Control of mobile robot formations using A-star algorithm and artificial potential fields

Formations or groups of robots become essential in cases where a single robot is insufficient to satisfy a given task. With an increasingly automated world, studies on various topics related to robotics have been carried out in both the industrial and academic arenas. In this paper, the control of the formation of differential mobile robots based on the leader-follower approach is presented. The leader's movement is based on the least cost path obtained by the A-star algorithm, thus ensuring a safe and shortest possible route for the leader. Follower robots track the leader's position in real time. Based on this information and the desired distance and angle values, the leader robot is followed. To ensure that the followers do not collide with each other and with the obstacles in the environment, a controller based on Artificial Potential Fields is designed. Stability analysis using Lyapunov theory is performed on the linearized model of the system. To verify the implemented technique, a simulator was designed using the MATLAB programming language. Seven experiments are conducted under different conditions to show the performance of the approach. The distance and orientation errors are less than 0.1 meters and 0.1 radians, respectively. Overall, mobile robots are able to reach the goal position, maintaining the desired formation, in finite time.

A position control-based approach to haptic rendering of stiff objects using piece-wise linear model

In traditional force rendering approaches, it is quite popular to model a virtual stiff wall as a spring-damper system to compute the interaction force, which can easily lead to unstable behavior. In this paper, we present an approach to ensure no penetration into the wall by position control. The approach approximates the nonlinear model of a 6-DOF parallel-structure haptic device by a piece-wise linear model to improve the performance compared with a controller designed from a one-point linearized model in haptic rendering. A simulation-based performance comparison study shows that the new controller can render higher stiffness than the previous solution.

Tuning for robust and optimal dynamic positioning control in BlueROV2

A tuning approach for the robust and optimal dynamic positioning control of BlueROV2 subjected to currents with varying speeds and headings is presented. A 2D planar dynamic model of BlueROV2 is developed in Matlab/Simulink and used for the study. The surge, sway and yaw motions are controlled by individual PID controllers. An extensive sensitivity study is carried out on a total of nine cases with different current speeds, current headings, and measurement noise levels. The results show that tuning a model solely using step responses from a linearized model might not produce optimal results. Further it is important to verify the system responses in time domain after tuning. Finally, it is observed that re-tuning the controllers for each simulation case may lead to better performance. However, it is also shown that the base case controller gains are sufficiently robust and lead to good performances for the other simulation cases.

Model Based Indirect Conicity Estimation Technique for Solid Axle Railway Wheelset

Conicity is an important characteristic that helps the railway vehicle to steer itself down the track. However during the operation, the conicity tends to change inconsistently due to frictional contact at the wheel-rail interface. Safety, reliability and ride comfort which are utmost importance for journey are adversely affected due to the changes in conicity level beyond certain limit. Several techniques have been employed for monitoring the health of the railway wheelset however still a significant potential exists to investigate the wheelset conicity. This paper presents a model based technique to monitor the wheelset condition which contributes to the wheel flats due to decrease in conicity level and the problem of false flanges due to increased level of conicity. In this paper an unconstrained solid axle railway wheelset is considered for study. The dynamic behavior of the wheelset is analyzed at different conicity levels to understand the effect of the conicity on the wheelset. In order to demonstrate the potential of this research work a simulation model is developed in Matlab/ Simulink to mimic the behavior of an actual wheelset. Simplified linearized model of the wheelset is used to estimate the dynamics of the wheelset. From the simulation results it is evident that the frequency of vibration is changing with the changes in conicity level. In this way using the proposed method the conicity level is indirectly identified. The results produced by simulation model are satisfactory.

On Determining the Optimal Lifting Law of the Walking Propulsion Device Foot of an Underwater Robot from the Bottom

The problem of lifting the foot of the walking propulsion device of an underwater mobile robot is considered, taking into account the additional “compression” force acting on it. A mathematical model has been developed for the detachment of a propulsion foot from the ground, based on Henry's laws establishing the concentration of dissolved air in a liquid, the law of gas expansion at a constant temperature, Darcy's law on fluid filtration and the theorem on the motion of the center of mass of a solid body. The linearized model allows to obtain and analytical solutions. Based on the solution of the variational problem, optimal modes of lifting the foot of the walking propulsion of an underwater mobile robot are established.

A Two Wheel Self-Balancing Vehicle

This paper deals with the development of the equation of motion and practical implementation of low cost two-wheel self-balancing model of a Segway transporter. The experimental model of cart was designed and made under this study. Nonlinear equations of motion of real model and linearized model were derived. To develop the mathematical model, Matlab/Simulink was applied. The mechanical part was implemented into Simulink, and a DC motor was considered as a linear system. The real model was tested for its balance by implementation of a control algorithm consisting of a complementary filter and PID algorithm on an Arduino development board with peripheral devices. The fully functional self-balancing model was used as a demonstration in the teaching process of the Mechatronics courses.

Robust Tracker of Hybrid Microgrids by the Invariant-Ellipsoid Set

This paper introduces a new ellipsoidal-based tracker design to control a grid-connected hybrid direct current/alternating current (DC/AC) microgrid (MG). The proposed controller is robust against both parameters and load variations. The studied hybrid MG is modelled as a nonlinear dynamical system. A linearized model around an operating point is developed. The parameter changes are modelled as norm-bounded uncertainties. We apply the new extended version of the attractive (or invariant) ellipsoid for this tracking problem. Convex optimization is used to obtain the region’s minimal size where the tracking error between the state trajectories and the reference states converges. The sufficient conditions for stability are derived and solved based on linear matrix inequalities (LMIs). The proposed controller’s validity is shown via simulating the hybrid MG with various operational scenarios. In each scenario, the performance of the controller is compared with a recently proposed sliding mode controller. The comparison clearly illustrates the superiority of the developed controller in terms of transient and steady-state responses.

The Four Equation New Keynesian Model

This paper develops a New Keynesian model featuring financial intermediation, short- and long-term bonds, credit shocks, and scope for unconventional monetary policy. The log-linearized model reduces to four equations – Phillips and IS curves as well as policy rules for the short-term interest rate and the central bank's long-bond portfolio (QE). Credit shocks and QE appear in both the IS and Phillips curves. In equilibrium, optimal monetary policy entails adjusting the short-term interest rate to offset natural rate shocks, but using QE to offset credit market disruptions. Use of QE significantly mitigates the costs of a binding zero lower bound.