Balance-bot

Research on inverted pendulum has gained momentum over the last decade on a number of robotic laboratories over the world; due to its unstable proprieties is a good example for control engineers to verify a control theory. To verify that the pendulum can balance we can make some simulations using a closed-loop controller method such as the linear quadratic regulator or the proportional–integral–derivative method. Also the idea of robotic teleoperation is gaining ground. Controlling a robot at a distance and doing that precisely. However, designing the tool to takes the best benefit of the human skills while keeping the error minimal is interesting, and due to the fact that the inverted pendulum is an unstable system it makes a compelling test case for exploring dynamic teleoperation. Therefore this thesis focuses on the construction of a two-wheel inverted pendulum robot, which sensor we can use to do that, how they must be integrated in the system and how we can use a human to control an inverted pendulum. The inverted pendulum robot developed employs technology like sensors, actuators and controllers. This Master thesis starts by presenting an introduction to inverted pendulums and some information about related areas such as control theory. It continues by describing related work in this area. Then we describe the mathematical model of a two-wheel inverted pendulum and a simulation made in Matlab. We also focus in the construction of this type of robot and its working theory. Because this is a mobile robot we address the theme of the teleoperation and finally this thesis finishes with a general conclusion and ideas of future work.

Efficient fuzzy control of a rotary inverted pendulum based on LQR mapping

This paper develops fuzzy methods for control of the rotary inverted pendulum, an underactuated mechanical system. Two control laws are presented, one for swing up and another for the stabilization. The pendulum is swung up from the vertical down stable position to the upward unstable position in a controlled trajectory. The rules for the swing up are heuristically written such that each swing results in greater energy build up. The stabilization is achieved by mapping a stabilizing LQR control law to two fuzzy inference engines, which reduces the computational load compared with using a single fuzzy inference engine. The robustness of the balancing control is tested by attaching a bottle of water at the tip of the pendulum.

A study on bullock carts. Part 1. Engineering analysis of the two-wheel bullock cart design

An engineering analysis of the design of two-wheel bullock carts has been carried out with the aid of a mathematical model. Non-dimensional expressions for the pull and the neck load have been developed. In the first instance, the cart is assumed to be cruising at constant velocity on a terrain with the effective coefficient of rolling friction varying over a wide range (0.001 to 0.5) and the gradient varying between +0.2 to −0.2. Subsequently, the effect of inertia force due to an acceleration parallel to the ground is studied. In the light of this analysis, two modifications to the design of the cart have been proposed and the relative merits of the current designs and the proposed designs are discussed.

Physical constraints, fundamental limits, and optimal locus of operating points for an inverted pendulum based actuated dynamic walker

The inverted pendulum is a popular model for describing bipedal dynamic walking. The operating point of the walker can be specified by the combination of initial mid-stance velocity (v(0)) and step angle (phi(m)) chosen for a given walk. In this paper, using basic mechanics, a framework of physical constraints that limit the choice of operating points is proposed. The constraint lines thus obtained delimit the allowable region of operation of the walker in the v(0)-phi(m) plane. A given average forward velocity v(x,) (avg) can be achieved by several combinations of v(0) and phi(m). Only one of these combinations results in the minimum mechanical power consumption and can be considered the optimum operating point for the given v(x, avg). This paper proposes a method for obtaining this optimal operating point based on tangency of the power and velocity contours. Putting together all such operating points for various v(x, avg,) a family of optimum operating points, called the optimal locus, is obtained. For the energy loss and internal energy models chosen, the optimal locus obtained has a largely constant step angle with increasing speed but tapers off at non-dimensional speeds close to unity.

Strong structural controllability and the multi-link inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

Strong structural controllability and the multilink inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

From inverted pendulum to N-link chain: inertial sensors-based assessment of movement kinematics and dynamics for functional evaluation and rehabilitation

