Homework #10              ECE 417 --- ROBOTICS            Spring 2021


The following is known about a smooth trajectory: p(0) = 0, v(0) = 0, 
p(3) = 2, p(7) = 0, v(7) = 0 and velocity and acceleration are 
continuous everywhere.  

  a) What is the lowest degree single polynomial which could be used?  
  b) Give two advantages to using a spline curve instead. 
  c) What degree polynomials would you suggest for the splines?  
  d) Write the polynomials.  
  e) Write the set of equations which would be used to solve for the 
     coefficients. Do not use normalized time. 
  f) Solve for the coefficients.
  g) Write the set of equations which would be used to solve for the 
     coefficients. Use normalized time. 
  h) Solve for the coefficients.