Rovers are robotic vehicles that are widely used for operations within remote and sometime dangerous
environments e.g. bomb disposal, space exploration. In order for rovers to perform these duties they
must be able to manoeuvre accurately, which depends on their drive control systems. This assignment
involves 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 assignment
Wheeled rovers, as the name suggests, are robotic vehicles that have propulsion systems based on the
motion of motor driven wheels. Various different configurations of wheels have been employed in the
design of rovers e.g. 6 wheel rocker-bogie used in design of the Curiosity Rover (see Figure 1).
Figure 1: Curiosity Rover
This type of rover has both drive motors (for moving the wheels and ultimately the vehicle) and
steering motors (for changing the direction of the vehicle). This type of system is complex and
considerably difficult to control effectively.
Other types of rovers depend on the differential motion of wheels on either side of the vehicle. An
example of this, which will be the focus of this assignment, is the 4 wheel rover shown in Figure 2.
Figure 2: 4 Wheel Rover
The motion of this vehicle is determined by the relative motions of the motor driven wheels. The
forward propulsion of the rover is produced by the sum of the force produced by the wheels (see Figure
3(a)). Whereas the turning motion of this type of rover is determined by the difference in forces
produced by each set of wheels on either side of the vehicle e.g. if the two wheels on the right hand
side 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 Motion
Figure 3: Rover Motions and Wheel Forces
The turning motion described in Figure 3(b) is the focus of this assignment as outlined in the Problem
The motion of the rover is regulated by automatic control systems that determine the necessary speed
and direction of the vehicle. In order to achieve this, the rover must be equipped with the necessary
systems to ensure its automatic guidance within it operating environment. The general principle of
completely automated guidance systems is to feed information from the heading and speed sensors to
the rover’s control system.
In this study we will consider the development of a simulation that represents the heading control
system only. This system changes the voltage applied to the wheel motors to produce the required
turning 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 manoeuvre
The turning control system produces the required wheel speeds to generate a coordinated turning
manoeuvre that changes the rover’s heading or yaw angle. It achieves this by comparing the actual
yaw angle, ψ (radians), with the reference heading, ψref (radians). A diagram of the total system is
shown in Figure 5.
Figure 5: Rover Turning Control System
From Figure 5 it can be seen that the Turning Control System uses the error difference between the
reference yaw angle, ψref, and the rover’s actual yaw angle, ψ. In this case the value for ref (the
reference heading) is taken to be 40° which passes through the Signal Conditioning system
Rover & wheel
(represented by a simple gain KC). The yaw angle, ψ, is measured using the Heading Compass which
is represented by a simple gain KH. The control system is effectively a PI controller of the following
c 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 motors
to generate an appropriate heading for the rover to follow (). It achieves this by means of a
proportional gain GC and an integral term with gain KI. These gains determine the performance of the
control 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 wheel
motors. In Figure 5 this system is regarded as the conversion process between the commanded voltage
difference, V, and the actual heading of the rover, . This process is more involved than this
simplified system diagram would lead you to believe.
The voltage difference from the control system is combined with the drive voltage, VD (volts), to
produce the corresponding input voltage for each wheel motor. The forces generated by the wheels
are then used to influence the turning dynamics of the rover. A detailed description of this system and
how it interacts with the rover can be seen in Figure 6.
Figure 6: Rover and Wheel Motors
It is assumed that the 2 wheel motors on each side have the same voltage applied and produce the same
force. Therefore, the total combined force on the left side is represented by FL (N) and the total
combined force on the right side is represented by FR (N). The difference in these forces generates the
turning 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 dt
di L (2)
b K i
J s t
Here i is the motor current (A), m is the speed of rotation of the motor (rad/s), is the difference in
speed between the motor and the wheel (rad/s), Jm is the moment of inertia for the motor armature
), L is the inductance (H), R is the resistance (), bs is the damping coefficient, Kt is the torque
constant and Ke is the back emf constant. The inputs to the motors are Vin = VD V depending on the
which side is being considered.
