NVERTED pendulum has been the subject of numerous studies in automatic control since the forties. In this paper, the development of the theme inspired by the well known Segway robot is described. This kind of robots has induced a lot of interest recently . This is due to the fact that it provides rich opportunities for application of control design, signal processing, distributed control systems and consideration of realtime constraint for implementation issues. A scaled down prototype of a Digital Signal Processor controlled two–wheeled vehicle called JOE based on the invertedpendulum with weights attached to the system to simulate a human driver was considered in . A linear state space controller utilizing sensory information from a gyroscope and motor encoders is used to stabilize the system. With small carts built utilizing this technology allows humans to travel short distances in a small area or factories instead of using car or buggies which is more polluting .
tion mode transformation of a mobilerobot with wheel-arms. The proposed method aims at transformation from a four-wheeled mode for high speed mobility to an invertedpendulum mode, which has advantages of high viewing position and small turning radius. Since the initial state of the system is far away from the target equilibrium point of the wheeled invertedpendulum system, we use a nonlinear controller based on sliding mode control. In contrast that the previous transformation methods cannot control the robot velocity until the robot body is lifted up, the proposed method can take into account the robot velocity from the beginning of the transformation, which enables to complete the transformation in a smaller space. To analyze the asymptotic stability of the control system on the sliding surface, we derive an invariant set in which the system state converges to the origin without going out. Furthermore, the effectiveness of the proposed method is demonstrated in both simulations and realrobot experiments.
Problems like pollution, congestion, parking availability, which are caused by conventional vehicles, have made life difficult these days. To overcome the situation, Two Wheeled InvertedPendulum (TWIP) mobile robots (Figure 1) have been introduced [1-7] to overcome these problems. Due to its much smaller in size compared with conventional four wheeled vehicles, TWIPs can occupy less parking space than other vehicles, hence reducing congestion and solving availability of parking space issue. Also TWIP uses DC motors for operation hence eliminating carbon pollution, hence safer environment. However, they are categorized as under actuated mobile robots which makes it difficult to control. Many researchers in the past two decades have been working in developing
Wheeled inverse pendulum model have evoked a lot of interest recently at the research, industrial and hobby level and at least one commercial product (Segway) is available ,,,,. The robot are characterized by two driving wheels connected to an intermediate body carrying actuation, sensor, control and communication subsystem. Two independent driving wheels in same axis, and the gyro type sensor to know the inclination angular velocity of the body and rotary encoders to know wheels rotation. Due to its configuration with two coaxial wheels, each wheel is coupled to a geared dc motor. The vehicle is able to do stationary U-turns while keeping balance it pole. Such vehicles are of interest because they have a small foot-print and can turn on dime. The kinematics model of the system has been proved to be uncontrollable and therefore balancing of the pendulum is only achieved by considering dynamic effects. Such robots are characterized by the ability to balance on two
It can be concluded that, after implementation of this project, the stability of Auto-Balancing Two Wheeled InvertedPendulumRobot can be achieved with improved response time. We have considered the system of robot as a classical control system and proposed the algorithmic approach to stabilize the system. Through this paper we are implementing Kalman filter algorithm and PID controller digital control algorithm on a micro-controller, which gives cost-effective option for solving InvertedPendulumcontrol system problem with reduced oscillations and improved stability. Our emphasis is on achieving zero degree vertical equilibrium of robot body when it is in rest or when it is in a straight line motion, in shortest possible time. Further study can be done on achieving the stability of robot while rotating about its vertical axis.
Doitsidis, Murphy, Long, et. al. [13–15] studied the use of a distributed framework for autonomous multi-robotcontrol. The distributed field robot architecture, also known as DFRA or distributed-SFX, builds a layer on top of the existing software architecture used for individual robots. The layer itself is designed around Sun Microsystem’s Jini, which is a network architecture for building modular service-based distributed systems. The entire architecture is based on Java, and uses Jini as a middle-ware layer. Work done in [13, 14] describes an integration of distributed-SFX with the MATLAB environment for rapid prototyping of behavioral and control modules. Multi-sensor fuzzy logic controllers, implemented in MATLAB, would evaluate the sensor data and determine the necessary inputs to the robot drive system for navigation. Experimental results show the applicability of the system for controlling two wheeled robots in an outdoor environment.
