A robotic system with independently controllable higher derivatives is disclosed. An indication is received of a trajectory through which an end effector comprising a robotic arm is to be moved. A plan is determined to use a combination of one or more motors and one or more energy removal devices to move one or more elements comprising the robotic arm in a manner that will result in the end effector being moved through the trajectory, including by using the one or more motors to apply torque to said one or more elements comprising the robotic arm during a first interval and using the one or more energy removal devices to remove energy from one or more of said elements during a second interval that starts after the start of the first interval. Commands to implement the plan are sent via a communication interface.