Abstract: Two-wheel inverted pendulum robot (TWIPR) is designed with two-hub DC motors for human riding and motion control evaluation. In order to measure the tilt angle and angular velocity of the inverted pendulum robot, accelerometer and gyroscope sensors are chosen. The mobile robot’s moving position and velocity were estimated based on DC motor built in hall sensors. The control kernel of this electric mobile robot is designed with embedded Arduino Nano microprocessor. A handle bar was designed to work as steering mechanism. The intelligent model-free fuzzy sliding mode control (FSMC) was employed as the main control algorithm for this mobile robot motion monitoring with different control purpose adjustment. The intelligent controllers were designed for balance control, and moving speed control purposes of this robot under different operation conditions and the control performance were evaluated based on experimental results.
Abstract: The wheelchair is the major means of transport for
physically disabled people. However, it cannot overcome architectural
barriers such as curbs and stairs. In this paper, the authors proposed
a method to avoid falling down of a wheeled inverted pendulum type
robotic wheelchair for climbing stairs. The problem of this system
is that the feedback gain of the wheels cannot be set high due to
modeling errors and gear backlash, which results in the movement
of wheels. Therefore, the wheels slide down the stairs or collide with
the side of the stairs, and finally the wheelchair falls down. To avoid
falling down, the authors proposed a slider control strategy based on
skyhook model in order to decrease the movement of wheels, and a
rotary link control strategy based on the staircase dimensions in order
to avoid collision or slide down. The effectiveness of the proposed
fall avoidance control strategy was validated by ODE simulations and
the prototype wheelchair.
Abstract: A two wheel inverted pendulum (TWIP) vehicle is built with two hub DC motors for motion control evaluation. Arduino Nano micro-processor is chosen as the control kernel for this electric test plant. Accelerometer and gyroscope sensors are built in to measure the tilt angle and angular velocity of the inverted pendulum vehicle. Since the TWIP has significantly hub motor dead zone and nonlinear system dynamics characteristics, the vehicle system is difficult to control by traditional model based controller. The intelligent model-free fuzzy sliding mode controller (FSMC) was employed as the main control algorithm. Then, intelligent controllers are designed for TWIP balance control, and two wheels synchronization control purposes.
Abstract: The inverted pendulum system is a classic control
problem that is used in universities around the world. It is a suitable
process to test prototype controllers due to its high non-linearities and
lack of stability. The inverted pendulum represents a challenging
control problem, which continually moves toward an uncontrolled
state. This paper presents the possibility of balancing an inverted
pendulum system using sliding mode control (SMC). The goal is to
determine which control strategy delivers better performance with
respect to pendulum’s angle and cart's position. Therefore,
proportional-integral-derivative (PID) is used for comparison. Results
have proven SMC control produced better response compared to PID
control in both normal and noisy systems.
Abstract: Optimizing the parameters in the controller plays a
vital role in the control theory and its applications. Optimizing the
PID parameters is finding out the best value from the feasible
solutions. Finding the optimal value is an optimization problem.
Inverted Pendulum is a very good platform for control engineers to
verify and apply different logics in the field of control theory. It is
necessary to find an optimization technique for the controller to tune
the values automatically in order to minimize the error within the
given bounds. In this paper, the algorithmic concepts of Harmony
search (HS) and Genetic Algorithm (GA) have been analyzed for the
given range of values. The experimental results show that HS
performs well than GA.
Abstract: Recent fifteen years witnessed fast improvements in the field of humanoid robotics. The human-like robot structure is
more suitable to human environment with its supreme obstacle avoidance properties when compared with wheeled service robots.
However, the walking control for bipedal robots is a challenging task
due to their complex dynamics. Stable reference generation plays a very important role in control.
