Robotic system with independently controllable higher order derivatives

Abstract

A robotic system with independently controllable higher order derivatives is disclosed. An indication of a trajectory along which an end effector of the robot arm should be moved is received. A plan is determined utilizing a combination of one or more motors and one or more energy removal devices to move one or more elements of the robot arm such that the end effector is moved through the trajectory, including using one or more motors to apply torque to one or more elements of the robot arm during a first interval and using one or more energy removal devices to remove energy from one or more of the elements during a second interval beginning after the start of the first interval. Commands to execute the plan are transmitted via a communications interface.

Description

CROSS-REFERENCE TO OTHER APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 301,693, entitled "ROBOTIC SYSTEM WITH INDEPENDENTLY CONTROLLABLE HIGHER DERIVATIVES," filed January 21, 2022, which is incorporated by reference herein for all purposes. [Background technology]

[0002] Robots (robot arms and end effectors (e.g., suction bases, grippers, etc.)) are actuated using motors, air-actuated pistons, vacuum / suction, and other actuators. The robot arms or other robots may be operated under the control of a control system, which sends commands to control the operation of the actuators to move the robot (e.g., to grasp and move objects, etc.). The robot control system may control one or more of the position, velocity, acceleration, or other higher order derivatives of the motion of the robot and / or parts thereof (such as end effectors), and / or the torques and / or currents applied by / to the actuators.

[0003] Critical control (fast rise, critical damping, no overshoot) requires accurate damping, whether controlling position, velocity, torque, current, etc. Accurate damping requires estimation of the derivatives of the controlled states, or higher order derivatives if the system is beyond second order and has unusual dynamics.

[0004] Finding the instantaneous values ​​of these higher order derivatives is very difficult. The sensor is probably measuring the state, not the derivative of the state. The sensor is digital, the algorithms are running on the CPU, and have inherent latency. State estimation of higher order derivatives is difficult and prone to error, causing instability and erroneous energy injection when trying to control a system (such as a robotic system). Thus, instantaneous measurements are always delayed, sensors are always noisy, derivatives of the noise produce very noisy results, requiring filtering to produce inaccurate estimates, and CPU jitter and latency produce even larger errors in both magnitude and phase.

[0005] Finally, the higher derivatives are the most difficult to control. There is no direct level of control over the higher derivatives, so energy must be injected at the right time to control the derivative state. If the amount or timing of the injected energy is improper, unexpected results (e.g., instability, poor settling time, non-optimal control, etc.) can result. [Brief description of the drawings]

[0006] Various embodiments of the invention are disclosed in the following detailed description and the accompanying drawings.

[0007] [Figure 1A] FIG. 1 illustrates an embodiment of a robotic system with independently controllable higher order derivatives.

[0008] [Figure 1B] FIG. 1 illustrates an embodiment of a robotic system with independently controllable higher order derivatives.

[0009] [Diagram 2] FIG. 1 illustrates one embodiment of a robotic system control element.

[0010] [Diagram 3] FIG. 1 illustrates an embodiment of a robotic system with independently controllable higher order derivatives.

[0011] [Figure 4A] 1 is a flow chart illustrating one embodiment of a process for controlling a robotic system with independently controllable higher order derivatives.

[0012] [Figure 4B] 1 is a flow chart illustrating one embodiment of a process for controlling a robotic system with independently controllable higher order derivatives.

[0013] [Figure 5A] FIG. 10 shows a comparison of the velocity profile of a conventional robot and a robotic system with independently controllable higher order derivatives.

[0014] [Figure 5B] FIG. 1 illustrates energy applied by actuators and damping elements to control a robotic system with independently controllable higher order derivatives. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] The present invention may be embodied in various forms, including as a process, an apparatus, a system, a composition of matter, a computer program product embodied on a computer-readable storage medium, and / or a processor configured to execute instructions stored in and / or provided by a memory coupled to the processor. These embodiments or any other form the present invention may take may be referred to herein as techniques. In general, the order of steps of a disclosed process may be altered within the scope of the present invention. Unless otherwise noted, components such as a processor or memory described as configured to perform a task may be implemented as general components temporarily configured to perform the task at a given time, or as specific components manufactured to perform the task. As used herein, the term "processor" refers to one or more devices, circuits, and / or processing cores configured to process data, such as computer program instructions.

