A real-time trajectory modification algorithm

This paper presents a real-time algorithm for modifying the trajectory of a manipulator approaching a moving target. The algorithm is based on the superposition scheme; a model developed based on human motion behaviour. The algorithm generates a smooth trajectory toward the new target by calculating the vectorial sum between the first trajectory (initial position and first target) and second trajectory (between first and second target location). The algorithm searches for the switch hme that will result in a minimum time trajectory. The idea of the algorithm is to define some domain where the optimal switching time can be found, reduce this domain as much as possible to decrease the number of the points that must be checked and try every remaining candidate in this domain to find numerically the best (optimal) switch time. The algorithm was implemented on an Adept-one robotic system taking into account velocity constraints. The actual velocity profile was found to be less smooth than specified by the mathematical model. When the switch occurs at the middle of the trajectory when the speed is close to its maximum, the change in the movement direction is performed more gently.