Patent Publication Number: US-8985354-B2

Title: Movement system configured for moving a payload in a plurality of directions

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Patent Application No. 61/555,859 filed on Nov. 4, 2011, which is hereby incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to a movement system that is configured for moving a mass in a plurality of directions. 
     BACKGROUND 
     Overhead bridge cranes are widely used to lift and relocate large payloads. Generally, the displacement in a pick and place operation involves three translational degrees of freedom and a rotational degree of freedom along a vertical axis. This set of motions, referred to as a Selective Compliance Assembly Robot Arm (“SCARA”) motions or “Schönflies” motions, is widely used in industry. A bridge crane allows motions along two horizontal axes. With appropriate joints, it is possible to add a vertical axis of translation and a vertical axis of rotation. A first motion along a horizontal axis is obtained by moving a bridge on fixed rails while the motion along the second horizontal axis is obtained by moving a trolley along the bridge, perpendicularly to the direction of the fixed rails. The translation along the vertical axis is obtained using a vertical sliding joint or by the use of a belt. The rotation along the vertical axis is obtained using a rotational pivot with a vertical axis. 
     There are partially motorized versions of overhead bridge cranes that are displaced manually along horizontal axes and rotated manually along the vertical axis by a human operator, but that include a motorized hoist in order to cope with gravity along the vertical direction. Also, some bridge cranes are displaced manually along all of the axes, but the weight of the payload is compensated for by a balancing device in order to ease the task of the operator. Such bridge cranes are sometimes referred to as assist devices. Balancing is often achieved by pressurized air systems. These systems need compressed air in order to maintain pressure or vacuum—depending on the principle used—which requires significant power. Also, because of the friction in the compressed air cylinders, the displacement is not very smooth and can even be bouncy. Balancing can be achieved using counterweights, which add significant inertia to the system. Although helpful and even necessary for the vertical motion, such systems attached to the trolley of a bridge crane add significant inertia regarding horizontal motion due to moving the mass of these systems. In the case of balancing systems based on counterweights, the mass added can be very large, even larger than the payload itself. If the horizontal traveling speed is significant, the inertia added to the system becomes a major drawback. 
     There are also fully motorized versions of such bridge cranes that require powerful actuators, especially for the vertical axis of motion which has to support the weight of the payload. These actuators are generally attached to the trolley or bridge and are then in motion. The vertical translation actuator is sometimes attached to the bridge and linked to the trolley by a system similar to what is used in tower cranes. 
     SUMMARY 
     A movement system is configured for moving a payload. The movement system includes a bridge crane, a trolley, and a movement device. The bridge crane is configured for movement along an X axis. The trolley is movably attached to the bridge crane and configured for movement along a Y axis, in perpendicular relationship to the X axis. The movement device depends from the trolley. The movement device includes an attachment portion, a plurality of housings, a first curved element, a second curved element, a cable, and a cable angle sensor. The housings each operatively extend from the attachment portion. The first curved element and the second curved element extend between respective ends. The ends of the first and second curved elements are pivotally attached to a respective one of the plurality of housings. Each of the first and second curved elements form a partial circle. The first curved element defines a first slot and the second curved element defines a second slot. The first curved element perpendicularly overlaps with the second curved element such that the first slot of the first curved element is in perpendicular relationship to the second slot of the second curved element. The first curved element is configured to pivot about a first axis and the second curved element is configured to pivot about a second axis, which extends in perpendicular relationship to the first axis. The cable extends from the attachment portion and through each of the first slot and the second slot. The cable is configured to pivot relative to the attachment portion such that the cable angularly displaces at least one of the first and second curved elements about the respective first and second axis. The cable angle sensor is configured to measure the angular displacement of the at least one of the first and second curved elements. 
     A movement device is configured to determine a direction of intended movement of a payload. The movement device includes an attachment portion, a plurality of housings, a first curved element, a second curved element, a cable, and a cable angle sensor. Each of the housings operatively extend from the attachment portion. The first and second curved elements each extend between respective ends. The ends of the first and second curved elements are pivotally attached to a respective one of the plurality of housings. Each of the first and second curved elements form a partial circle. The first curved element defines a first slot and the second curved element defines a second slot. The first curved element perpendicularly overlaps with the second curved element such that the first slot of the first curved element is in perpendicular relationship to the second slot of the second curved element. The first curved element is configured to pivot about a first axis and the second curved element is configured to pivot about a second axis, which extends in perpendicular relationship to the first axis. The cable extends from the attachment portion and through each of the first and second slots. The cable is configured to pivot relative to the attachment portion such that the cable angularly displaces at least one of the first and second curved elements about the respective first and second axis. The cable angle sensor is configured to measure the angular displacement of the at least one of the first and second curved elements. 