In this paper, we present the real-time implementa- tion of a LQR-based feedback control for the stabiliza- tion about the upright position of the double invertedpendulum mounted on a cart. The apparatus of the DIP system, which was provided by Quanser Consulting Inc. (119 Spy Court, Markham, Ontariio, L3R 5H6, Canada), is depicted in Fig. 1. The DIP system consists of two aluminum rods; one seven inches long and the other 12 inches long. The aluminums are mounted on the linear servo base unit (IP02) consisting of a cart driven by a DC motor and two encoders. One encoder is used to measure the cart’s position while the other encoder is used to sense the short link angle. The longer link angle is measured by an encoder mounted on the pendulum itself. Based on these measurements of the cart position and the twopendulum angles, a voltage is computed using the LQR control theory to move the cart back and forth to balance the two pendulums in the upright, vertical position.
The TWIP mobilerobot is driven by two DC motors, which is driven by a 24v motor driver. The designed controller is implemented on a host PC using MATLAB and Simulink, with Fio Std board microcontroller as the data accusation device  . In order to obtain the horizontal displacement of the robot for feedback control, two optical encoder with a resolution of 500 pulses/rev is attached to the shaft of each DC motor . The quadrature encoder signals generated by the optical encoders attached to the motors are connected to Fio Std board which are fed to the host PC for converting pulse to direction in meters, the derivative of the directions is the measured velocity of the mobilerobot. . PWM signals are generated according to the designed control law and also supplied to PWM driver via the Fio microcontroller that drive each dc motor. A current sensor  is used to measure the current consumed by the motors.
A new kind of quadruped-imitating walking robot is designed, which is composed of a body bracket, leg brackets and walking legs. The walking leg of the robot is comprised of a first swiveling arm, a second swiveling arm and two striding leg rods. Each rod of the walking leg is connected by a rotary joint, and is directly controlled by the steering gear. The walking motion is realized by two striding leg rods alternately contacting the ground. Three assumptions are put forward according to the kinematic characteristics of the quadruped-imitating walking robot, and then the centroid equation of the robot is established. On this basis, this paper simplifies the striding process of the quadruped-imitating walking robot into an invertedpendulum model with a constant fulcrum and variable pendulum length. According to the invertedpendulum model, the stability of the robot is not only related to its centroid position, but also related to its centroid velocity. Takes two typical movement cases for example, such as walking on flat ground and climbing the vertical obstacle, the centroid position, velocity curves of the invertedpendulum model are obtained by MATLAB simulations. The results show that the quadruped-imitating walking robot is stable when walking on flat ground. In the process of climbing the vertical obstacle, the robot also can maintain certain stability through real-timecontrol adjusted by the steering gears.
Fig. 11 and Fig. 12 show two sets of results comparing the application of fuzzy control and conventional control (PID controller) techniques to the invertedpendulum problem simulation. For the same system parameters here, the PID controller proportional gain, Kp, derivative gain, Kd and integral gain, Ki are found to be 9, 14, and 0.06 respectively. The first two graph show that the fuzzy logic controller gives a smaller overshoot and shorter settling time. In the second set, the mass of the cart is changed without modifying the controllers. Fig. 14 shows that the conventional controller totally failed to balance the pendulum as it was designed for the nominal value of cart mass. On the other hand, the fuzzy logic controller exhibited small performance degradation due to this parameter change as shown in Fig. 13. This proves that fuzzy logic is not based on the mathematical model of the invertedpendulum and more robust to mass variations.
Balancing an invertedpendulummobilerobot using LQG and LQR has been proposed by Hauser and Saccon (2005), and their performances were compared. Modelling and a predictive controller based on the nonlinear model of the system have been presented in Chalupa (2008). Similarly, Prasad (2014), Singh and Yadav (2012) and Gupta (2014) compared the stabilization and swing up control performances of LQR and PID controllers for an invertedpendulum. The stabilization control of an invertedpendulum using Pole Placement and LQR has been presented in Kumar et al (2012), a comparison of the control algorithms has also been presented.
tilt angle and orientation angle as 0, π/6 rad and 0 respectively. Fig. 3 through 7 shows the simulation results. From fig. 3 it can be seen that the two controllers balanced the robot, both controllers settled the tilt angle in about 8.5 seconds, with an overshoot of 12.8%. Fig. 4 shows the velocity tracking response for the two controllers, both controllers settled in about 10.5 seconds, with an overshoot of about 25.9%. Both controllers’ tracks the reference orientation as shown in fig. 5, both controllers settled the orientation angle in about 1.5 seconds, with an overshoot of 0%. Figures 6 and 7 shows the control inputs for wheel 1 and wheel 2 required for the two controllers, from the result it can be seen that the proposed controller require slightly higher starting torque compare to the conventional controller under this condition.