Linear Inverted Pendulum Model (LIPM) and the Zero Moment Point (ZMP) criterion are applied in a number of studies for stable
walking reference generation of biped walking robots. This paper follows this main approach too. We propose a natural and continuous ZMP reference trajectory for a stable and human-like walk. The ZMP reference trajectories move forward under the sole of the support foot when the robot body is supported by a single leg. Robot center of mass trajectory is obtained
from predefined ZMP reference trajectories by a Fourier series
approximation method. The Gibbs phenomenon problem common with Fourier approximations of discontinuous functions is avoided by employing continuous ZMP references. Also, these ZMP reference
trajectories possess pre-assigned single and double support phases,
which are very useful in experimental tuning work.
The ZMP based reference generation strategy is tested via threedimensional
full-dynamics simulations of a 12-degrees-of-freedom
biped robot model. Simulation results indicate that the proposed reference trajectory generation technique is successful.
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: Markov games can be effectively used to design
controllers for nonlinear systems. The paper presents two novel
controller design algorithms by incorporating ideas from gametheory
literature that address safety and consistency issues of the
'learned' control strategy. A more widely used approach for
controller design is the H∞ optimal control, which suffers from high
computational demand and at times, may be infeasible. We generate
an optimal control policy for the agent (controller) via a simple
Linear Program enabling the controller to learn about the unknown
environment. The controller is facing an unknown environment and
in our formulation this environment corresponds to the behavior rules
of the noise modeled as the opponent. Proposed approaches aim to
achieve 'safe-consistent' and 'safe-universally consistent' controller
behavior by hybridizing 'min-max', 'fictitious play' and 'cautious
fictitious play' approaches drawn from game theory. We empirically
evaluate the approaches on a simulated Inverted Pendulum swing-up
task and compare its performance against standard Q learning.
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: This paper proposes a balance control scheme for a biped robot to trace an arbitrary path using image information. While moving, it estimates the zero moment point(ZMP) of the biped robot in the next step using a Kalman filter and renders an appropriate balanced pose of the robot. The ZMP can be calculated from the robot's pose, which is measured from the reference object image acquired by a CCD camera on the robot's head. For simplifying the kinematical model, the coordinates systems of individual joints of each leg are aligned and the robot motion is approximated as an inverted pendulum so that a simple linear dynamics, 3D-LIPM(3D-Linear Inverted Pendulum Mode) can be applied. The efficiency of the proposed algorithm has been proven by the experiments performed on unknown trajectory.
Abstract: In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown.
Abstract: The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].
Abstract: The influence of physical (external added weight) and
neurophysiological (fatigue) factors on static and dynamic balance in
sport related activities was typified statically by the Romberg test
(one foot flat, eyes open) and dynamically by jumping and hopping
in both horizontal and vertical directions. Twenty healthy males were
participated in this study. In Static condition, added weight increased
body-s inertia and therefore decreased body sway in AP direction
though not significantly. Dynamically, added weight significantly
increased body sway in both ML and AP directions, indicating
instability, and the use of the counter rotating segments mechanism to
maintain balance was demonstrated. Fatigue on the other hand
significantly increased body sway during static balance as a
neurophysiological adaptation primarily to the inverted pendulum
mechanism. Dynamically, fatigue significantly increased body sway
in both ML and AP directions again indicating instability but with a
greater use of counter rotating segments mechanism. Differential
adaptations for each of the two balance mechanisms (inverted
pendulum and counter rotating segments) were found between one
foot flat and two feet flat dynamic conditions, as participants relied
more heavily on the first in the one foot flat conditions and relied
more on the second in the two feet flat conditions.
Abstract: This paper presents the application of discrete-time
variable structure control with sliding mode based on the 'reaching
law' method for robust control of a 'simple inverted pendulum on
moving cart' - a standard nonlinear benchmark system. The
controllers designed using the above techniques are completely
insensitive to parametric uncertainty and external disturbance. The
controller design is carried out using pole placement technique to find
state feedback gain matrix , which decides the dynamic behavior
of the system during sliding mode. This is followed by feedback gain
realization using the control law which is synthesized from 'Gao-s
reaching law'. The model of a single inverted pendulum and the
discrete variable structure control controller are developed, simulated
in MATLAB-SIMULINK and results are presented. The response of
this simulation is compared with that of the discrete linear quadratic
regulator (DLQR) and the advantages of sliding mode controller over
DLQR are also presented
Abstract: In this paper, the performance of two adaptive
observers applied to interconnected systems is studied. The
nonlinearity of systems can be written in a fractional form. The first
adaptive observer is an adaptive sliding mode observer for a Lipchitz
nonlinear system and the second one is an adaptive sliding mode
observer having a filtered error as a sliding surface. After comparing
their performances throughout the inverted pendulum mounted on a
car system, it was shown that the second one is more robust to
estimate the state.