Despite several clinical tests that have been developed to qualitatively describe complex motor tasks by functional testing, these methods often depend on clinicians' interpretation, experience and training, which make the assessment results inconsistent, without the precision required to objectively assess the effect of the rehabilitative intervention. A more detailed characterization is required to fully capture the various aspects of motor control and performance during complex movements of lower and upper limbs. The need for cost-effective and clinically applicable instrumented tests would enable quantitative assessment of performance on a subject-specific basis, overcoming the limitations due to the lack of objectiveness related to individual judgment, and possibly disclosing subtle alterations that are not clearly visible to the observer. Postural motion measurements at additional locations, such as lower and upper limbs and trunk, may be necessary in order to obtain information about the inter-segmental coordination during different functional tests involved in clinical practice. With these considerations in mind, this Thesis aims: i) to suggest a novel quantitative assessment tool for the kinematics and dynamics evaluation of a multi-link kinematic chain during several functional motor tasks (i.e. squat, sit-to-stand, postural sway), using one single-axis accelerometer per segment, ii) to present a novel quantitative technique for the upper limb joint kinematics estimation, considering a 3-link kinematic chain during the Fugl-Meyer Motor Assessment and using one inertial measurement unit per segment. The suggested methods could have several positive feedbacks from clinical practice. The use of objective biomechanical measurements, provided by inertial sensor-based technique, may help clinicians to: i) objectively track changes in motor ability, ii) provide timely feedback about the effectiveness of administered rehabilitation interventions, iii) enable intervention strategies to be modified or changed if found to be ineffective, and iv) speed up the experimental sessions when several subjects are asked to perform different functional tests.

Fuzzy Optimal Control for Double Inverted Pendulum

In this paper a fuzzy optimal control for stabilizing an upright position a double inverted pendulum (DIP) is developed and compared. Modeling is based on Euler-Lagrange equations. This results in a complicated nonlinear fast reaction, unstable multivariable system. Firstly, the mathematical models of double pendulum system are presented. The weight variable fuzzy input is gained by combining the fuzzy control theory with the optimal control theory. Simulation results show that the controller, which the upper pendulum is considered as main control variable, has high accuracy, quick convergence speed and higher precision.

Operator, organizational, direct support, and general support maintenance manual : compressor, rotary, air, diesel engine driven, 250 cfm, 100 psi, trailer mounted, two wheel (Davey model 14M250RPV) FSN 4310-256-9319, component of pneumatic tool and compressor outfit, FSN 3820-950-8584.

"June 1972."

Operator, organizational, direct support and general support maintenance manual : compressor, rotary, air, diesel engine driven, 250 CFM, 100 PSI, trailer mounted, two wheel (Davey model 14M250 RPV) FSN 4310-256-9319, component of pneumatic tool and compressor outfit, FSN 3820-950-8584.

Includes index.

Parametric resonances in a base-excited double pendulum

Two parametrically-induced phenomena are addressed in the context of a double pendulum subject to a vertical base excitation. First, the parametric resonances that cause the stable downward vertical equilibrium to bifurcate into large-amplitude periodic solutions are investigated extensively. Then the stabilization of the unstable upward equilibrium states through the parametric action of the high-frequency base motion is documented in the experiments and in the simulations. It is shown that there is a region in the plane of the excitation frequency and amplitude where all four unstable equilibrium states can be stabilized simultaneously in the double pendulum. The parametric resonances of the two modes of the base-excited double pendulum are studied both theoretically and experimentally. The transition curves (i.e., boundaries of the dynamic instability regions) are constructed asymptotically via the method of multiple scales including higher-order effects. The bifurcations characterizing the transitions from the trivial equilibrium to the periodic solutions are computed by either continuation methods and or by time integration and compared with the theoretical and experimental results.

An Optimal Fuzzy Logic Controller tuned with Artificial Immune System

In this paper, a method for the tuning the membership functions of a Mamdani type Fuzzy Logic Controller (FLC) using the Clonal Selection Algorithm(CSA) a model of the Artificial Immune System(AIS) paradigm is examined. FLC's are designed for two problems, firstly the linear cart centering problem and secondly the highly nonlinear inverted pendulum problem. The FLC tuned by AIS is compared with FLC tuned by GA. In order to check the robustness of the designed PLC's white noise was added to the system, further, the masses of the cart and the length and mass of the pendulum are changed. The PLC's were also tested in the presence of faulty rules. Finally, Kruskal Wallis test was performed to compare the performance of the GA and AIS. An insight into the algorithms are also given by studying the effect of the important parameters of GA and AIS.

Preliminary results from a real time control system using optical information

Successful results from training an adaptive controller to use optical information to balance an inverted pendulum are presented in comparison to the training requirements using traditional controller inputs. Results from research into the psychology of the sense of balance in humans are presented as the motivation for the investigation of this new type of controller. The simulated model of the inverted pendulum and the virtual reality environments used to provide the optical input are described The successful introduction of optical information is found to require the preservation of at least two of the traditional input types and entail increased training time for the adaptive controller and reduced performance (measured as the time the pendulum remains upright).