In today’s post we will discuss the kinematic model of the differential wheel mobile robot in greater detail.
We took 2 cases
- only straight motion
- only rotation
Now it’s time to generalize the motion model for any motion in plane. (aka inverse-kinematic model)
The algorithm can be written as Get Distance travelled Left Encoder Get Distance travelled Right Encoder if (left Dist == right Dist) { pos_x = prev_x + left_dist cos (current angle) pos_y = prev_y + left_dist sin(current angle) } else { delta angle = ( left Dist - right Dist ) / Width current angle = angle + delta angle pos_x = prev_x + (left_dist + right_dist )/ 2 * cos (current angle) pos_y = prev_y + (left_dist + right_dist )/ 2 * sin(current angle) } start again
Using the Above mentioned algorithm you can make a code by yourself that can be estimate the Odometry of the Robot. So using this, we can estimate the position of the robot. in other term we can say it as feedback. But to drive the Robot, we need just opposite (aka kinematics) to this algorithm that can send the motor command according to the given velocity like, Case 1.) go straight It should send the same velocity command to both the motor. Case 2.) rotate only It should send the same velocity with opposite direction.
Now we will generalize the command given to the motor left and right. vel_left = linear velocity + angular velocity part vel_right = linear velocity - angular velocity part angular velocity part = ( angular velocity / width )
By implementing this algorithm we can have the code that can send the lower level velocity command to the motors to reach to the desired position. here the “Velocity Motion Model” is described and in robotics generally this is used. You can make the “Displacement Motion Model” too with the same algorithm by feeding the displacement data instead of velocity.