ar feed ot system. The sche- atics a LQG is in essence similar to that depicted in nce, the observer gain matrix in this figure can now be defined as the Kalman gain. nation of a Kalman filter with a regular LQR controller. The se- paration principle guarantees that these can be designed and computed independently . LQG controllers can be used both in linear time-invariant systems as well as in linear time-variant systems. The application to linear time-variant systems enables the design of line - back controllers for non-linear uncertain systems, which is the case for the pendulum-rob
performance level is limited due to approximations, while most of nonlinear controllers performed better but are complex to design and difficult to implement. Using T-S fuzzy model-based control, it is possible to combine the advantages of both linear and nonlinear controllers (i.e. simplicity and better performance). A T-S fuzzy model can effectively represent the system dynamics of a nonlinear system such as TWIP mobilerobot using linear rule consequence, which makes it easier to apply linear control techniques in the analysis and control synthesis for the system. Numerous works on the stability analysis and control synthesis of T-S fuzzy model-based control systems have been reported in literature [10-12].
I N 1990 the International Federation of Automatic Control (IFAC) Theory Committee published a set of benchmark problems that can be used to compare the benefits of new and existing control methods. One of these problems involves the stabilization of an invertedpendulum . Despite its simple structure, the invertedpendulum is among the most difficult systems to control. This difficulty arises because the equations of motion governing the system are inherently nonlinear and because the upright position is an unstable equilibrium. Furthermore, the system is under-actuated as it has two degrees of freedom, one for the cart’s horizontal motion and one for the pendulum’s angular motion, but only the cart’s position is actuated, while the pendulum’s angular motion is indirectly controlled. Many of the previously proposed nonlinear control techniques for the stabilization of an invertedpendulum are too complex and impractical for real-time implementation . In this paper, we present the successful real-time implementation of a nonlinear controller for the stabilization of a single invertedpendulum (SIP) on a cart. The controller is based on the power series approximation to the solution to the Hamilton
The driver circuit used for brushed DC motor is of H bridge topology. The IC used for this purpose is L6203. The IC is a full bridge driver for motor control applications realized in Multipower -BCD technology which combines isolated DMOS power transistors with CMOS and Bipolar circuits on the same chip. Each channel (half-bridge) of the device is controlled by a separate logic input, while a common enable controls both channels. Two 15 nF capacitors connected between motor output and CBOOT1 and CBOOT2 pins of IC are called as boostrap capacitors these ensures efficient driving of the upper and lower power DMOS transistor. It also includes anti-parallel protection diodes connected across transistors. It works on 24V. Figure3 shows schematic of motor driver circuit designed in eagle.
The invertedpendulum is an intriguing subject from the control point of view due to their intrinsic nonlinearity. The problem is to balance a pole on a mobile platform that can move in only two directions, to the left or to the right. This control problem is fundamentally the same as those involved in rocket or missile propulsion.
In the past decade one may observe augmented attention on under- actuated systems in research field. The under -actuated systems have fewer actuators than the degrees of freedom to be controlled. These systems have applications in free-flying Space robots, Underwater robots, Surface vessels, Manipulators with structural flexibility, etc. The invertedpendulum has been considered as benchmark example in nonlinear control studies as a under-actuated system.Dynamics of the invertedpendulum are quintessential for the balance in wheeled Mobile robots, Robo walk and Robo thrusters [2-6]. With single input and two outputs, invertedpendulum has remained an exacting control problem owing to its characteristics like instability,non- linearity. It has two equilibrium points; one being stable while other is unstable .Various control strategies can be found in literature to stabilize the pendulum around unstable equilibrium point Researchers have analysed PID based control , neural network control ,fuzzy control , optimisation tools like linear quadratic regulator [10, 13].Sliding mode control has emerged as promising method for control of invertedpendulum. [15-17]
Figure 1 shows a diagram of the Single InvertedPendulum (SIP) mounted on an IP02 linear cart. The positive sense of rotation is defined to be counterclockwise, when facing the cart. The perfectly vertical upward pointing position of the invertedpendulum corresponds to the zero angle, modulus 2π, (i.e. α = 0 rad [2π]). The positive direction of the cart’s displacement is to the right when facing the cart, as indicated by the Cartesian frame of coordinates presented in Figure 1.
‘Requirements engineering process’ has the most dominant impact on the capabilities of the resulting product, because an incomplete or poor RE affects the quality of the final software, and errors are more expensive to fix later in project lifecycles[12; 13]. This is why many approaches have been developed and many efforts have been made to enhance this process (Barry Boehm investigation). Requirements engineering process is composed by seven main activities: project creation, elicitation, interpretation and structuring, negotiation . Verification & validation, change management .and tracing . After RE phase, when developers move next to software construction phase (domain model, class diagram and so on), they feel the gap between this two phases; this gap is presented as a non-possibility to map from “scenario-based RE ” . models to object models as shown in figure 1.