The wheel can be treated as load on the motor’s shaft and therefore have its own dynamics. This can
be represented by the following equation.
Here w is the speed of rotation of the wheel (rad/s) and Jw is the moment of inertia for the wheel
In this case VD = 2V. The current from each motor can be used to generate the total wheel forces on
the left and right sides i.e.
Here Rw (m) is the radius of the wheel. These forces influence the sway and yaw dynamics as described
by the following two equations:
S T V L R
K v V r K F F
T D Y L R M
dr V r K v K F F R
Here RM is the moment arm for the motor relative to the rover’s centre of gravity and VT is the resultant
forward velocity of the rover.
The combination of all these elements produces a mathematical model for the Turning Control System
for 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 based
simulation of the Rover Turning Control System in Matlab. Employ a suitable numerical
integration method with a suitable step-size in the simulation of your system. Do not use the
in-built Matlab integration functions.
- Analyse the dynamic response of the system. Do you think this a good design for the Turning
- Using basic blocks in Simulink, construct a block diagram simulation of the Rover Turning
- 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 integral
term within the Turning Control System for the Rover. Use your Matlab simulation to
investigate 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 way
to incorporate these dynamics is to vary the resultant forward speed of the Rover, VT. Within
your Matlab simulation use the data presented in Table 1 (Appendix B) to represent the change
in the speed of the rover as time progresses. Implement Newton’s Divided Difference
interpolation 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 the
in-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 model
and simulation, and your assessment of this system. The report form can be found on the moodle page
for this course. Your report should be submitted before 4pm on 4
th December 2020.
Appendix A: Parameter Values
The following parameters are typical for the Rover and its Turning Control System:
VD = 2 V
L = 0.1 H
R = 4
Kt = 0.35 Nm/A
Ke = 0.35 V/rad/s
bs = 0.03Nm/rad/s
Jm = 0.003 kgm2
Jw = 0.001 kgm2
KC = 2.5
KD = 18.14
KH = 2.1
KS = 9.81
KV = 0.466
KY = 29.94
VT = 0.5 m/s
Rw = 0.064m
Rm = 0.124m
Gc = 7.5
KI = 0.1 (but taken as zero in the initial stages of this work)
Typical initial conditions are:
o = -15
ro = 0 rad/s
vo = 0 m/s
VT = 0.5 m/s
Appendix B: Velocity Variation
The following table contains data points that describe how the resultant forward velocity of the rover
changes with time:
Table 1: Velocity Data
(s) 0 2.1 4.6 6.3 8.5 10.0
0.5 0.7 0.9 0.8 1.0 1.2
Dr Euan McGookin
The United States is home to the absolute generally infamous and productive chronic executioners ever. Names, for example, Ted Bundy, Gary Ridgeway, and the Zodiac Killer have become commonly recognized names because of the terrible idea of their violations. One of the most productive chronic executioners in American history is John Wayne Gacy. Nicknamed the Killer Clown in light of his calling, Gacy assaulted and killed at any rate 33 adolescent young men and youngsters somewhere in the range of 1972 and 1978, which is one of the most noteworthy realized casualty checks. Gacy's story has become so notable that his wrongdoings have been included in mainstream society and TV shows, for example, American Horror Story: Hotel and Criminal Minds. Legal science has, and keeps on playing, a significant part in the fathoming of the case and recognizable proof of the people in question. John Wayne Gacy's set of experiences of sexual and psychological mistreatment was instrumental in arousing examiner's curiosity of him as a suspect. John Wayne Gacy was conceived on March 17, 1942, in Chicago, Illinois. Being the main child out of three kids, Gacy had a stressed relationship with his dad, who drank intensely and was regularly harsh towards the whole family (Sullivan and Maiken 48). In 1949, a temporary worker, who was a family companion, would caress Gacy during rides in his truck; be that as it may, Gacy never uncovered these experiences to his folks because of a paranoid fear of revenge from his dad (Foreman 54). His dad's mental maltreatment proceeded into his young grown-up years, and Gacy moved to Las Vegas where he worked quickly in the rescue vehicle administration