     A method of moving a movement device along at least one of an X axis and a Y axis includes providing a cable angle sensor configured to measure angular displacement of at least one of a first and a second curved element about a respective first and second axis. A cable is disposed vertically through each of a first and a second slot defined in the respective first and second curved element. An angle is imparted to the cable such that the cable causes an angular displacement of at least one of the first and second curved elements about the respective first and second axis. The angular displacement of the at least one of the first and second curved elements about the respective first and second axis is determined. The movement device is moved along the at least one of the X axis and the Y axis in response to the determination of the angular displacement of the at least one of the first and second curved elements about the respective first and second axis until the cable is vertical. 
     The above features and advantages, and other features and advantages of the present disclosure, will be readily apparent from the following detailed description of the embodiment(s) and best mode(s) for carrying out the described invention when taken in connection with the accompanying drawings and appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic perspective view of a movement system including a movement device which is connected to a support structure and configured for moving a payload attached to a cable; 
         FIG. 2  is a schematic perspective view of cable angle sensor configured for measuring an angular displacement of the cable; 
         FIG. 3  is an exploded schematic perspective view of a housing, sensors, and a shaft of the cable angle sensor of  FIG. 2 ; 
         FIG. 4  is a schematic perspective view of the movement device supporting the payload; 
         FIGS. 5A-5C  are schematic diagrammatic views of parameter definitions of the movement system; 
         FIG. 6  is a schematic block diagram of a high frequency oscillation scheme usable with the controller shown in  FIG. 1 ; 
         FIG. 7  is a schematic block diagram of a control scheme usable with the controller shown in  FIG. 1 ; 
         FIG. 8  is a schematic block diagram of an acceleration estimation with a fusion method; 
         FIG. 9  is a schematic block diagram of a float mode control scheme; and 
         FIG. 10  is another schematic block diagram of a control scheme of the float mode. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to the drawings, wherein like reference numbers refer to like components, a movement system  10  configured for moving a payload  12  in a plurality of directions is shown at  10  in  FIG. 1 . The movement system  10  is mounted to a stationary support structure  14  that is configured to support the movement system  10  and the payload  12 . The support structure  14  includes, but is not limited to a pair of parallel rails  16  or runway tracks. 
     Referring to  FIG. 1 , the movement system  10  includes a bridge crane  18 , a trolley  20 , and a movement device  22 . The bridge crane  18  is a structure that includes at least one girder  30  that spans the pair of parallel rails  16 . The bridge crane  18  is adapted to carry the payload  12  along an Y axis  17 . The trolley  20  is movably attached to girders  30  of the bridge crane  18  such that the trolley  20  is adapted to carry the payload  12  along an X axis  19 , in generally perpendicular relationship to the Y axis  17 . The movement device  22  is operatively attached to the trolley  20 . A Z axis  21  extends in a vertical direction, with respect to the ground G, and is defined between the intersection of the X axis  19  and the Y axis  17 . 
     Referring to  FIGS. 1 and 2 , the movement device  22  includes a cable angle sensor  24 , a suspended cable  26 , a cart  28 , and a controller  32 . The cable  26  is configured for supporting the payload  12 . The cable angle sensor  24  is configured to measure two degrees-of-freedom of the cable  26 . Additionally, the movement device  22  is configured to allow the operator  33  to place their hands  35  anywhere directly on the payload  12 . By being in close contact with the payload  12 , it is easier for the operator to manipulate and to guide the movement device  22 . When the operator is not restricted as to where to place their hands  35 , the operator&#39;s  33  hand  35  placement can be adjusted to be more efficient, productive, comfortable, and to provide the operator with a clearer view of the task at hand. Direct placement of the operator&#39;s  33  hands  35  on the payload  12  may also allow the operator to maneuver the payload  12  with only one hand  35 , while using the other hand  35  for another aspect of the task. Additionally, direct access to the payload  12  may allow many operators  33  to contact the payload  12  at the same time, since the system is configured to measure the result of the operators  33  combined applied forces to the payload  12 . 
     Referring to  FIGS. 1 and 5 , during operation, the operator  33  imparts an angle θ 1  and θ 2  to the cable  26 , by pushing or otherwise applying a force F to the payload  12  in an X-Y plane. These angles θ 1  and θ 2  are measured by the cable angle sensor  24 . The controller  32  is operatively connected to the movement device  22 . The controller  32  is configured to move the cart  28  along the X axis  19  and/or the Y axis  17  in order to keep the cable  26  vertical (along the Z axis  21 ). Thus, the cart  28  moves in the direction desired by the operator  33  (direction of cable  26  displacement), while controlling the cable  26  sway, resulting in assistance to the operator  33  in moving the payload  12  along the X axis  19  and the Y axis  17 . Since the controller  32  ensures that the cable  26  remains vertical, the operator  33  is not required to stop the payload  12  manually, since the controller  32  manages to cause the payload  12  to stop. Additionally, an autonomous mode, where the payload  12  position is prescribed, while reducing cable  26  sway may also be provided. 
