Operational Boundaries and Velocity Planning for Camera-tower on Rails
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The company Electric Friends AS has developed a new camera system for indoor television production. The system moves on rails and can be controlled remotely. Currently the system drives with constant velocity, not allowing the camera to drive faster on straight paths than in a curve. Also, the velocity and acceleration are manually adapted for each camera-tower. Therefore, the company is interested in a mathematical way of establishing operational bounds, determining tolerable acceleration before tilting and tolerable velocity for the camera-tower in a curve. Following, a motion control algorithm implementing the operational bounds is wanted. A method determining operational bounds has been developed by looking at moment balance around the centre of mass, which is a result of forces working at point of tilt. This lead to an expression for acceleration limit and velocity limit in a curve with a given radius. Because the system already had a functioning controller, a way of determining set points for the controller was the only aspect needed to control motion. A velocity planning algorithm was suggested, computing a velocity profile for a given path and traversal time, by minimizing the total jerk. The method determining operational bounds made sense from a physical perspective. Resulting boundary values for normal acceleration were reasonable, and consequently also the velocity in a curve with a given radius. Because the shape of the camera-towers foot is trapezoidal and there is only a single wheel on the shortest parallel side of the trapezoid, the resulting boundary value for tangential acceleration was significantly low. The suggested velocity planning algorithm was deemed a fitting suggestion. Although the implementation of the algorithm did not produce an optimal velocity profile, due to implementation issues, it demonstrated the functionality of the algorithm.