Abstract: Markov games are a generalization of Markov
decision process to a multi-agent setting. Two-player zero-sum
Markov game framework offers an effective platform for designing
robust controllers. This paper presents two novel controller design
algorithms that use ideas from game-theory literature to produce
reliable controllers that are able to maintain performance in presence
of noise and parameter variations. A more widely used approach for
controller design is the H∞ optimal control, which suffers from high
computational demand and at times, may be infeasible. Our approach
generates an optimal control policy for the agent (controller) via a
simple Linear Program enabling the controller to learn about the
unknown environment. The controller is facing an unknown
environment, and in our formulation this environment corresponds to
the behavior rules of the noise modeled as the opponent. Proposed
controller architectures attempt to improve controller reliability by a
gradual mixing of algorithmic approaches drawn from the game
theory literature and the Minimax-Q Markov game solution
approach, in a reinforcement-learning framework. We test the
proposed algorithms on a simulated Inverted Pendulum Swing-up
task and compare its performance against standard Q learning.
Abstract: The two cart inverted pendulum system is a good
bench mark for testing the performance of system dynamics and
control engineering principles. Devasia introduced this system to
study the asymptotic tracking problem for nonlinear systems. In this
paper the problem of asymptotic tracking of the two-cart with an
inverted-pendulum system to a sinusoidal reference inputs via
introducing a novel method for solving finite-horizon nonlinear
optimal control problems is presented. In this method, an iterative
method applied to state dependent Riccati equation (SDRE) to obtain
a reliable algorithm. The superiority of this technique has been shown
by simulation and comparison with the nonlinear approach.
Abstract: This paper presents three new methodologies for the
basic operations, which aim at finding new ways of computing union
(maximum) and intersection (minimum) membership values by
taking into effect the entire membership values in a fuzzy set. The
new methodologies are conceptually simple and easy from the
application point of view and are illustrated with a variety of
problems such as Cartesian product of two fuzzy sets, max –min
composition of two fuzzy sets in different product spaces and an
application of an inverted pendulum to determine the impact of the
new methodologies. The results clearly indicate a difference based on
the nature of the fuzzy sets under consideration and hence will be
highly useful in quite a few applications where different values have
significant impact on the behavior of the system.
Abstract: This paper includes a review of three physics simulation packages that can be used to provide researchers with a virtual ground for modeling, implementing and simulating complex models, as well as testing their control methods with less cost and time of development. The inverted pendulum model was used as a test bed for comparing ODE, DANCE and Webots, while Linear State Feedback was used to control its behavior. The packages were compared with respect to model creation, solving systems of differential equation, data storage, setting system variables, control the experiment and ease of use. The purpose of this paper is to give an overview about our experience with these environments and to demonstrate some of the benefits and drawbacks involved in practice for each package.
Abstract: A new nonlinear PID controller and its stability
analysis are presented in this paper. A nonlinear function is deduced
from the similarities between the control effort and the electric-field
effect of a capacitor. The conventional linear PID controller can be
modified into a nonlinear one by this function. To analyze the stability
of the nonlinear PID controlled system, an idea of energy equivalence
is adapted to avoid the conservativeness which is usually arisen from
some traditional theorems and Criterions. The energy equivalence is
naturally related with the conceptions of Passivity and T-Passivity. As
a result, an engineering guideline for the parameter design of the
nonlinear PID controller is obtained. An inverted pendulum system is
tested to verify the nonlinear PID control scheme.