Abstract:
A method for detecting collisions between an obstacle and an electromechanical system having a mechanical output controlled by a servo system includes inputting a forcing function x i  to the servo system to direct the mechanical output to move in an intended manner. A difference signal is generated at a monitoring point M representing a difference between forcing function x i  and a feedback signal dependent upon the mechanical output. The method further includes injecting a feed forward signal into the servo system. The feed forward signal is dependent upon the forcing function and effective to increase a detection threshold for collision stimulus at monitoring point M. The method also includes processing the difference signal to detect a collision.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     This invention relates generally to imaging and, more particularly, to methods and systems for facilitating a reduction in unintentional collisions between an automatically moving structure and an object in proximity to the moving structure.  
         [0002]     Moving devices that are used for medical diagnostic data gathering or therapeutic purposes are subject to collisions with obstructions, or with a patient or other object in proximity to the moving device. Movement is accomplished by a servo system (i.e., a digital/electrical/mechanical system that performs mechanical movement under software control, and that also uses feedback). Various means have been devised to abort motion when a collision-in-progress is occurring. These means include pressure and proximity sensors associated with bumpers or other targeted regions on the medical device, and collision sensing associated with feedback signals within the servo system of the device. Each type of sensing has important applications. The feedback sensing signals may provide more universal sensing capability than the use of pressure and proximity sensors because the feedback will indicate resistance to the directed motion that occurs anywhere along the moving structure. However, normal operation of the servo system can also create feedback signals that are not due to a collision but that are similar to a signal that a collision would induce. Additionally, the feed forward/feedback may be processed in a way that allows the system to inherently be less aggressive in powering motion against a collision, even before a collision is detected, while at the same time retaining the desired aggressiveness in powering motion resulting from an input control signal.  
       BRIEF DESCRIPTION OF THE INVENTION  
       [0003]     In one aspect, a method for differentiating if a feedback signal is a result of an unintentional collision in a servo system is provided. The method includes injecting a feed forward term in the servo system.  
         [0004]     In another aspect, a method of configuring a servo system with an initial aggressiveness level for responding to a collision and a desired aggressiveness level for responding to an input control signal is provided. The method includes reducing the initial aggressiveness level for responding to a collision, and maintaining the desired aggressiveness level for responding to the input.  
         [0005]     In another aspect, an imaging system is provided. The imaging system includes a radiation source, a radiation detector positioned to receive radiation emitted by the source, a servo system configured to position at least one of the source, the detector, an object to be scanned, and a computer operationally coupled to the source, the detector, and the servo system. The computer is configured to inject a feed forward term in the servo system.  
         [0006]     In yet another embodiment, a computer-readable medium encoded with a program is provided. The program is configured to instruct a computer to inject a feed forward term in a servo system. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]      FIG. 1  illustrates an imaging system.  
         [0008]      FIG. 2  illustrates a mobile C-arm X-ray system.  
         [0009]      FIG. 3  illustrates a servo system.  
         [0010]      FIG. 4  illustrates a specific example of an electromechanical servos system shown more generically in  FIG. 3 .  
         [0011]      FIG. 5  illustrates a virtual loop gain Bode plot for x i .  
         [0012]      FIG. 6  illustrates a loop gain Bode plot for x 2 .  
         [0013]      FIG. 7  illustrates a simulated response output for y o  from a step input x i  (forcing function to command the mechanism to move), and for y 0  from a step input x 2  (collision signal) with and without feed forward.  
         [0014]      FIG. 8  illustrates a simulated response output for y o  from a step input x i , and for y o  from a pulse input x 2  with and without feed forward. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0015]     Herein described are methods and apparatus for facilitating the differentiation of whether a feedback signal in a servo system is the result of an legitimate operation (e.g., mechanical loading) or the result of an unintended collision.  
         [0016]      FIG. 1  illustrates an embodiment of an imaging system  10  in which the herein described apparatus and methods are implemented. Examples of imaging system  10  include an x-ray imaging system, an ultrasound imaging system, a magnetic resonance imaging (MRI) system, a single photon emission computed tomography (SPECT) imaging system, a computed tomography (CT) imaging system, and a positron emission tomography (PET) imaging system. Imaging system  10  scans an object  4 , such as a heart, a liver, or a lung, and generates original projection data. In one embodiment imaging system includes a Physiological information device (PID)  6  coupled to object  4 . An example of PID  6  includes an electrocardiograph that generates an electrocardiogram (EKG). PID  6  generates physiological cycle signals, such as EKG signals or respiratory signals, including a plurality of phases, such as cardiac phases or respiratory cycle phases.  
