Faster, less computational intense, and more robust techniques to optimize velocity of robots or portions thereof without violating constraints on acceleration and jerk (derivative of acceleration with respect to time) are described. A nonlinear problem of optimizing velocity without violating acceleration constraints is linearized, and produces acceleration constrained velocity estimates. A nonlinear problem of optimizing velocity without violating jerk constraints in linearized, and produces jerk constrained velocity estimates, and may be feed by the acceleration constrained velocity estimates. Configuration and timing may be generated and provided, e.g., as vectors, to control operation of a robot, robotic appendage or other structure.