[0016] A detailed description of one or more embodiments of the present invention will now be given with reference to the drawings illustrating the principles of the present invention. The present invention will be described in connection with such embodiments, but is not limited to any of them. The scope of the present invention is limited only by the claims, and the present invention includes many alternatives, modifications, and equivalents. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. These details are for the purpose of example, and the present invention may be practiced according to the claims without some or all of these specific details. For simplicity, technical matters well known in the art related to the present invention have not been described in detail so as not to unnecessarily obscure the present invention.

[0017] Techniques are disclosed for controlling the derivatives of a robot state (e.g., velocity, acceleration) with or without estimation of the derivative states themselves. In various embodiments, one or more electrical, electromagnetic, and / or electromechanical components are provided and utilized to inject energy at the appropriate times to control the derivative states. In some embodiments, passive elements are used to control the dynamics of the system with guaranteed stability.

[0018] In various embodiments, robot control actuators are used that do not require state estimation and act directly on the level of higher derivatives. For example, in some embodiments, one or more of various types of brakes may be used to directly reduce the speed.

[0019] In some embodiments, actuators are used that may require estimation, but are truly passive in the conditions they are trying to control, so they are guaranteed to remain stable. Examples include, but are not limited to, resistors, capacitors, and other energy storage elements.

[0020] In some embodiments, motors are constructed with control systems incorporating the higher order derivative control techniques disclosed herein. Conventional drive train assemblies utilize brakes only to bring the system to a sudden halt or remove regenerative braking energy. In various embodiments, braking is used as an integral part of the control system, reducing the need for actuators themselves (e.g., robotic joint motors) to slow the system or remove energy.

[0021] In some embodiments, a combination of dampers and purely passive elements (such as damping resistors) are used to schedule actuation at different moments of time and state for optimal utilization of the actuators. These higher order derivative control elements have much higher capacity than actuators and allow motion to be damped instantly, simplifying control and reducing the time required to reach the target state.

[0022] In various embodiments, velocity (or other higher derivative level) control is performed, at least in part, as described in U.S. Patent Application No. 17 / 482,162, entitled "Velocity Controlled-based Robotic System," filed September 22, 2021, and published as U.S. Patent Application Publication No. 2022-0088778 on March 24, 2022, the entire contents of which are incorporated herein by reference for all purposes.

[0023] In various embodiments, brakes or similar energy removal systems are used to directly control speed by removing energy with a structure that cannot add energy. Traditionally, reverse motor torque has been used to slow and stop the movement of a robot arm. However, latency in making measurements or signal noise (especially at low speeds) can lead to errors in estimating speed. If the motion oscillates such that the robot / its components are moving in the opposite direction to that estimated, application of torque intended to slow the motion can instead add energy and make the motion larger, resulting in instability and lag as the system adjusts and dampens the oscillations. Utilizing brakes or similar devices or systems that can only remove energy ensures that such outcomes or conditions do not occur.

[0024] In some embodiments, the braking systems disclosed herein apply a braking force to a motor or motor shaft, hi some embodiments, the motor and motor shaft drive a reduction gearbox that drives a joint, and the braking force disclosed herein is applied at the output of the gearbox, reducing wear and tear on the gearbox (e.g., compared to using the motor to apply a counter torque to remove energy).

[0025] FIG. 1A illustrates an embodiment of a robotic system with independently controllable higher order derivatives. In the illustrated example, the robotic system and environment 100 includes a robotic arm 102 having an adhesive-type end effector 104. The robotic arm 102 includes multiple segments connected by joints 102a, 102b, and 102c. In some embodiments, the robotic arm 102 includes a six degree of freedom (DOF) industrial robot. In some embodiments, the robotic arm 102 includes more or less than six DOFs. A motor and associated motor controller is provided at each of the joints 102a, 102b, and 102c to bend or rotate the associated segment of the robotic arm 102, for example, by supplying voltage and current to the motor to apply torque to move the associated segment in one of the six (or more) DOFs.

[0026] In the depicted example, the robotic arm 102 and the end effector 104 are in wireless communication with a control computer 106. In some embodiments, the control computer 106 is integrated within and / or with the robotic arm 102. For example, the control computer 106 can be an internal processor that is part of the robotic arm 102 or a processor or computer mounted on or in the same chassis as the robotic arm 102.

