State + relational control
1 i j k 𝒬° OPERATOR scalar / identity rotation basis rotation basis rotation basis
q = a + bi + cj + dk
Quaternion = orientation state · 𝒬° ≠ fifth component
Two rails + moving belt
L R S = R − L 0.00 −1 +1
ξQ = 2(x − L)/(R − L) − 1 ∈ [−1,+1]
Rails = bounds · belt = channel · width = scale
Joystick coordinate ξQ0.00
qstate· 𝒬°operator· ξQcontrol coordinate· wᵢpressures / weights· Δqorientation change