hydraulics nonlinearities in the inner loop.
A nonlinear disturbance observer was proposed to estimate
uncertain external disturbances. The stability of the inner
loop control with nonlinear disturbance observer was provided
based on the Lyapunov functions method. It was assumed
that “some existing nonlinear control methods can be directly
employed in the outer loop”.
In [66], Pi and Wang proposed a trajectory tracking con-
troller with uncertain load disturbances. They designed a
discontinuous projection-based parameter adaptation for pa-
rameters in hydraulic dynamics. Platform rigid body dynamics
were neglected in the Lyapunov-based stability analysis.
Chen and Fu [67] proposed an observer-based backstepping
control. Similar to [64], this method considered both the plat-
form dynamics and the dynamics of the hydraulic actuators.
An observer-based forward kinematics solver was applied to
prevent transformation between different states in the platform
dynamics (task-space) and in the actuator (joint-space) dynam-
ics. As a distinction from [62], [64]–[66], a friction compen-
sation was added in the controller. The rigorous stability proof
for the system was given with convergence of control errors.
As the above review shows, papers [64] and [67] provide
theoretically the most rigorous solutions for the control of
parallel hydraulic manipulators. Next, the state of the art in
hydraulic manipulators free-space motion control is evaluated
for parallel hydraulic manipulators, as well as for serial
hydraulic manipulators.
3) Evaluation of the State of the Art: Evaluation of re-
sults and the state of the art in the field of robotics and
automation can be difficult [18]. The majority of the studies in
Sections II-A1 and II-A2 have reported the maximum position
tracking error(s) |e|
max
(in actuator space or Cartesian space).
However, using the maximum position error alone to compare
different control methods does not give a realistic picture of the
control performance, because different sizes of manipulators
were used with different rates of applied dynamics. In the
survey of Patel and Sobl [68], a variety of performance
measures for manipulators were introduced. However, they
mainly focus on the evaluation of manipulator structure and