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Interpolation with 3rd order polynomial trajectory for position control

bin gao1
Prodigy 20 points

Dear Sirs,

    I use TI DSP for driver development. For position loop, my TI DSP receive target command position from Ethernet every 1 ms while our positition loop in DSP is running at 125us per cycle. 

   Therefore, I need 3rd order polynomial interpolation algorithm to get another 7 target position in DSP.

   Could you help tell me where we can find standard  polynomial interpolation algorithm ?

  Thanks in advance