Differential tracked robot prototype

APPENDIX C

Differential tracked robot prototype Contents C.1 Tracked robot 131 C.1.1 Tracked robot model 132

C.2 Prototype 133 Chapter points •

Tracked robots

•

Tracked robot prototype

C.1 Tracked robot Tracked robots walk on continuous tracks instead of wheels, and their main advantage is that they can be used to navigate on rough terrains [26,70]. The thrust force developed by a wheeled vehicle will generally be less than the thrust force generated by a comparable tracked vehicle [70], which is the reason why they are used in a wide variety of applications where the terrain conditions are difficult or unpredictable, such as [26,62]: • • • • • •

Urban recognition. Silviculture. Mining. Farming. Rescue mission scenarios. Autonomous planetary explorations.

Also, traction robots offer the following advantages: • • •

They are versatile and can be used in different terrain conditions and climates. They generate little pressure in the field, which conserves the environment. Their design prevents the sinking or stagnation of equipment in soft ground.

131

132 Appendix C

Figure C.1: Schematic model of a traction robot, where x, y are the coordinates of P0 , θ is the direction angle of the robot.

C.1.1 Tracked robot model Kinematics of an electrically driven tracking robot are described by the following state space model [16,48]: x˙1 = J (x1 )x2 , x˙2 = M x˙3 =

(C.1)

−1

(−C(x˙1 )x2 − Dx2 − τd −1 La (u − Ra x3 − NKE x2 ),

+ NKT x3 ),

where each subsystem is defined as x1 = [x11 , x12 , x13 ] = [x, y, θ ] , x2 = [x21 , x22 ] = [v1 , v2 ] , 

(C.2)



x3 = [x31 , x32 ] = [ia1 , ia2 ] , u = [u1 , u2 ] , where x and y are the coordinates of P0 , θ is the direction angle of the robot (Fig. C.1), v1 and v2 are angular speeds, ia1 and ia2 are the currents of the robot, u1 and u2 are the input voltages, and x3 is the dynamics of the actuator.

Differential tracked robot prototype 133 Is important to remark that this model is only presented as a reference since this model is not necessary for the RHONN identifier and observers presented in this book. We have

⎡

⎤ cos(x13 ) cos(x13 ) J (x1 ) = 0.5r ⎣ sin(x13 ) sin(x13 ) ⎦ , R −1 −R −1   x11 x12 , M= x12 x11

(C.3)

(C.4)



 n1 0 N= , 0 n2

(C.5)

 Kt 1 0 , KT = 0 Kt2

(C.6)



 0 , la2

(C.7)

 ra1 0 Ra = , 0 ra2

(C.8)



l La = a1 0 



Ke1 KE = 0

 0 , Ke2

(C.9)

where R is half the width of the tracked robot and r is the radius of the wheels that move the tracks; M is the positive and symmetric matrix of inertia defined by the physical parameters of the robot, KT is the motor torque constant, La is the inductance, KE is the coefficient of rear electromotive force, and Ra is the resistance of the actuator.

C.2 Prototype The tracked robot prototype is composed of computer equipment where the model with identifier, observer, and controller is programmed in MATLAB® /Simulink. A block is added to this model that includes the code to connect wirelessly to the physical robot. The tracked robot is a modified differential all-terrain tank robot model HD21 Treaded ATR Tank Robot Platform (Fig. C.2). Among the modifications, a router is mounted to enable the wireless connection.

134 Appendix C

Figure C.2: HD2 Treaded ATR Tank Robot Platform.

Figure C.3: Internal components of the modified HD2 Treaded ATR Tank Robot Platform.

Fig. C.2 shows the differential all-terrain tank robot. Fig. C.3 shows the interior of the modified HD2 Treaded ATR Tank Robot Platform. The modifications mainly consist of the replacement of the original board with a system based on Arduino2 and the addition of current and velocity sensors. It is important to mention that the information about the model and values of the parameters of this robot with its modifications are unknown, which makes this prototype ideal to test control models that do not need knowledge of the model of the system to be controlled.

1 HD2 is a registered trademark of SuperDroid Robots. 2 Arduinois a registered trademark of Arduino LLC.