[0027] In the context of FIG. 1A, the robotic arm 102 and end effector 104 are configured to be utilized to pick items from a conveyor 108 and place them on a pallet 110 under the control of a control computer 106. Three-dimensional (or two-dimensional) image / depth data from a camera 112 is received by the control computer 106 and utilized to generate a three-dimensional view of the workspace illustrated in FIG. 1A. In various embodiments, the control computer 106 includes a computer vision subsystem configured to construct such a view. The image data, in various embodiments, is utilized by the control computer 106 to identify an item (such as item 114 in the illustrated example) as the next item to be picked / placed. The image data and / or other center data and / or stored data may be utilized to determine one or more attributes (such as size, shape, weight, material, stiffness, etc.) of the item 114. Such attributes may be utilized to determine a strategy for grasping, moving, and / or placing the item 114. Once an item 114 is grasped, further attributes may be determined, such as weight and quality of the grasp (eg, suction force as measured by a pressure sensor).

[0028] In various embodiments, the control computer 106 determines a plan and strategy for grasping an item (such as item 114). As shown in FIG. 1A, the end effector 104 is being moved toward the item 114, as indicated by the arrow emanating from near the end effector 104. In various embodiments, the robotic arm 102 includes motors and associated controls at one or more of the joints 102a, 102b, and 102c for applying torques for each degree of freedom at each such joint to move the associated components of the robotic arm 102 in a first direction (e.g., forward), and brakes or other energy removal devices (and associated actuators) configured to apply energy in a direction opposite (reverse) the first direction. The control computer uses a model of the robotic arm 102 and its motors and brakes to determine and execute a set of control commands for actuating the joint motors, or a subset thereof, to move the end effector 104 along a trajectory to a position where it can grasp the item 114. The end effector 104 is moved relatively quickly (e.g., at or near its maximum speed) to a position relatively close to the item 114, and then a braking (or other energy removal) system is activated with precise timing to enable the speed of the end effector 104 to be reduced to zero relatively close to the item 114 without overshooting or oscillation.

[0029] Once the item 114 is grasped, for example by moving a suction cup under the end effector 104 into contact or proximity with the item 114 and applying a suction force to grasp the item 114, the item 114 is moved along a trajectory to a destination location where the item 114 is placed. In various embodiments, a maximum speed at which the item 114 and end effector 104 are moved through the workspace is determined based on, for example, one or more attributes or limitations of the robotic arm 102, the end effector 104, and / or the item 114. For example, the maximum speed may be slower if the item 114 is heavy or if a pressure sensor indicates that the grip is not strong.

[0030] 1B illustrates an embodiment of a robotic system with independently controllable higher order derivatives. In the example and state illustrated in FIG. 1B, an item 114 has already been grasped and moved to a determined destination location indicated by a dashed outline on the top surface of the pallet 110. An arrow emanating from near the end effector 104 indicates the vector that the item 114 follows as it is moved to the destination location. In various embodiments, the item 114 is moved at or near a maximum velocity (such as the maximum velocity of the robot arm 102 or a maximum velocity determined to move the item 114 in the conditions illustrated).

[0031] In various embodiments, the trajectory and associated planned control signals for moving the item 114 to the destination position include applying torque (at or near maximum) to one or more motors associated with the joints 102a, 102b, and / or 102c during at least a portion of a first interval, and activating a brake or other energy removal device during a second interval beginning after the start of the first interval. The brake or other energy removal device directly controls velocity, allowing the robotic arm 102 and end effector 104 to be moved at or near maximum speed and then reduced in speed relatively quickly, with or without the ability to measure or estimate velocity.

[0032] 2 is a diagram illustrating one embodiment of the robotic system control elements. In the illustrated example, the control computer 106 sends (e.g., digital) control signals 206 to a motor controller 202 that controls a motor 204. For example, each of the joints 102a, 102b, and 102c may have one or more motors 204, each of which may have an associated motor controller 202. The motor controller 202 provides voltage, current, and / or other analog or low-level inputs to the motors 204 to cause them to operate for controlled intervals and / or apply controlled amounts of torque. The motors 204 optionally provide position, temperature, velocity, or other feedback 210 to the controller 202, which optionally provides associated feedback signals 212 to the control computer 106.

[0033] The feedback 210, 212, in various embodiments, may include position or other information that can be used to estimate state. However, as discussed above, the measured information may be inaccurate, especially for velocity or other higher order derivatives of position, and there is always some latency to convert the measured state information into an estimated state of the robot and / or its components. In various embodiments, velocity control is provided as disclosed herein without (necessarily) estimating higher order derivatives of the state, allowing for more efficient and optimized robot utilization, such as by controlling the robot using velocity (or other higher order derivative) control.