         [0017]     In an exemplary embodiment, and as illustrated in  FIG. 2 , imaging system  10  is a mobile C-arm X-ray system  10 . System  10  includes a C-arm  12  having inner and outer circumferences  14  and  16 , respectively, and terminating in opposing upper and lower distal ends  18  and  19 . C-arm  12 , in the exemplary embodiment has a uniformly circular C-shape, but may alternatively include any arc-shaped member.  
         [0018]     C-arm  12  is held in a suspended position by support means such as structure, generally designated at  20 , which includes a support arm  22  mounted upon a wheeled base  24 . Support arm  22  provides for rotational movement of C-arm  12  about an axis of lateral rotation  30 , either by a bearing assembly between support arm  22  and C-arm  12 , or by support  22  itself being rotatably mounted with respect to base  24 .  
         [0019]     Wheeled base  24  enables transport of C-arm  12  from a first location to a second location. As such, the wheels of the base operate as transporting means coupled to support structure  20  for transporting support arm  22  and C-arm  12  from a first location to a second location because it may be desirable to move X-ray equipment from one room to another. The mobile nature of the apparatus  10  as provided by the wheeled base  24  offers increased access by patients in many different rooms of a hospital, for example.  
         [0020]     Support arm  22  is slidably mounted to the outer circumference  16  of C-arm  12  and support structure  20  includes structure and mechanisms necessary to enable selective, sliding orbital motion of C-arm  12  about an axis of orbital rotation  26  to a selected position. Axis  26  coincides with a center of curvature of C-arm  12  and with axis of lateral rotation  30 . It will be appreciated that the sliding orbital motion causes the C-arm  12  to move through various sliding points of attachment  28  to the support arm  22 . The support structure  20  further includes mechanisms for laterally rotating the support arm  22  selectable amounts about axis of lateral rotation  30  to a selected lateral position. The combination of sliding orbital motion and lateral rotation enables manipulation of C-arm  12  in two degrees of freedom, i.e. about two perpendicular axes. This provides a kind of spherical quality to the movability of C-arm  12  (e.g., the sliding orbital motion and lateral rotation enable an X-ray source  32  coupled to C-arm  12  to be moved to substantially any latitude/longitude point on a lower hemisphere of an imaginary sphere about which C-arm  12  is moveable).  
         [0021]     System  10  includes an X-ray source  32  and an image receptor  34  as known generally in the X-ray diagnostic art, mounted upon opposing locations, respectively, on C-arm  12 . X-ray source  32  and image receptor  34  may be referred to collectively as the X-ray source/image receptor  32 / 34 . Image receptor  34  can be an image intensifier or the like. The orbital and laterally rotational manipulation of C-arm  12  enables selective positioning of X-ray source/image receptor  32 / 34  with respect to the width and length of a patient located within an interior free space  36  of C-arm  12 . More specifically, system  10  includes a servo system (i.e., a digital/electrical/mechanical system that performs mechanical movement under software control, and that also uses feedback) coupled to a computer  38 . The sliding orbital movement of C-arm  12  causes the X-ray source/image receptor  32 / 34  to move along respective arcuate movement paths. Image receptor  34  is, in one embodiment, secured to inner circumference  14  of C-arm  12  and X-ray source  32  may also be secured to inner circumference  14 .  
         [0022]     As used herein, an element or step recited in the singular and preceded with the word “a” or “an” should be understood as not excluding plural the elements or steps, unless such exclusion is explicitly recited. Furthermore, references to “one embodiment” of the present invention are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features.  
         [0023]     In one embodiment, computer  38  includes a device (not shown), for example, a floppy disk drive or CD-ROM drive, for reading instructions and/or data from a computer-readable medium, such as a floppy disk or CD-ROM. In another embodiment, computer  38  executes instructions stored in firmware (not shown). Computer  38  is programmed to perform functions described herein, and as used herein, the term computer is not limited to just those integrated circuits referred to in the art as computers, but broadly refers to processors, microcontrollers, microcomputers, programmable logic controllers, application specific integrated circuits, and other programmable circuits, and these terms are used interchangeably herein.  
