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Table 1
Motion planning algorithm for all positioner robots.
| Trajectory planning algorithm | |
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|
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| Inputs: | Initial end-effector position of all the positioners: Qinit = [q1,q2,...,qN] |
| and target position of all fibers assigned to each positioner: Qgoal = [q1T,q2T,...,qNT] | |
| Outputs: | A sequence of motor speed values for each positioner |
| Ω1 = [ω1(1),...,ω1(M)] | |
| Ω2 = [ω2(1),...,ω2(M)] | |
|
|
| ΩN = [ωN(1),...,ωN(M)] | |
|
|
|
| m = 0 | |
| repeat until ∇ψ = 0 | |
| for each positioner (i = 1:N) | |
| ωi(m) = −∇ψ(qi(m),qiT,Q(m)) (see Table 2) | |
| qi(m + 1) = qi(m + 1) + dt.ωi(m) | |
| m = m + 1 | |
| ∇ψ = maxi(∇ψ(qi(m),qiT,Q(m))) | |
| end for | |
| end repeat | |
Notes. T0 and Tf are the beginning and end times of the algorithm, respectively, dt is the time step and M is the number of time steps, i.e., 
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