[0034] Figure 3 illustrates an embodiment of a robotic system with independently controllable higher order derivatives. In the illustrated example, in addition to the control and drive elements shown in Figure 2, control computer 106 is configured to provide a control signal 306 to an energy eliminator controller 302 that is configured to activate an energy eliminator 304 (e.g., one or more braking systems or devices) by sending a low level signal 308 and / or applying a voltage, current, air pressure, etc. to activate an energy eliminator 304.

[0035] In the illustrated example, the energy eliminator 310 provides measured information 310 to the energy eliminator controller 302, which in turn may provide status information 312 to the control computer 106. The information 310, 312 may be used to monitor and control the operation of the energy eliminator 304 in various embodiments.

[0036] The velocity of a robotic element (such as an end effector or joint) is difficult to calculate and even more difficult to control. To remove velocity from a robotic system, in various embodiments, a force is applied in the opposite direction of the robot / joint motion.

[0037] If the velocity is oscillating, the application of force must be precisely timed, and applying it out of phase will increase the velocity instead of decreasing it. Thus, in a conventional robot with only joint motors, for example, it is difficult to precisely slow the robot down by simply applying current to the motors, especially if they are oscillating. The solution disclosed herein, as implemented in some embodiments, is to have a braking system or other energy removal system or device to remove the velocity. In various embodiments, a control input directly proportional to the amount of velocity to be removed is determined and applied to the braking system. Examples of such braking systems or devices include, but are not limited to, eddy current brakes, braking resistors, and other non-contact brakes, as well as disk brakes and other friction brakes.

[0038] In some embodiments, eddy current brakes are used to remove energy from robotic arm elements (such as joints driven by joint motors). Eddy current brakes (also known as induction brakes, electric brakes, or electric retarders) are devices used to slow or stop moving objects by generating eddy currents. In some embodiments, a non-ferromagnetic conductive disk rotates perpendicularly through a toroidal magnetic field. As the disk rotates, it induces eddy currents. Power is then dissipated across the disk to create a braking torque force.

[0039] In various embodiments, the braking systems described herein do not require speed estimation since their engagement directly removes speed / energy. In various embodiments, the braking systems are selectively engaged while an actuator (such as a motor) is adding energy to remove the damping term in the control of the motor, thereby removing the speed estimation step and the need for the motor current to damp. In various embodiments, precisely controlled versions of these braking systems are used to precisely control speed / energy removal instead of just a generic "brake".

[0040] Other methods of removing energy, yet being passive, include braking resistors on the motor. The motor has a coil that rotates within a magnetic field, which induces an electromotive force (EMF). This EMF, also known as the "back EMF," acts against the applied voltage that is primarily causing the motor to rotate, reducing the current through the motor's coils. The motor back EMF voltage is directly proportional to the motor speed. In various embodiments, a resistor is selectively engaged across the motor wiring to remove energy and reduce speed.

[0041] FIG. 4A is a flow chart illustrating an embodiment of a process for controlling a robotic system with independently controllable higher order derivatives. In various embodiments, the process 400 of FIG. 4A may be implemented by a control computer (such as the control computer 106 of FIGS. 1A and 1B). In the illustrated example, at step 402, the next leg of the trajectory is determined. For example, referring to FIG. 1A, a trajectory may be determined for moving the end effector 104 from the position shown in the figure to a gripping position adjacent the item 114. At step 404, a combination and sequence for applying motor torques and brakes, for example, for each of one or more motors and / or joints that make up the robot arm 102, to move the end effector 104 through the planned trajectory is determined. In various embodiments, a model of the robot arm 102 and its motors, controllers, and brake systems may be used to determine at least a locally optimal and / or feasible sequence for applying motor torques and brakes to move the elements of the robot arm 102 in a coordinated manner to move the end effector 104 along the determined trajectory / leg. In step 406, the determined sequence of control of the motor and braking systems is performed to synchronously apply torque and remove energy through braking to rapidly move the end effector 104 through the determined trajectory / section.

[0042] FIG. 4B is a flow chart illustrating one embodiment of a process for controlling a robotic system with independently controllable higher order derivatives. In various embodiments, the process of FIG. 4B implements step 406 of FIG. 4A. In the illustrated example, at step 420, a corresponding signal is sent to an associated motor controller to apply torque to each of one or more motors at a prescribed amount for a prescribed time. At step 422, a control signal is sent to a braking system (or other energy removal system or device) to remove energy at a predetermined time and / or according to a predetermined profile (e.g., vary the degree or amount of energy removal over time, e.g., vary how much braking force is applied over time). In various embodiments, braking force begins to be applied after the corresponding motor torque has been applied, e.g., for a prescribed or calculated interval. At step 424, final adjustments may be made as necessary / if required to complete the trajectory / leg. For example, if braking causes the end effector to stop just short of a final position, a small amount of torque may be applied for a short interval to move the end effector 104 more fully into position. In the case of placement, force control may be used to snap an item (such as item 114) into place (e.g., adjacent to one or more previously placed items).