         [0024]     Although the specific embodiment mentioned above refers to a mobile C-arm x-ray apparatus, the herein described methods equally apply to all other imaging modalities, as well as any application utilizing servos around objects which it is desirable not to collide with.  
         [0025]     Additionally, although the herein described methods are described in a medical setting, it is contemplated that the benefits of the methods accrue to non-medical imaging systems such as those systems typically employed in an industrial setting or a transportation setting, such as, for example, but not limited to, a baggage scanning system for an airport, other transportation centers, government buildings, office buildings, and the like. The benefits also accrue to micro x-ray, PET, and CT systems which are sized to study lab animals as opposed to humans.  
         [0026]     The herein described methods and apparatus use feed forward to enhance the detection of an unwanted collision between an electromechanical motion system and some obstacle in the path of the intended motion. Additionally, the method allows optimization of feed forward and feedback in such a way that allows the system to inherently be less aggressive in powering motion against a collision, even before a collision is detected, while at the same time retaining the desired aggressiveness in powering motion resulting from an input control signal (forcing function).  FIG. 3  illustrates a servo system  100  including a feedback mechanism  102  (block H) that receives information about motion or position, and converts the information into a signal that can be subtracted from an input forcing function x i    104 . x i  forcing function  104  is the control signal or digital command that directs the entire servo system to respond, such that a mechanical output y o    106  moves in an intended way. A plurality of blocks  108  (G 1  and G 2 ) represent various parts of the servo system structure such as data processed in a computer, an electrical motor, and a mechanism that converts rotation of the motor shaft into a useful motion or position of the device. A signal x 2  represents a load function  110 , e.g., a parameter such as friction or other mechanical loading that tends to resist movement driven by a motor shaft. A monitor point  112  (M) provides data to the system that represents the difference between x i  forcing function  104  and a feedback signal  114  that has passed through H feedback block  102 . The value of M is generally small (depending on the many parameters that define servo system  100 ). However, M may temporarily have larger values when servo system  100  is being subjected to certain types of stimulus transients that are applied to either x i  or x 2 . By proper interpretation of M, it is possible to determine if servo system  100  has encountered a (undesired) collision-in-progress. Under this condition servo system  100  performance can be altered to avoid the unwanted result of a collision from a fully executed movement. Feed forward through a block F 1    116  allows special processing of the x i  forcing function to achieve an enhanced detectability to collisions at M  112 . Note that F 1  could be summed into the system at points other than that shown in  FIG. 3 , with variations in the results. Also, monitor point M  112  can be placed at locations other than that shown in  FIG. 3 , with variations in the results. Also, multiple points for injecting feedback ( 114 ) could be used, in addition to those points shown in  FIG. 3 . Depending on characteristics of any system, the placement of feed forward injection, the monitoring point, and feedback may vary.  
         [0027]     One can consider the various parts of servo system  100  illustrated in  FIG. 3  as being represented in the Laplace domain. Then, treating the two inputs x i  and x 2  separately by superposition, and by using Mason&#39;s law, one obtains  
                   y   0       x   i       =         (       F   1     +   1     )     ⁢     G   1     ⁢     G   2         1   +       G   1     ⁢     G   2     ⁢   H           ,             1   ⁢   A     )                   y   0       -     x   2         =       G   2       1   +       G   1     ⁢     G   2     ⁢   H                   1   ⁢   B     )             
 
         [0028]     G 1  can be chosen to make y o /x 2  behave optimally for collision detection and avoidance. An alternative version of G 1  is selected and defined as G 1 ′, which is chosen to make y o /x i  behave optimally from the point of view of the forcing function x i  but without using feed forward (F 1 =0). Finally, using G 1  and F 1  (but not G 1 ′), require a transfer function for y o /x i  that behaves identically to the prior y o /x i , and solve for the required F 1  to force this result. The following equations show this process.  
