Abstract: This paper presents a multi-objective optimal design of
a cascade control system for an underactuated mechanical system.
Cascade control structures usually include two control algorithms
(inner and outer). To design such a control system properly, the
following conflicting objectives should be considered at the same
time: 1) the inner closed-loop control must be faster than the outer
one, 2) the inner loop should fast reject any disturbance and prevent
it from propagating to the outer loop, 3) the controlled system
should be insensitive to measurement noise, and 4) the controlled
system should be driven by optimal energy. Such a control problem
can be formulated as a multi-objective optimization problem such
that the optimal trade-offs among these design goals are found.
To authors best knowledge, such a problem has not been studied
in multi-objective settings so far. In this work, an underactuated
mechanical system consisting of a rotary servo motor and a ball
and beam is used for the computer simulations, the setup parameters
of the inner and outer control systems are tuned by NSGA-II
(Non-dominated Sorting Genetic Algorithm), and the dominancy
concept is used to find the optimal design points. The solution of
this problem is not a single optimal cascade control, but rather a set
of optimal cascade controllers (called Pareto set) which represent the
optimal trade-offs among the selected design criteria. The function
evaluation of the Pareto set is called the Pareto front. The solution
set is introduced to the decision-maker who can choose any point
to implement. The simulation results in terms of Pareto front and
time responses to external signals show the competing nature among
the design objectives. The presented study may become the basis for
multi-objective optimal design of multi-loop control systems.
Abstract: The control problem of underactuated spacecrafts has
attracted a considerable amount of interest. The control method for
a spacecraft equipped with less than three control torques is useful
when one of the three control torques had failed. On the other hand,
the quantized control of systems is one of the important research
topics in recent years. The random dither quantization method that
transforms a given continuous signal to a discrete signal by adding
artificial random noise to the continuous signal before quantization
has also attracted a considerable amount of interest. The objective of
this study is to develop the control method based on random dither
quantization method for stabilizing the rotational motion of a rigid
spacecraft with two control inputs. In this paper, the effectiveness of
random dither quantization control method for the stabilization of
rotational motion of spacecrafts with two torque inputs is verified
by numerical simulations.
Abstract: Underactuated biped robots control is one of the interesting topics in robotics. The main difficulties are its highly nonlinear dynamics, open-loop instability, and discrete event at the end of the gait. One of the methods to control underactuated systems is the partial feedback linearization, but it is not robust against uncertainties and disturbances that restrict its performance to control biped walking and running. In this paper, fuzzy partial feedback linearization is presented to overcome its drawback. Numerical simulations verify the effectiveness of the proposed method to generate stable and robust biped walking and running gaits.
Abstract: The problem of finding control laws for underactuated
systems has attracted growing attention since these systems are
characterized by the fact that they have fewer actuators than the
degrees of freedom to be controlled. The acrobot, which is a planar
two-link robotic arm in the vertical plane with an actuator at the elbow
but no actuator at the shoulder, is a representative in underactuated
systems. In this paper, the dynamic model of the acrobot is
implemented using Mathworks’ Simscape. And the sliding mode
control is constructed using MATLAB and Simulink.
Abstract: This paper describes an underactuated robot hand operated by low-power actuators. It can grasp objects of various shapes using easy operations. This hand is suitable for use as a lightweight prosthetic hand that can grasp various objects using few input channels. To realize operations using a low-power actuator, a cross section deformation spring is proposed. The design procedure of the underactuated robot finger is proposed to realize an adaptive grasping movement. The validity of this mechanism and design procedure are confirmed through an object grasping experiment. Results demonstrate the effectiveness of across section deformation spring in reducing the actuator power. Moreover, adaptive grasping movement is realized by an easy operation.
Abstract: The challenge in the swing-up problem of double
inverted pendulum on a cart (DIPC) is to design a controller that
bring all DIPC's states, especially the joint angles of the two links,
into the region of attraction of the desired equilibrium. This paper
proposes a new method to swing-up DIPC based on a series of restto-
rest maneuvers of the first link about its vertically upright
configuration while holding the cart fixed at the origin. The rest-torest
maneuvers are designed such that each one results in a net gain
in energy of the second link. This results in swing-up of DIPC-s
configuration to the region of attraction of the desired equilibrium. A
three-step algorithm is provided for swing-up control followed by the
stabilization step. Simulation results with a comparison to an
experimental work done in the literature are presented to demonstrate
the efficacy of the approach.
Abstract: This paper addresses the problem of trajectory
tracking control of an underactuated autonomous underwater vehicle
(AUV) in the horizontal plane. The underwater vehicle under
consideration is not actuated in the sway direction, and the system
matrices are not assumed to be diagonal and linear, as often found in
the literature. In addition, the effect of constant bias of environmental
disturbances is considered. Using backstepping techniques and the
tracking error dynamics, the system states are stabilized by forcing
the tracking errors to an arbitrarily small neighborhood of zero. The
effectiveness of the proposed control method is demonstrated through
numerical simulations. Simulations are carried out for an
experimental vehicle for smooth, inertial, two dimensional (2D)
reference trajectories such as constant velocity trajectory (a circle
maneuver – constant yaw rate), and time varying velocity trajectory
(a sinusoidal path – sinusoidal yaw rate).
Abstract: In the last decade, energy based control theory has undergone a significant breakthrough in dealing with underactated mechanical systems with two successful and similar tools, controlled Lagrangians and controlled Hamiltanians (IDA-PBC). However, because of the complexity of these tools, successful case studies are lacking, in particular, MIMO cases. The seminal theoretical paper of controlled Lagrangians proposed by Bloch and his colleagues presented a benchmark example–a 4 d.o.f underactuated pendulum on a cart but a detailed and completed design is neglected. To compensate this ignorance, the note revisit their design idea by addressing explicit control functions for a similar device motivated by a vector thrust body hovering in the air. To the best of our knowledge, this system is the first MIMO, underactuated example that is stabilized by using energy based tools at the courtesy of the original design idea. Some observations are given based on computer simulation.
Abstract: State Dependent Riccati Equation (SDRE) approach is
a modification of the well studied LQR method. It has the capability of being applied to control nonlinear systems. In this paper the technique
has been applied to control the single inverted pendulum (SIP) which represents a rich class of nonlinear underactuated systems. SIP
modeling is based on Euler-Lagrange equations. A procedure is developed
for judicious selection of weighting parameters and constraint handling. The controller designed by SDRE technique here gives better results than existing controllers designed by energy based techniques.