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Anatomy of a Robot Part 5

Tham khảo tài liệu 'anatomy of a robot part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 66 CHAPTER TWO Other cost functions beyond LMS are available. LMS still requires multiplication which can eat up computer time and resources. LMS multiplies the step size by the differential error X1 - X1d to get the iteration step size. This can be approached in other ways Use just the sign of X1 - X1d not the magnitude. The sign simply indicates which way X1 is off. The entire step size is then simply added or subtracted from X1 to iterate to the next value. This makes the iteration step a simple addition or subtraction and avoids the multiplication. This can be of particular value if we choose to use a small microcomputer that has no multiplier. Use the relative size of X1 - X1d to pick the step size from a table of step sizes. This can work well and also avoids multiplication. It can converge faster when the cost function is large and can remain fairly quiet about the optimal solution. Care must be taken when switching gears in an arbitrary manner like this. Please reread the earlier A Caution section. Multivariable systems have other peculiarities to worry about as well. Issues of stability convergence and speed of operation all must be addressed here Stability As already discussed if the step size is too large the system may oscillate about the solution point in an unacceptable manner. Further all the variables may not be able to reach an optimal solution at the same time. The system may remain noisy forever even if the inputs stop moving. Convergence It s possible in some situations that the control system will not actually move to an acceptable solution Finding a solution Sometimes the starting position of the robot can affect whether it will move to the desired location or not. The control system always has a set of points beyond which it cannot recover. In the design and operation of our robot s control system we must assure ourselves that the robot will not be asked to recover from such a situation. Note that we must determine what an acceptable solution