                     (       F   1     +   1     )     ⁢     G   1     ⁢     G   2         1   +       G   1     ⁢     G   2     ⁢   H         =         G   1   ′     ⁢     G   2         1   +       G   1   ′     ⁢     G   2     ⁢   H           ⁢     
     ⁢     Solving   ⁢           ⁢   for   ⁢           ⁢     F   1     ⁢     :               2   )                 F   1     =           G   1   ′     ⁡     (     1   +       G   1     ⁢     G   2     ⁢   H       )       -       G   1     ⁡     (     1   +       G   1   ′     ⁢     G   2     ⁢   H       )             G   1     ⁡     (     1   +       G   1   ′     ⁢     G   2     ⁢   H       )                 3   )             
 
         [0029]     Thus, using a feed forward term F 1  in the servo system enables it to be optimized for both y o /x i  and y o /x 2 , such that collision detection monitoring at M is enhanced without compromising responsiveness to the forcing function x i . Additionally injecting a feed forward term to optimize y o /x i  allows for the separate and independent optimizing of y o /x 2  via the standard existing loop parameters without the influence of feed forward.  
         [0030]      FIG. 4  illustrates a specific example of an electromechanical servos system shown generically in  FIG. 3 . The closed loop response for  FIG. 4  inputs x i  and x 2  are given  
               y   0     =         x   i     ⁢                 (     F   +   1     )     ⁢         K   2     ⁢     K   3     ⁢     K   5           Z   5     ⁢     Z   6         ⁢     s   2       +                   (     F   +   1     )     ⁢     (       1     Z   5       +     1     Z   6         )     ⁢     K   2     ⁢     K   3     ⁢     K   5     ⁢   s     +       (     F   +   1     )     ⁢     K   2     ⁢     K   3     ⁢     K   5                           1       P   2     ⁢     P   6         ⁢     s   4       +       (       1     P   2       +     1     P   6         )     ⁢     s   3       +       (           K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5           Z   5     ⁢     Z   6         +   1     )     ⁢     s   2       +                   (       1     Z   5       +     1     Z   6         )     ⁢     K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5     ⁢   s     +       K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5                   ⁢     
     -       x   2     ⁢               K   1     ⁢     K   3         P   6       ⁢     s   2       +       K   1     ⁢     K   3     ⁢   s                   1       P   2     ⁢     P   6         ⁢     s   4       +       (       1     P   2       +     1     P   6         )     ⁢     s   3       +       (           K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5           Z   5     ⁢     Z   6         +   1     )     ⁢     s   2       +                   (       1     Z   5       +     1     Z   6         )     ⁢     K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5     ⁢   s     +       K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5                             4   )               
         [0031]     Next, for y o /x i  preferred terms K′ 5  and Z′ 5  are selected instead of K 5  and Z 5 . With no feed forward (F=0) this result in:  
                 y   0       x   i       =               K   2     ⁢     K   3     ⁢     K   5   ′           Z   5   ′     ⁢     Z   6         ⁢     s   2       +       (         K   5   ′       Z   5   ′       +       K   5   ′       Z   6         )     ⁢     K   2     ⁢     K   3     ⁢   s     +       K   2     ⁢     K   3     ⁢     K   5   ′                     1       P   2     ⁢     P   6         ⁢     s   4       +       (       1     P   2       +     1     P   6         )     ⁢     s   3       +       (           K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′           Z   5   ′     ⁢     Z   6         +   1     )     ⁢     s   2       +                   (       1     Z   5   ′       +     1     Z   6         )     ⁢     K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′     ⁢   s     +       K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′                         5   )             
 
 From inspection of  FIG. 4  it is clear that 6) M=x i −y 0 K 4  
 
 F can be determined using equation 3) to obtain equation 7).  
