IntroductionRovers are robotic vehicles that are widely used for operations within remote and sometime dangerousenvironments e.g. bomb disposal, space exploration. In order for rovers to perform these duties theymust be able to manoeuvre accurately, which depends on their drive control systems. This assignmentinvolves the development of a simulation of a heading control system for a wheeled rover. Firstly,background information is provided, followed by the problem specification for the assignmentsimulation.BackgroundWheeled rovers, as the name suggests, are robotic vehicles that have propulsion systems based on themotion of motor driven wheels. Various different configurations of wheels have been employed in thedesign of rovers e.g. 6 wheel rocker-bogie used in design of the Curiosity Rover (see Figure 1).Figure 1: Curiosity RoverThis type of rover has both drive motors (for moving the wheels and ultimately the vehicle) andsteering motors (for changing the direction of the vehicle). This type of system is complex andconsiderably difficult to control effectively.Other types of rovers depend on the differential motion of wheels on either side of the vehicle. Anexample of this, which will be the focus of this assignment, is the 4 wheel rover shown in Figure 2.Figure 2: 4 Wheel RoverThe motion of this vehicle is determined by the relative motions of the motor driven wheels. Theforward propulsion of the rover is produced by the sum of the force produced by the wheels (see Figure3(a)). Whereas the turning motion of this type of rover is determined by the difference in forcesproduced by each set of wheels on either side of the vehicle e.g. if the two wheels on the right handside of the vehicle move slower than those on the left hand side then the rover will turn to the right(see Figure 3(b)).(a) Forward Motion (b) Turning MotionFigure 3: Rover Motions and Wheel ForcesThe turning motion described in Figure 3(b) is the focus of this assignment as outlined in the ProblemSpecification below.ROVERRHWHEELFORCELHWHEELFORCERESULTINGVEHICLEMOTIONROVERRHWHEELFORCELHWHEELFORCERESULTINGVEHICLEMOTIONProblem SpecificationThe motion of the rover is regulated by automatic control systems that determine the necessary speedand direction of the vehicle. In order to achieve this, the rover must be equipped with the necessarysystems to ensure its automatic guidance within it operating environment. The general principle ofcompletely automated guidance systems is to feed information from the heading and speed sensors tothe rover’s control system.In this study we will consider the development of a simulation that represents the heading controlsystem only. This system changes the voltage applied to the wheel motors to produce the requiredturning motion and thus change the heading of the rover.The geometry of this turning manoeuvre is shown in Figure 4.Figure 4: Geometry of turning manoeuvreThe turning control system produces the required wheel speeds to generate a coordinated turningmanoeuvre that changes the rover’s heading or yaw angle. It achieves this by comparing the actualyaw angle, ψ (radians), with the reference heading, ψref (radians). A diagram of the total system isshown in Figure 5.Figure 5: Rover Turning Control SystemFrom Figure 5 it can be seen that the Turning Control System uses the error difference between thereference yaw angle, ψref, and the rover’s actual yaw angle, ψ. In this case the value for ref (thereference heading) is taken to be 40° which passes through the Signal Conditioning systemVTv (swayvelocity)r(yaw rate)Ψref(referenceyaw angle)ψ (yawangle)FFLFBLFFRFBRTurningcontrolRover & wheelmotors+_ψref V HeadingCompassSignalConditioning(represented by a simple gain KC). The yaw angle, ψ, is measured using the Heading Compass whichis represented by a simple gain KH. The control system is effectively a PI controller of the followingform: sKV GIc 1 (1)Here is a function that is related to the difference between reference and actual heading angles.The resulting commanded motor voltage difference V (volts) is then used to control the wheel motorsto generate an appropriate heading for the rover to follow (). It achieves this by means of aproportional gain GC and an integral term with gain KI. These gains determine the performance of thecontrol system. This is an overview of the entire system.A key part of the overall Rover Turning Control System is the rover and its interaction with the wheelmotors. In Figure 5 this system is regarded as the conversion process between the commanded voltagedifference, V, and the actual heading of the rover, . This process is more involved than thissimplified system diagram would lead you to believe.The voltage difference from the control system is combined with the drive voltage, VD (volts), toproduce the corresponding input voltage for each wheel motor. The forces generated