Movement of Robots

  • Locomotion: Mechanical process that generates motion (Legs, Wheels, Flippers…)
  • Kinematics: Position, velocity, acceleration…
  • Dynamics: motion caused by forces ($\frac{d}{dx} mv = F$)
  • Motion Control: choice of input to generate motion for a goal

Pose: body-fixed frame, spatial variable, position (x, y) and orientation (ex, ey) (for 2D)

Pose of a robot: origin of BFF, orientation of BFF, w.r.t. reference frame {A}

Pose in 2D: $\begin{bmatrix} x
y
\theta \end{bmatrix}$, (x, y) is the location of robot centre, $\theta$ is the relative orientation of the robot.

Velocity in 2D:

  • body-frame velocity in inertial coordinates: d/dt (x y) = (vx vy)
  • body-frame velocity in body coordinates: (u 0) = $\left( \begin{matrix} cos(\theta) & sin(\theta)
    -sin(\theta) & cos(\theta)
    \end{matrix} \right) \left( \begin{matrix} v_x
    v_y
    \end{matrix} \right)$
  • Angular velocity $\theta$: anti-clockwise, body velocity.

Angles of rotation of the wheels are configuration varibles or states.

Distinction between configuration state (internal) and pose state (external)

Configuration: (q1, q2, q3,…, qn)
Pose: (PE, RE)

Pose = $f$(Configuration)
Configuration = $f^{-1}$(Pose)

f is not one-to-one.

Wheel angles are not related algebraically to the position.