Automatic tuning of motion controllers using search techniques

Claim 2

A carrier medium which stores program instructions for automatically tuning a motion control system, wherein the program instructions are executable by a processor to perform: receiving a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions, wherein each dimension corresponds to an axis of the motion controller; initializing values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space; receiving a response trajectory of the controller and motion control system in response to the desired trajectory; determining an error between the response trajectory and the desired trajectory; and experimentally searching the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory; wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

Claim 3

The carrier medium of claim 1 , wherein said determining the error between the response trajectory and the desired trajectory comprises: computing a norm of a difference between the response trajectory and the desired trajectory.

Claim 4

The carrier medium of claim 2 , wherein the norm comprises a Euclidean norm.

Claim 5

The carrier medium of claim 3 , wherein the Euclidean norm, L 2 , comprises:  d  2 = ( ∑ i = 0 N ⁢ ( y ⁡ ( i ) - x ⁡ ( i ) ) 2 ) 1 2 , wherein x comprises the desired trajectory, and wherein y comprises the response trajectory.

Claim 6

The carrier medium of claim 2 , wherein the norm comprises a finite norm.

Claim 7

The carrier medium of claim 2 , wherein the norm comprises an L 1 norm, comprising:  d  1 = ( ∑ i = 0 N ⁢ ( y ⁡ ( i ) - x ⁡ ( i ) ) ) , wherein x comprises the desired trajectory, and wherein y comprises the response trajectory.

Claim 8

The carrier medium of claim 2 , wherein the norm comprises an L p norm, comprising:  d  p = ( ∑ i = 0 n ⁢ ( y ⁡ ( n ) - x ⁡ ( n ) ) p ) 1 p , wherein x comprises the desired trajectory, and wherein y comprises the response trajectory.

Claim 9

The carrier medium of claim 7 , wherein p is greater than 2.

Claim 10

The carrier medium of claim 7 , wherein p is greater than 3.

Claim 11

The carrier medium of claim 7 , wherein p is less than 1.

Claim 12

The carrier medium of claim 7 , wherein p is infinite.

Claim 13

The carrier medium of claim 7 , wherein p is equal to a maximum deviation between the desired trajectory and the response trajectory.

Claim 14

The carrier medium of claim 1 , wherein the controller comprises a PID controller, and wherein the one or more gains comprise: a proportional gain, an integral gain, and a derivative gain for each respective dimension of the one or more dimensions.

Claim 15

The carrier medium of claim 1 , wherein the controller operates in accordance with the relation: u ( t )=ƒ( e ( t )) e ( t )= y ( t )− x ( t ) wherein y(t) and x(t) represent observed and desired values, respectively, of a variable, and wherein the one or more gains comprise a corresponding one or more coefficients or parameters of ƒ(e(t)).

Claim 16

The carrier medium of claim 14 , wherein y(t), x(t), and ƒ(e(t)) are multivariable functions, and wherein the one or more gains comprise coefficients or parameters for each respective dimension of the one or more dimensions.

Claim 17

The carrier medium of claim 1 , wherein said initializing values of the one or more gains comprises: selecting a point in the gain space.

Claim 18

The carrier medium of claim 16 , wherein selecting a point in the gain space comprises: selecting a random, pseudo-random, or quasi-random point in the gain space.

Claim 19

The carrier medium of claim 1 , wherein said experimentally searching the gain space comprises: experimentally searching the gain space using stochastic means.

Claim 20

The carrier medium of claim 18 , wherein said experimentally searching the gain space using stochastic means comprises: performing simulated annealing to search the gain space.

Claim 21

The carrier medium of claim 19 , wherein said performing simulated annealing comprises: a) evaluating a current response trajectory of the system and controller using current values of the one or more gains, thereby computing a current error of the current response trajectory with respect to the desired trajectory; b) stochastically determining new values of the one or more gains, wherein the new values are in a specified neighborhood of the current values; c) evaluating a new response trajectory of the system and controller using the new values of the one or more gains, thereby computing a new error of the new response trajectory with respect to the desired trajectory; d) if the new error is less than the current error, setting the current values of the one or more gains to the new values; and setting the current error to the new error; e) iteratively performing b) through d) until a stopping condition occurs; wherein, after said iteratively performing, the controller is operable to control the motion control system.

Claim 22

The carrier medium of claim 20 , wherein d) further comprises: if the new error is not less than the current error, stochastically determining whether to set the current values of the one or more gains to the new values based on a temperature schedule; and if the determination is made to set the current values of the one or more gains to the new values based on a temperature schedule, setting the current values of the one or more gains to the new values.

Claim 23

The carrier medium of claim 21 , wherein the program instructions are further executable to perform: f) if the stopping condition occurs, updating the temperature in accordance with the temperature schedule; and iteratively performing b) through f) until a halting condition occurs.

Claim 24

The carrier medium of claim 1 , wherein said experimentally searching the gain space comprises: experimentally searching the gain space using pseudo-random means.

Claim 25

The carrier medium of claim 1 , wherein said experimentally searching the gain space comprises: experimentally searching the gain space using quasi-random means.

Claim 26

The carrier medium of claim 24 , wherein said experimentally searching the gain space using quasi-random means is performed using a Halton sequence.