by the wheelsare then used to influence the turning dynamics of the rover. A detailed description of this system andhow it interacts with the rover can be seen in Figure 6.Figure 6: Rover and Wheel MotorsIt is assumed that the 2 wheel motors on each side have the same voltage applied and produce the sameforce. Therefore, the total combined force on the left side is represented by FL (N) and the totalcombined force on the right side is represented by FR (N). The difference in these forces generates theturning motion of the rover. These cause the sway velocity, v (m/s), yaw rate, r (rad/s) and yaw angle,ψ, to change (note that r ).The motors in this case are d.c. motors and each can be represented by the following relationships:Ri Ke m Vin dtdi L (2)b K idtdJ s tmm (3)Here i is the motor current (A), m is the speed of rotation of the motor (rad/s), is the difference inspeed between the motor and the wheel (rad/s), Jm is the moment of inertia for the motor armature(kgm2), L is the inductance (H), R is the resistance (), bs is the damping coefficient, Kt is the torqueLeftMotorsRoverswayand yaw+_ vVFLrRightMotors++FRVDconstant and Ke is the back emf constant. The inputs to the motors are Vin = VD V depending on thewhich side is being considered.The wheel can be treated as load on the motor’s shaft and therefore have its own dynamics. This canbe represented by the following equation. 0sww bdtdJ (4)Here w is the speed of rotation of the wheel (rad/s) and Jw is the moment of inertia for the wheel(kgm2).In this case VD = 2V. The current from each motor can be used to generate the total wheel forces onthe left and right sides i.e.LwtLiRKF2 (5)RwtRiRKF2 (6)Here Rw (m) is the radius of the wheel. These forces influence the sway and yaw dynamics as describedby the following two equations: TS T V L RVvK v V r K F Fdtdv (7)T D Y L R M dr V r K v K F F Rdt (8)Here RM is the moment arm for the motor relative to the rover’s centre of gravity and VT is the resultantforward velocity of the rover.AssignmentThe combination of all these elements produces a mathematical model for the Turning Control Systemfor the Rover. Using this model as a basis, perform the following investigations:

Use the description given above to derive the state space model for the Rover Turning System.Use this model and the parameter values given in the Appendix A to produce an equation basedsimulation of the Rover Turning Control System in Matlab. Employ a suitable numericalintegration method with a suitable step-size in the simulation of your system. Do not use thein-built Matlab integration functions.Analyse the dynamic response of the system. Do you think this a good design for the TurningControl System?Using basic blocks in Simulink, construct a block diagram simulation of the Rover TurningSystem.Use the responses from this block diagram simulation to validate your Matlab model from part(2) and simulation responses from part (3).In order to improve the performance of the coupler it is normal practice to include an integralterm within the Turning Control System for the Rover. Use your Matlab simulation toinvestigate the effect of introducing the integral term.Find values for KI and Gc that provide the best performance from this system.So far the longitudinal dynamics of the Rover have been considered to be constant. One wayto incorporate these dynamics is to vary the resultant forward speed of the Rover, VT. Withinyour Matlab simulation use the data presented in Table 1 (Appendix B) to represent the changein the speed of the rover as time progresses. Implement Newton’s Divided Differenceinterpolation method to determine the speed values that fall between and on these data points.Implement this interpolated speed change within your Matlab simulation code. Do not use thein-built Matlab interpolation functions i.e. write your own code.Once you have finished your study, complete a report form outlining the development of your modeland simulation, and your assessment of this system. The report form can be found on the moodle pagefor this course. Your report should be submitted before 4pm on 4th December 2020.Appendix A: Parameter ValuesThe following parameters are typical for the Rover and its Turning Control System:VD = 2 VL = 0.1 HR = 4 Kt = 0.35 Nm/AKe = 0.35 V/rad/sbs = 0.03Nm/rad/sJm = 0.003 kgm2Jw = 0.001 kgm2KC = 2.5KD = 18.14KH = 2.1KS = 9.81KV = 0.466KY = 29.94VT = 0.5 m/sRw = 0.064mRm = 0.124mGc = 7.5KI = 0.1 (but taken as zero in the initial stages of this work)Typical initial conditions are:o = -15ro = 0 rad/svo = 0 m/sVT = 0.5 m/sAppendix B: Velocity VariationThe following table contains data points that describe how the resultant forward velocity of the roverchanges with time:Table 1: Velocity DataTime(s) 0 2.1 4.6 6.3 8.5 10.0VT(m/s)0.5 0.7 0.9 0.8 1.0 1.2Dr Euan McGookin

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