Abstract: A new method for smooth trajectory planning of robot manipulators is described in this paper. In order to ensure that the resulting trajectory is smooth enough, an objective function containing a term proportional to the integral of the squared jerk (defined as the derivative of the acceleration) along the trajectory is considered. Moreover, a second term, proportional to the total execution time, is added to the expression of the objective function. In this way it is not necessary to define the total execution time before running the algorithm. Fifth-order B-splines are then used to compose the overall trajectory. With respect to other trajectory optimization techniques, the proposed method enables one to set kinematic constraints on the robot motion, expressed as upper bounds on the absolute values of velocity, acceleration and jerk. The algorithm has been tested in simulation yielding good results, which have also been compared with those provided by another important trajectory planning technique.