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layout: post title: "Robotics Notes 2" date: 2022-8-1 23:14:00 +0800

categories: [Notes, Robotics]

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.