A computer-implemented method of determining a series of control signals for controlling an autonomous vehicle to implement a planned speed change maneuver, the method comprising: receiving from a maneuver planner a position target for the planned speed change maneuver; selecting, from a predetermined family of kinematic functions, a kinematic function for carrying out the planned speed change maneuver, each kinematic function being a first or higher order derivative of acceleration with respect to time; and using the selected kinematic function to determine a series of control signals for implementing the planned speed change maneuver; wherein the kinematic function is selected in a constrained optimization process as substantially optimizing a cost function defined for the speed change maneuver, subject to a set of hard constraints that: (i) require a final acceleration, speed and position corresponding to the selected kinematic function to satisfy, respectively, an acceleration target, a speed target and the position target, given an initial speed and acceleration of the autonomous vehicle, and (ii) impose a jerk magnitude upper limit on the selected kinematic function; wherein the family of kinematic functions is defined by a set of function parameters, over which the cost function is defined, and the kinematic function is selected by computing values of the function parameters that substantially optimize the cost function subject to the set of hard constraints; characterized in that the common form of the kinematic functions is such that each kinematic function may be integrated analytically with respect to time, wherein the requirement pertaining to the final acceleration, speed and position is embodied as a set of closed form final acceleration, speed and position functions of the function parameters, and is imposed without numerically integrating the selected kinematic function. receiving from a maneuver planner a position target for the planned speed change maneuver; selecting, from a predetermined family of kinematic functions, a kinematic function for carrying out the planned speed change maneuver, each kinematic function being a first or higher order derivative of acceleration with respect to time; and using the selected kinematic function to determine a series of control signals for implementing the planned speed change maneuver; wherein the kinematic function is selected in a constrained optimization process as substantially optimizing a cost function defined for the speed change maneuver, subject to a set of hard constraints that: (i) require a final acceleration, speed and position corresponding to the selected kinematic function to satisfy, respectively, an acceleration target, a speed target and the position target, given an initial speed and acceleration of the autonomous vehicle, and (ii) impose a jerk magnitude upper limit on the selected kinematic function; (i) require a final acceleration, speed and position corresponding to the selected kinematic function to satisfy, respectively, an acceleration target, a speed target and the position target, given an initial speed and acceleration of the autonomous vehicle, and (ii) impose a jerk magnitude upper limit on the selected kinematic function; wherein the family of kinematic functions is defined by a set of function parameters, over which the cost function is defined, and the kinematic function is selected by computing values of the function parameters that substantially optimize the cost function subject to the set of hard constraints; characterized in that the common form of the kinematic functions is such that each kinematic function may be integrated analytically with respect to time, wherein the requirement pertaining to the final acceleration, speed and position is embodied as a set of closed form final acceleration, speed and position functions of the function parameters, and is imposed without numerically integrating the selected kinematic function.