             F   =               K   5   ′     ⁢         s     Z   5   ′       +   1     s     ×         s     Z   6       +   1         s     P   6       +   1       ×     K   2     ×                 (     1   +       K   5     ×         s     Z   5       +   1     s     ×         s     Z   6       +   1         s     P   6       +   1       ×     K   2     ×     1       s     P   2       +   1       ×       K   3     s     ×     K   4         )     -                 K   5     ×         s     Z   5       +   1     s     ×         s     Z   6       +   1         s     P   6       +   1       ×     K   2     ×     (     1   +       K   5   ′     ×         s     Z   5   ′       +   1     s     ×                             s     Z   6       +   1         s     P   6       +   1       ×     K   2     ×     1       s     P   2       +   1       ×       K   3     s     ×     K   4       )                     K   5     ×         s     Z   5       +   1     s     ×         s     Z   6       +   1         s     P   6       +   1       ×     K   2     ×               (     1   +       K   5   ′     ×         s     Z   5   ′       +   1     s     ×         s     Z   6       +   1         s     P   6       +   1       ×     K   2     ×     1       s     P   2       +   1       ×       K   3     s     ×     K   4         )                     7   )             
 
 Rearranging equation 7), one obtains  8 )  
             F   =               (             K   2     ⁢     K   5   ′           Z   5   ′     ⁢     Z   6         ⁢     s   2       +       (       1     Z   5   ′       +     1     Z   6         )     ⁢     K   2     ⁢     K   5   ′     ⁢   s     +       K   2     ⁢     K   5   ′         )     ⁢     (         1       P   2     ⁢     P   6         ⁢     s   4       +                       (       1     P   2       +     1     P   6         )     ⁢     s   3       +       (           K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5           Z   5     ⁢     Z   6         +   1     )     ⁢     s   2       +                       (       1     Z   5       +     1     Z   6         )     ⁢     K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5     ⁢   s     +       K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5         )     -                 (             K   2     ⁢     K   5           Z   5     ⁢     Z   6         ⁢     s   2       +       (       1     Z   5       +     1     Z   6         )     ⁢     K   2     ⁢     K   5     ⁢   s     +       K   2     ⁢     K   5         )     ⁢     (         1       P   2     ⁢     P   6         ⁢     s   4       +                       (       1     P   2       +     1     P   6         )     ⁢     s   3       +       (           K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′           Z   5   ′     ⁢     Z   6         +   1     )     ⁢     s   2       +                     (       1     Z   5   ′       +     1     Z   6         )     ⁢     K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′       +       K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′         )                     (             K   2     ⁢     K   5           Z   5     ⁢     Z   6         ⁢     s   2       +       (       1     Z   5       +     1     Z   6         )     ⁢     K   2     ⁢     K   5     ⁢   s     +       K   2     ⁢     K   5         )     ⁢     (         1       P   2     ⁢     P   6         ⁢     s   4       +                       (       1     P   2       +     1     P   6         )     ⁢     s   3       +       (           K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′           Z   5   ′     ⁢     Z   6         +   1     )     ⁢     s   2       +                     (       1     Z   5   ′       +     1     Z   6         )     ⁢     K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′     ⁢   s     +       K   2     ⁢     K   3     ⁢     K   4     ⁢     K   5   ′         )                     8   )             
 
 For simplification, a change of notation is used, referencing equation 8).  
             F   =                 (       As   2     +   Bs   +   C     )     ⁢     (       Ds   4     +     Es   3     +     Ps   2     +   Gs   +   H     )       -                 (       Is   2     +   Js   +   K     )     ⁢     (       Ds   4     +     Es   3     +     Ls   2     +   Ms   +   N     )                 (       Is   2     +   Js   +   K     )     ⁢     (       Ds   4     +     Es   3     +     Ls   2     +   Ms   +   N     )                 9   )             
 
 Finally,  
             F   =                 (     AD   -   ID     )     ⁢     s   6       +       (     AE   +   BD   -   IE   -   JD     )     ⁢     s   5       +                   (     AP   +   BE   +   CD   -   IL   -   JE   -   KD     )     ⁢     s   4       +                   (     AG   +   BP   +   CE   -   IM   -   JL   -   KE     )     ⁢     s   3       +                   (     AH   +   BG   +   CP   -   IN   -   JM   -   KL     )     ⁢     s   2       +                   (     BH   +   CG   -   JN   -   KM     )     ⁢   s     +   CH   -   KN                     IDs   6     +       (     IE   +   JD     )     ⁢     s   5       +       (     IL   +   JE   +   KD     )     ⁢     s   4       +     (     IM   +   JL   +                       KE   )     ⁢     s   3       +       (     IN   +   JM   +   KL     )     ⁢     s   2       +       (     JN   +   KM     )     ⁢   s     +   KN                     10   )             
 
         [0032]     For the example application, the loop gain Bode plot that is optimized for x i  is given in  FIG. 5  with associated optimized parameters listed in Table 1. Note, the loop gain Bode plot in  FIG. 5  was optimized for x i  using K 5 ′ and Z 5 ′. Because of the feed forward parameter F (equation 10), this plot&#39;s phase margin can be used to predict the transient response of y o /x i . Note that for true stability, a Bode plot using K 5  and Z 5  (not K 5 ′ and Z 5 ′) can be used.  