[0043] FIG. 5A shows a comparison of velocity profiles of a conventional robot and a robotic system with independently controllable higher order derivatives. The x-axis corresponds to time and the y-axis shows velocity (such as the velocity of the end effector 104 or the velocity of the joint actuator (e.g., motor or gearbox output shaft) or the structure that constitutes the joint or is mechanically coupled to the joint). The horizontal line "Vmax" shows the maximum velocity, which may reflect one or more of the physical limitations of the robot arm 102 and the maximum velocity at which the end effector 104 (or other structure) should be moved given one or more attributes of the item being moved (such as weight) and / or dynamically measured / determined factors (such as grip quality). The dashed curve 502 shows an example of velocity over time for moving an item from a starting position {x0, y0, z0} to a destination position {x1, y1, z1} using velocity control (or other control) without utilizing the energy removal system / apparatus disclosed herein. In the illustrated example, the end effector 104 (or other structure) never reaches its maximum velocity Vmax before it needs to begin to decelerate to allow zero velocity to be achieved when the end effector 104 reaches the arrival position {x1, y1, z1} at the time in this example.

[0044] Solid curve 504 illustrates a velocity profile that may be achieved when moving the same item from a starting position {x0, y0, z0} to a destination position {x1, y1, z1} using velocity control (or other control) while utilizing the energy removal system / device disclosed herein. In the illustrated example, the same actuator (e.g., motor) is utilized, so the end effector (or other structure) accelerates in the same manner as shown in curve 502, but the structure continues to accelerate to achieve a velocity near / at maximum velocity Vmax (which may be sustained for an interval in various embodiments) before the velocity is quickly and directly reduced by the activation of a braking system (or other direct energy removal device / system). Utilization of the technology disclosed herein moves the item to a position at time t much more quickly than would be the case if braking / energy removal were not utilized, as shown in curve 502. new It is possible to reach the destination position {x1, y1, z1} by

[0045] FIG. 5B illustrates energy applied by actuators and braking elements to control a robotic system with independently controllable higher order derivatives as a function of time (or position). In various embodiments, FIG. 5B illustrates energy addition and removal profiles associated with the velocity profile illustrated in FIG. 5A. In the illustrated example, curve 522 is shown as a dashed line including a first (left / energy addition) portion 522a and a second (right / energy removal) portion 522b, illustrating application of torque without utilizing direct energy removal using brakes or other energy removal systems described herein to achieve the velocity profile 502 of FIG. 5A. Portion 522a illustrates energy added by applying torque using, for example, a joint motor, and portion 522b illustrates removal of energy, such as by applying torque in the opposite direction.

[0046] Curve 524 illustrates the application of torque synchronously with direct removal of energy, e.g., by braking, as represented by curve 526, to achieve the velocity profile represented by curve 504 of FIGURE 5A by directly reducing the velocity of the end effector through energy removal (e.g., braking). Energy is added in the same way, as shown by the coincidence of curve 524 and curve portion 522a, but by utilizing a brake or other direct energy removal system as disclosed herein, energy is removed much more directly and quickly, without risk of overshoot or error, resulting in a reduction in the velocity profile represented by curve 504 of FIGURE 5A at time t new Complete energy removal can be achieved by

[0047] In FIG. 5B, the brake is applied for a time t such that braking overlaps with the application of torque, as represented by curve 524. brake Although shown as applied at 100° C., in various embodiments, the torque application interval may or may not overlap with the brake application interval.

[0048] Using the techniques disclosed herein, velocity control can be performed without necessarily and / or quickly / accurately estimating the state and / or derivatives (such as velocity) of the robotic system. In various embodiments, active and / or passive elements are utilized to remove energy from the elements (such as any motors or joints) that make up the robot, allowing velocity to be directly controlled with or without estimating the state of velocity or other derivatives. Such direct control of velocity (or higher order derivatives) without relying on state estimation allows control of velocity and higher order derivatives to be performed, which may allow for more effective and / or optimal utilization of the robotic arm or other robot, such as by allowing higher end effector velocities to be achieved before an energy removal system is utilized to slow / stop the end effector, which in turn may allow for higher throughput and utilization to be achieved. In various embodiments, the control structures and techniques disclosed herein allow for precise control of such systems, thereby allowing for the provision of very powerful, high performance, and high gain systems.

