1. MiniSkybot: Kinematics
l: Distance between wheels
r: Wheel's radius X R , Y R
: Local frame
MiniSkybot
l=85mm
r=30mm

2. Kinematics Model (I): Local frame

3. Kinematics Model (II): Global frame
: Robot's orientation θ
Translating from local to global frame:
𝑃 𝑔 =𝑅𝑜𝑡𝑧 θ 𝑃 𝑅
Point referred to the
global frame
Point referred to the
local frame
𝑅𝑜𝑡𝑧 θ =  cosθ −sinθ 0 sinθ cosθ 
Rotation matrix
(around z axis)

4. Velocities in the local frame
Differential drive mobile robot:
Two wheels that rotate around XR axis
Constraint: no displacement along XR axis
Linear velocity:
It only has a component v along the YR axis.
No component along the XR axis
Angular velocity: w
Instant local velocity vector:
This vector includes the linear and angular velocities
referred to the local frame
𝑣 𝑅 =  𝑉 0 𝑊 

5. Velocities in the global frame
 𝑉 𝑥 𝑉 𝑦 𝑊𝑔  =  cosθ −sinθ 0 sinθ cosθ   𝑉 0 𝑊 
𝑉 𝑔 =𝑅𝑜𝑡𝑧 θ 𝑉 𝑅
Global
velocity
Local
velocity
𝑉𝑦=𝑉𝑠𝑖𝑛θ
(1)
𝑉𝑥=𝑉𝑐𝑜𝑠θ
𝑊𝑔=𝑊

6. Local velocity in function of wheel's speed (I)
Linear velocity:
𝑤 1 , 𝑤 2
:Wheel's speed (Rad/s)
𝑣 = 𝑣 𝑣 2
r: Wheel's radius
Contribution of
wheel 1
Contribution of
wheel 2
𝑤 1 𝑟
𝑣 1
𝑣 2 =0 𝑙