The kinematic model describes the motion of a three-wheeled robot. The robot has the following dimensions:
- Radius of the wheels:
r - Distance between the front and rear wheels:
d - Distance between the front wheel and the center of mass:
h
The kinematic equations for the robot are as follows:
The position of the robot can be calculated using the following equations:
- x = r(ω1 + ω2 + ω3)cosθ
- y = r(ω1 + ω2 + ω3)sinθ
Here, ω1, ω2, and ω3 represent the angular velocities of the wheels, and θ is the orientation of the robot.
The orientation of the robot can be calculated using the following equation:
- θ = (r/d)(ω1 - ω3)
The position equations can be derived by considering the horizontal and vertical displacements of the robot's center of mass. The orientation equation can be derived by considering the rotational motion of the robot.
The horizontal displacement of the wheels is r(ω1 + ω2 + ω3)cosθ, and the vertical displacement is r(ω1 + ω2 + ω3)sinθ. The total horizontal and vertical displacements of the robot's center of mass can be calculated accordingly.
The orientation equation is derived by equating the angular momentum of the robot, which is given by Iω, where I is the moment of inertia, and ω is the angular velocity. Equating this expression with the angular momentum calculated using the wheel velocities results in the orientation equation.
The kinematic model of a three-wheeled robot is useful for simulating the robot's motion and testing different control strategies. By adjusting the wheel velocities, the robot's position and orientation can be predicted, allowing for optimization of its
The kinematic model describes the motion of a three-wheeled robot. The size of the robot is as follows.
- Radius of the wheel:
r - Distance between front and rear wheels:
d - Distance between front wheel and center of mass:
h
The motion equation of the robot is as follows.
The position of the robot can be calculated using the following equations.
- x = r (ω1 + ω2 + ω3) cosθ
- y = r (ω1 + ω2 + ω3)sinθ
Here, ω1, ω2, and ω3 represent the angular velocity of the wheel, and θ is the direction of the robot.
The orientation of the robot can be calculated using the following equation.
- θ = (r/d)(ω1 - ω3)
The position equations can be obtained by considering the horizontal and vertical dimensions of the center of mass of the robot. The orientation equation can be obtained by considering the rotation of the robot.
The slope of the disks is r(ω1 + ω2 + ω3)cosθ, and the slope is r(ω1 + ω2 + ω3)sinθ. Accordingly, both horizontal and vertical displacements of the center of mass of the robot can be calculated.
The orientation equation is obtained by equating the angular momentum of the robot, given by Iω , where I is the moment of inertia, and ω is the angular velocity of this term, which is the angular momentum calculated with the wheel velocity is equal to.
The kinematic model of a tricycle robot is useful for simulating the motion of the robot and testing different control strategies. By varying the speed of the wheels, the stopping position and movement of the robot can be controlled, allowing for optimization