                                                         TABLE 1                                   System   Servo                   Parameters   Inputs   Calculations                                        Kcomp =   0.07   Tm =   0.086           K4 =   1   K5′ =   0.006020           Z5′ =   5   P2 =   11.655           Tsample period =   0.002   Z6 =   11.656           Tcomp time =   0.002   K2 =   41.841           w start =   0.1   K1 =   2626.004           Scale Factor =   1.2   K3 =   318.310           Quad Enc Slits =   500   Km =   1.000           R =   1.5   Kloop@1r =   80.177           Ke =   0.0239           J =   3.27E−05           Kcount =   0.086           Kleadscrew =   318.31                      
 
         [0033]     The loop gain Bode plot that is optimized for x 2  is given in  FIG. 6  with associated optimized parameters listed in Table 2. The plot was optimized for x 2  using K 5  and Z 5 . Note, the plots margins can be used to predict the transient response of y o /x 2 .  
                                                         TABLE 2                                   System                       Parameters   Servo Inputs   Calculations                                        Kcomp =   0.01395   Tm =   0.086           K4 =   1   K5 =   0.001200           Z5 =   3   P2 =   11.655           Tsample period =   0.002   Z6 =   11.656           Tcomp time =   0.002   K2 =   41.841           w start =   0.1   K1 =   2626.004           Scale Factor =   1.2   K3 =   318.310           Quad Enc Slits =   500   Km =   1.000           R =   1.5   Kloop@1r =   15.978           Ke =   0.0239           J =   3.27E−05           Kcount =   0.086           Kleadscrew =   318.31                      
 
         [0034]     For an actual system represented by the example application, some blocks of  FIG. 4  (including the F term given in equation 10) could be implemented in a computer and those functions accomplished via software programming using z-transforms of the Laplace equations. Other parts of the system can be realized in the form of electronic circuitry, an electric motor, and mechanical drive parts and other physical mechanisms. By proper use of equations 4), 5), and 6) a simulation of responses for the example application can be obtained, as though the feed forward term defined in equation 10) had been applied to an actual servo system.  
         [0035]     In  FIG. 7  the simulated response output, y o , is shown for a step response input from x i  (forcing function to command the mechanism to move) for the topology of  FIG. 4 . Also shown in  FIG. 7  are the monitor point signals, M, for a step at x 2  (representing a collision) that would occur with and without using feed forward. The peak M monitor signal is larger when feed forward is applied, having a ratio of about 2.4. Note, the collision step is amplified in the plot so it can be seen, due to the units used in  FIG. 7 . Because the example system uses a feedback constant of 1 (that is, K 4=1 ), note that the output y o  is equivalent in magnitude to M (differing only by having an opposite polarity). Therefore, the plot for M/x 2  also represents the plot for y o /x 2  (except for polarity). It is noted that M/x 2  with feed forward changes more quickly than M/x 2  without feed forward. This indicates that y o  would also change more quickly, and that y o  would therefore be more responsive to the collision signal x 2 . With proper use of feed forward, the servo system would therefore not be as aggressive in powering motion through the collision, even before the M monitor point signal has been processed as a means to detect collision (and initiate a command to stop motion).  
         [0036]     In  FIG. 8  the simulated response output, y o , is shown for a step response input from x i , and is identical to the simulation for y o  shown in  FIG. 7 . Also shown in  FIG. 8  are the monitor point signals, M, that would occur with and without using feed forward for a 20 msec pulse at x 2  (representing a bump that might occur when an imperfect mechanism is in motion). In this case the ratio for the peak M monitor signal with and without feed forward is about 1.4. Note, the pulse is amplified in the plot so it can be seen, due to the units used in  FIG. 8 .  
         [0037]     The ratio of the simulated ratios with/without feed forward is 2.4/1.4=1.7. This means that the example servo system, when stimulated as described, can detect a smaller legitimate collision without also being subject to false alarms from a bump due to an imperfect mechanism. Therefore one technical effect is the enhanced sensitivity to collision stimulus. Because of the enhanced sensitivity to collision stimulus, the detection threshold at M could be increased. Then the servo system is less likely to generate a false alarm from a monitor signal that results from the x i  forcing function.  
         [0038]     While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.