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Motion planning, also path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of valid configurations that moves the object from the source to destination. The term is used in computational geometry, computer animation, robotics and computer games. For example, consider navigating a mobile robot inside a building to a distant waypoint. It should execute this task while avoiding walls and not falling down stairs.
A proportional–integral–derivative controller (PID controller or three-term controller) is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control. A PID controller continuously calculates an error value as the difference between a desired setpoint (SP) and a measured process variable (PV) and applies a correction based on proportional, integral, and derivative terms (denoted P, I, and D respectively), hence the name.
This paper considers a helicopter-like setup called the Toycopter. Its particularities reside first in the fact that the toycopter motion is constrained to remain on a sphere and second in the use of
In the 60's, control, signals and systems had a common linear algebraic background and, according to their evolution, their respective backgrounds have now dramatically differed. Recovering such a com