[0049] Although the above embodiments have been described in some detail for ease of understanding, the invention is not limited to the details provided. There are many alternative ways of implementing the invention. The disclosed embodiments are illustrative and are not intended to be limiting.

Claims

1. 1. A robot system comprising: A communication interface; a processor connected to the communication interface; Equipped with The processor, receiving instructions for a trajectory along which an end effector of a robot arm should move; determining a schedule for utilizing one or more motors in combination with one or more energy removal devices to move one or more elements of the robot arm such that the end effector is moved through the trajectory, the schedule including applying torque to one or more elements of the robot arm using one or more motors during a first interval and removing energy from one or more of the elements using one or more energy removal devices during a second interval beginning after the start of the first interval; The system is configured to send commands to execute the plan via the communications interface.

2. The system of claim 1 , wherein the trajectory includes a longer trajectory section.

3. The system of claim 1 , wherein the processor is configured to determine the trajectory.

4. 2. The system of claim 1, wherein the commands to execute the plan include a first set of commands to cause the one or more motors to apply torque to the one or more elements of the robot arm during the first interval.

5. 5. The system of claim 4, wherein the first set of commands includes one or more commands each transmitted to a corresponding motor controller via the communication interface.

6. 6. The system of claim 5, wherein the commands to execute the plan include a second set of commands to cause the one or more energy removal devices to remove energy from one or more of the elements during the second interval.

7. 2. The system of claim 1, wherein the second interval begins before the end of the first interval.

8. The system of claim 1 , wherein the second interval does not overlap the first interval.

9. The system of claim 1 , wherein the energy removal device comprises a braking system or device.

10. 2. The system of claim 1, wherein the energy eliminator directly controls the velocity of the one or more elements that make up the robotic arm.

11. The system of claim 1 , wherein the energy elimination device directly controls the velocity of the end effector.

12. 2. The system of claim 1, wherein the plan for using a combination of one or more motors and one or more energy removal devices to move one or more elements that make up the robotic arm is determined without estimating a state of the robotic system.

13. 2. The system of claim 1, wherein the plan to utilize a combination of one or more motors and one or more energy removal devices to move one or more elements that make up the robot arm is determined without estimating derivative states of the robot system.

14. 2. The system of claim 1, wherein using one or more motors in combination with one or more energy removal devices to move one or more elements that make up the robotic arm allows the end effector to be moved through the trajectory in a shorter time than would be required if the one or more motors were used alone.

15. 2. The system of claim 1, wherein utilizing one or more motors in combination with one or more energy removal devices to move one or more elements that make up the robotic arm increases the throughput of the robotic system compared to the throughput achieved when only the one or more motors are used.

16. 1. A method for controlling a robotic system, comprising: receiving instructions for a trajectory along which an end effector of a robot arm should move; determining a scheme for utilizing the one or more motors in combination with the one or more energy removal devices to move the one or more elements of the robot arm such that the end effector is moved through the trajectory, such as by using one or more motors to apply torque to the one or more elements of the robot arm during a first interval and using one or more energy removal devices to remove energy from one or more of the elements during a second interval beginning after the start of the first interval; sending commands to execute said plan via a communications interface; A method comprising:

17. 17. The method of claim 16, wherein the commands to execute the plan include a first set of commands to cause the one or more motors to apply torque to the one or more elements of the robot arm during the first interval.

18. 20. The method of claim 17, wherein the first set of commands includes one or more commands each transmitted to a corresponding motor controller via the communication interface.

19. 20. The method of claim 18, wherein the commands to execute the plan include a second set of commands to cause the one or more energy removal devices to remove energy from one or more of the elements during the second interval.

20. A computer program product embodied in a non-transitory computer-readable medium, computer instructions for receiving an indication of a trajectory along which an end effector of a robotic arm should be moved; computer instructions for determining a plan for utilizing one or more motors in combination with one or more energy removal devices to move one or more elements of the robot arm such that the end effector is moved through the trajectory, such as by using one or more motors to apply torque to one or more elements of the robot arm during a first interval and using one or more energy removal devices to remove energy from one or more of the elements during a second interval beginning after the start of the first interval; computer instructions for transmitting commands to execute the plan via a communications interface; A computer program product comprising:

Images