prior to turning into a morgue chaperon (Sullivan and Maiken 50). As a funeral home chaperon, Gacy was vigorously engaged with the treating cycle and conceded that one night, he moved into the casket of a perished young kid and touched the body (Cahill and Ewing 46). Stunned at himself, Gacy re-visitations of Chicago to live with his family and graduates from Northwestern Business College in 1963, and acknowledges an administration learner position with Nunn-Bush Shoe Company. In 1964, Gacy is moved to Springfield and meets his future spouse, Marlynn Myers. In Springfield, Gacy has his subsequent gay experience when an associate unsteadily performed oral sex on him (London 11:7). Gacy moves to Waterloo, Iowa, and starts a family with Myers. Nonetheless, after routinely undermining his significant other with whores, Gacy submits his initially known rape in 1967 upon Donald Vorhees. In the coming months, Gacy explicitly manhandles a few different young people and is captured and accused of oral homosexuality (Sullivan and Maiken 60). On December 3, 1968, Gacy is indicted and condemned to ten years at the Anamosa State Penitentiary. Gacy turns into a model prisoner at Anamosa and is allowed parole in June of 1970, an only a brief time after his condemning. He had to move to Chicago and live with his mom and notice a 10:00PM time limitation. Not exactly a year later, Gacy is accused again of explicitly attacking a high school kid yet the young didn't show up in court, so the charges were dropped. Gacy was known by numerous individuals in his locale to be an enthusiastic volunteer and being dynamic in network legislative issues. His part as "Pogo the Clown" the comedian started in 1975 when Gacy joined a nearby "Sprightly Joker" jokester club that consistently performed at raising money occasions. On January 3, 1972, Gacy submits his first homicide of Timothy McCoy, a 16-year old kid making a trip from Michigan to Omaha. Guaranteeing that McCoy went into his room using a kitchen blade, Gacy gets into an actual squabble with McCoy prior to wounding him over and again in the chest. Subsequent to understanding that McCoy had absentmindedly strolled into the live with the blade while attempting to plan breakfast, Gacy covers the body in his slither space. Gacy conceded in the meetings following his capture that executing McCoy gave him a "mind-desensitizing climax", expressing that this homicide was the point at which he "understood passing was a definitive rush" (Cahill and Ewing 349). Just about 2 years after the fact, Gacy submits his second homicide of a unidentified youngster. Gacy choked the kid prior to stuffing the body in his storeroom prior to covering him (Cahill 349). In 1975, Gacy's business was developing rapidly and his hunger for youngsters developed with it. Gacy regularly baited youngsters under his work to his home, persuading them to place themselves in binds, and assaulting and tormenting them prior to choking them (Cahill 169-170). The majority of Gacy's killings occurred somewhere in the range of 1976 and 1978, the first of this time occurring in April 1976. Huge numbers of the young people that were killed during this time were covered in a creep space under Gacy's home. For the rest of the killings, Gacy confessed to losing five bodies the I-55 extension into the Des Plaines River; in any case, just four of the bodies were ever recuperated (Linedecker 152). In December 1978, Gacy meets Robert Jerome Piest, a 15-year old kid working at a drug store and extends to him an employment opportunity at Gacy's firm. Piest advises his mom regarding this and neglects to restore that night. The Piest family records a missing individual's report and the drug specialist educates police that Gacy would no doubt be the man that Jerome addressed about a work. When addressed by the police, Gacy denied any inclusion in Piest's vanishing. Be that as it may, the police were not persuaded, and Gacy's set of experiences of sexual maltreatment and battery provoked the police to look through his home. Among the things found at Gacy's home were a 1975 secondary school class ring with the initials J.A.S., numerous driver's licenses, binds, dress that was excessively little for Gacy, and a receipt for the drug store that Piest had worked at. Throughout the span of the following not many days, examiners got numerous calls and tips about Gacy's rapes and the baffling vanishings of Gacy's workers. The