Claim 27

The carrier medium of claim 1 , wherein said experimentally searching the gain space comprises: experimentally searching the gain space using deterministic means.

Claim 28

The carrier medium of claim 1 , wherein said experimentally searching the gain space comprises: experimentally searching the gain space using a hill-climbing technique.

Claim 29

The carrier medium of claim 1 , wherein said one or more dimensions comprises two or more dimensions.

Claim 30

The carrier medium of claim 1 , wherein said one or more dimensions comprises three or more dimensions.

Claim 31

The carrier medium of claim 1 , wherein said one or more dimensions comprises four or more dimensions.

Claim 32

The carrier medium of claim 1 , wherein the program instructions are further executable to perform: operating the controller and motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

Claim 33

The carrier medium of claim 31 , wherein the program instructions are further executable to perform: performing adaptive automatic tuning of the controller and motion control system by iteratively performing said experimentally searching the gain space to determine successive final values of the one or more gains for the controller during said operating the controller and motion control system.

Claim 34

The carrier medium of claim 1 , wherein said experimentally searching the gain space to determine final values of the one or more gains for the controller comprises: a) evaluating a current response trajectory of the system and controller using current values of the one or more gains, thereby computing a current error of the current response trajectory with respect to the desired trajectory; b) determining new values of the one or more gains; c) evaluating a new response trajectory of the system and controller using the new values of the one or more gains, thereby computing a new error of the new response trajectory with respect to the desired trajectory; d) if the new error is less than the current error, setting the current values of the one or more gains to the new values; and setting the current error to the new error; e) iteratively performing b) through d) until a stopping condition occurs; wherein, after said iteratively performing, the controller is operable to control the motion control system.

Claim 35

A computer-based system for automatically tuning a motion control system, the computer system comprising: a processor; a memory medium coupled to the processor, wherein the memory medium stores program instructions executable by the processor to: receive a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions; initialize values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space; receive a response trajectory of the controller and motion control system in response to the desired trajectory; determine an error between the response trajectory and the desired trajectory; and experimentally search the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory; wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

Claim 36

A computer-based system for automatically tuning a motion control system, the computer system comprising: a processor; a memory medium coupled to the processor, wherein the memory medium stores program instructions executable by the processor to: receive a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions; initialize values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space; receive a response trajectory of the controller and motion control system in response to the desired trajectory; determine an error between the response trajectory and the desired trajectory; and experimentally search the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory; wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

Claim 37

The computer system of claim 34 , further comprising: a display device coupled to the processor, wherein the display device is operable to display the desired trajectory and the response trajectory.

Claim 38

The computer system of claim 34 , wherein the display device is further operable to display the error between the desired trajectory and the response trajectory.

Claim 39

A memory medium comprising program instructions for automatically tuning a motion control system, wherein the program instructions are computer-executable to perform: receiving a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions; initializing values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space; receiving a response trajectory of the controller and motion control system in response to the desired trajectory; determining an error between the response trajectory and the desired trajectory; and experimentally searching the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory; wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

Claim 40

A memory medium comprising program instructions for automatically tuning a motion control system, wherein the program instructions are computer-executable to perform: receiving a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions; initializing values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space; receiving a response trajectory of the controller and motion control system in response to the desired trajectory; determining an error between the response trajectory and the desired trajectory; and experimentally searching the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory; wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

Claim 41

A computer-implemented method for automatically tuning a controller coupled to a motion control system, the method comprising: a) initializing current values of one or more gains for the controller; b) providing an input signal to the controller and system, wherein the input signal specifies a position trajectory/motion profile for the motion control system in one or more dimensions; c) evaluating a current response of the system and controller to the input signal using the current values of the one or more gains, thereby computing a current value of a metric quantifying an error of the current response with respect to the input signal; d) determining new values of the one or more gains, wherein the new values are in a specified neighborhood of the current values; e) evaluating a new response of the system and controller to the input signal using the new values of the one or more gains, thereby generating a new value of the metric quantifying an error of the new response with respect to the input signal; f) if the new value of the metric and the current value of the metric indicate that the error of the new response is less than the error of the current response, setting the current values of the one or more gains to the new values; and setting the current value of the metric to the new value of the metric; and g) iteratively performing d) through f) until a stopping condition occurs; wherein, after said iteratively performing, the controller is operable to control the motion control system.

Claim 42

A computer-implemented method for automatically tuning a controller coupled to a motion control system, the method comprising: a) initializing current values of one or more gains for the controller; b) providing an input signal to the controller and system, wherein the input signal specifies a position trajectory/motion profile for the motion control system in one or more dimensions; c) evaluating a current response of the system and controller to the input signal using the current values of the one or more gains, thereby computing a current value of a metric quantifying an error of the current response with respect to the input signal; d) determining new values of the one or more gains, wherein the new values are in a specified neighborhood of the current values; e) evaluating a new response of the system and controller to the input signal using the new values of the one or more gains, thereby generating a new value of the metric quantifying an error of the new response with respect to the input signal; f) if the new value of the metric and the current value of the metric indicate that the error of the new response is less than the error of the current response, setting the current values of the one or more gains to the new values; and setting the current value of the metric to the new value of the metric; and g) iteratively performing d) through f) until a stopping condition occurs; wherein, after said iteratively performing, the controller is operable to control the motion control system.