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Mechanical Model and Kinematics Documentation

Robot Physical Parameters

  • Robot Radius (L): 61mm (distance from center to wheel)
  • Wheel Radius (r): 27mm
  • Wheel Installation Angles (the wheels tangential form the chassis (similar to traditional 3 wheel omnidirectial setup)):
    • Wheel 1 (Front-Right): $\theta_1 = -75^\circ = -\frac{5\pi}{12}$
    • Wheel 2 (Rear): $\theta_2 = 180^\circ = \pi$
    • Wheel 3 (Front-Left): $\theta_3 = 75^\circ = \frac{5\pi}{12}$

Motor Configuration

  • Motor Type: DJI M2006
  • Maximum Current: 0.6A
  • Motor IDs:
    • ID1 (index 0): Front-right wheel (-75¡ã)
    • ID2 (index 1): Rear wheel (180¡ã)
    • ID3 (index 2): Front-left wheel (+75¡ã)

Kinematic Model

Inverse Kinematics

Converts robot velocity to wheel velocities.

Matrix Form

$$ \begin{bmatrix} \omega_1 \\ \omega_2 \\ \omega_3 \end{bmatrix} = \frac{1}{r} \begin{bmatrix} \sin(\theta_1) & \cos(\theta_1) & L \\ \sin(\theta_2) & \cos(\theta_2) & L \\ \sin(\theta_3) & \cos(\theta_3) & L \end{bmatrix} \begin{bmatrix} v_x \\ v_y \\ \omega \end{bmatrix} $$

Where:

  • $\omega_{1,2,3}$ are wheel angular velocities
  • $v_x$ is robot velocity in x direction (right positive)
  • $v_y$ is robot velocity in y direction (forward positive)
  • $\omega$ is robot angular velocity (clockwise positive)

Expanded Form

$$ \begin{align*} \omega_1 &= \frac{1}{r}(v_x\sin(\theta_1) + v_y\cos(\theta_1) + L\omega) \\ \omega_2 &= \frac{1}{r}(v_x\sin(\theta_2) + v_y\cos(\theta_2) + L\omega) \\ \omega_3 &= \frac{1}{r}(v_x\sin(\theta_3) + v_y\cos(\theta_3) + L\omega) \end{align*} $$

Forward Kinematics

Converts wheel velocities to robot velocity.

Matrix Form

$$ \begin{bmatrix} v_x \\ v_y \\ \omega \end{bmatrix} = \frac{r}{3} \begin{bmatrix} \sin(\theta_1) & \sin(\theta_2) & \sin(\theta_3) \\ \cos(\theta_1) & \cos(\theta_2) & \cos(\theta_3) \\ 1/L & 1/L & 1/L \end{bmatrix} \begin{bmatrix} \omega_1 \\ \omega_2 \\ \omega_3 \end{bmatrix} $$

Expanded Form

$$ \begin{align*} v_x &= \frac{r}{3}(\omega_1\sin(\theta_1) + \omega_2\sin(\theta_2) + \omega_3\sin(\theta_3)) \\ v_y &= \frac{r}{3}(\omega_1\cos(\theta_1) + \omega_2\cos(\theta_2) + \omega_3\cos(\theta_3)) \\ \omega &= \frac{r}{3L}(\omega_1 + \omega_2 + \omega_3) \end{align*} $$

Velocity and Current Limits

Robot Velocity Limits

  • Maximum Linear Velocity: 1.0 m/s
  • Maximum Angular Velocity: 2.0 rad/s

Current Mapping

Motor current is proportional to wheel velocity: $$ I = \frac{\omega}{\omega_{max}} \cdot I_{max} $$

Where:

  • $I$ is motor current
  • $\omega$ is wheel angular velocity
  • $\omega_{max}$ is maximum angular velocity
  • $I_{max}$ is maximum current (0.6A)

Remote Control Mapping

  • Channel 2 (decoded[2]): Forward/backward movement ($v_y$)
  • Channel 3 (decoded[3]): Left/right movement ($v_x$)
  • Channel 0 (decoded[0]): Rotation ($\omega$)
  • Channel 4 (decoded[4]): AUX1 button (Reserved for future use)
  • Channel 5 (decoded[5]): AUX2 button (Reserved for future use)