Reference no: EM13296966
A cylindrical coordinate robot is to be used for palletizing boxes in a rectangular area.
Find the maximum rectangular area available within the annular footprint of the robot's workspace.
1. Formulate the optimal design problem. Clearly state the objective function, design variables and constraints.
2. Assuming r1 = 30 cm and r2 = 60 cm, perform the _rst three steps of the local optimization problem. Clearly indicate which algorithm you will be using and explain each and every step you take. 3. Solve problem analytically.
4. By hand, do the first four iterations using the steepest descent method. Use your computer program for Brent's polynomial approximation algorithm to help you obtain the optimal step size. Show all your work for determining the search directions.
5. By hand, do the first four iterations using the conjugate gradient method. Use your computer program for Brent's polynomial approximation algorithm to help you obtain the optimal step size. Show all your work for determining the search directions.
6. Using the programs you wrote in the previous labs, numerically solve the problem using:
(a) steepest descent method with golden section,
(b) steepest descent method with quadratic approximation (Brent's algorithm),
(c) conjugate gradient method with golden section,
(d) conjugate gradient method with quadratic approximation (Brent's algorithm)
7. Compare and comment on the results from the previous question.
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