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

Kinematics Model (I): Local frame

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 0 0 0 1  Rotation matrix (around z axis)

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 

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

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