class ring was in the long run followed back to John A. Szyc, one of Gacy's casualties in 1977. Futhermore, after inspecting Gacy's vehicle, specialists found a little group of strands looking like human hair, which were shipped off the labs for additional examination. That very night, search canines were utilized to recognize any hint of Piest in Gacy's vehicle, and one of the canines demonstrated that Piest had, truth be told, been available in the vehicle. On December 20, 1977, under the pressure of consistent police reconnaissance and examination, Gacy admits to more than 30 killings and educates his legal advisor and companion where the bodies were covered, both in the slither space and the waterway. 26 casualties were found in the slither space and 4 in the stream. Gacy is captured, indicted for 33 homicides, and condemned to death by deadly infusion. He endeavored a madness supplication however was denied, and was executed on May 10, 1994. There were a few scientific pointers that specialists used to attach Gacy to the homicides. A portion of these include fiber investigation, dental and radiology records, utilizing the decay cycle of the human body, and facial remaking in recognizing the people in question. Specialists discovered strands that took after human hair in both Gacy's vehicle and close to the slither space where the bodies were covered. Notwithstanding these hair tests, examiners additionally discovered strands that contained hints of Gacy's blood and semen in a similar region. Blood having a place with the casualties was found on a portion of the filaments, which would later straightforwardly attach Gacy to the wrongdoings. The filaments in Gacy's vehicle were dissected by scientific researchers and coordinated Piest's hair tests. Besides, the inquiry canines that discovered that Piest had been in Gacy's vehicle demonstrated this by a "demise response", which told specialists that Piest's dead body had been within Gacy's vehicle. Out of Gacy's 33 known casualties, just 25 were ever decisively distinguished. A large number of Gacy's casualties had comparative actual depictions and were along these lines hard to recognize by simply asking general society. To distinguish the people in question, specialists went to Betty Pat Gatliff, a pioneer in scientific science and facial reproduction. Facial remaking is the way toward reproducing the facial highlights of a person by utilizing their remaining parts. Certain facial highlights, for example, facial structures, nasal structure, and by and large face shape can be valuable in distinguishing a casualty even long in the afterlife. By utilizing these highlights, and with the assistance of program, criminological agents can make a picture of an individual's face, which is instrumental in distinguishing casualties after their bodies have rotted. Facial remaking should be possible in a few measurements. Two-dimensional facial reproductions is utilized with skull radiographs and depend on pre-demise photos and data. Nonetheless, this isn't really ideal on the grounds that cranial highlights are not generally noticeable or at the correct scale (Downing). To get a practical and more exact portrayal of the casualty's face, a craftsman and a measurable anthropologist are normally important (Downing). Three-dimensional facial reproduction is finished by models or high goal, three-dimensional pictures. PC programs can make facial reproductions by controlling filtered photos of the remaining parts and use approximations to reproduce facial highlights. These will in general deliver results that don't look fake (Reichs and Craig 491). Now and again, specialists will utilize a strategy called superimposition as a procedure for facial recreation. Shockingly, it's anything but an ordinarily utilized technique, as it expects examiners to have some information about the character of the remaining parts they are managing. By superimposing a photo of a person over the skeletal remaining parts, specialists can check whether the facial highlights line up with the anatomical highlights, permitting them to distinguish a casualty. On account of John Wayne Gacy's casualties, specialists had the option to utilize facial recreation to distinguish nine of the bodies found in the creep space. The accompanying realistic shows the facial reproductions of these nine casualties: Since facial remaking was insufficient to distinguish the entirety of the v>GET ANSWER