     The cable angle sensor  24  may be configured to be absolute, precise, low cost, and provide high resolution in order to achieve the control objectives. The controller  32  is based on simplified cable  26  dynamics with state space control to provide cooperative motion and autonomous motion. The controller  32  may be modified to vary parameters, such as the cable  26  length. Additionally, the controller  32  does not need a mass of the cart  28  or the payload  12 , but rather, adapts to varying parameters while being robust and intuitive to the operator  33 . 
     Referring again to  FIG. 2 , the cable angle sensor  24  includes a first curved element  36  and a second curved element  38 . Each curved element extends between respective ends  40 . The curved elements  36 ,  38  each form a partial circle and are concentric such that they share a common center. The first element  36  defines a first slot  44  and the second element  38  defines a second slot  46 . Each slot extends longitudinally between the respective ends  40 . The first curved element  36  perpendicularly overlaps the second curved element  38  such that the slot of the first curved element  36  is in perpendicular relationship to the slot of the second curved element  38 . The ends  40  of the curved elements  36 ,  38  are pivotally attached to a respective housing  48 . The housings  48  are operatively attached to a mounting plate  50  ( FIG. 4 ) such that the first curved element  36  pivots about a first axis  52  and the second curved element  38  pivots about a second axis  54 , which extends in perpendicular, intersecting relationship to the first axis  52 . A shaft  56  pivotally interconnects each of the ends  40  and the respective housing  48 . More specifically, referring to  FIG. 3 , the shafts  56  are supported in the respective housing  48  by two bearings  58 , ensuring that the rotation of the shaft  56  about the respective first and second axis  52 ,  54  is straight and the friction is low. 
     Referring to  FIG. 4 , the cable  26  passes through the first slot  44  and the second slot  46 . A pivot point  60  of the cable  26  should be aligned with each of the slots  44 ,  46  such that the cable  26  passes straight through the curved elements  36 ,  38  to prevent biased readings that might otherwise result due to the cable  26  bending around the curved elements  36 ,  38 . Additionally, a portion of the slot  44  of the first curved element  36  overlaps with a portion of the slot  46  of the second curved element  38 , throughout the angular displacement θ 1  and θ 2  of the first and second curved elements  36 ,  38 , caused by the movement of the cable  26 , which passes through the slots  44 ,  46 . A guide  85  may be used to make sure the cable pivot point  60  stays the same. The slots  44 ,  46  may be configured to be slightly larger than the diameter of the cable  26 . Flexible elements may be disposed in the slots  44 ,  46  to close the gap. The flexible elements may help prevent backlash from the cable  26  interfering with the slot, while maintaining easy movement of the cable  26  within the slots  44 ,  46 . 
     Because there are two shafts  56  for each of the first axis  52  and the second axis  54 , and each shaft  56  has two sides  62 , several sensors  64  may be used for each axis. By way of a non-limiting example, an encoder  66  and a Hall effect sensor  68  may be used for each of the first axis  52  and the second axis  54 . Although only one sensor per axis may be sufficient, combining the encoder  66  with the Hall effect sensor  68  provides many benefits. First of all, the signals from the encoder  66  and the Hall effect sensor  68  may be combined using data fusion to obtain a signal of better quality. Second of all, it is possible to compare both signals to detect problems, i.e., inaccuracies in the individual signals. Finally, the absolute signal of the Hall effect sensor  68  may be used, while taking advantage of the encoder  66  precision. Other sensors  64  could also be used. Absolute encoders  66 , potentiometers or linear accelerometers (used as inclinometers) could be used as position sensor. A gyroscope could be used to obtain the angular velocity while an accelerometer could be used to obtain angular acceleration. Accelerometers or gyroscopes placed on the slotted parts could also help determine different dynamical effects. Photointerruptors could also be used at strategic places. Finally, the above signal can be derived/integrated to obtain corresponding signals. 
     The cart  28  is configured for moving the bridge crane  18  and/or the trolley  20  along the respective X axis  19  and Y axis  17  in response to the application of the force F to the payload  12 . As the force F is applied to the payload  12  a direction along the X axis  19  and/or the Y axis  17 , movement of the cable  26  within the slots  44 ,  46  of the curved elements  36 ,  38  causes the curved elements  36 ,  38  to rotate an angle θ 1 , θ 2  about the respective first and second axes  52 ,  54 . The sensors  64  measure an angle of rotation θ 1 , θ 2  of the curved elements  36 ,  38  about the respective first and second axes  52 ,  54 . 
     In order to be desensitized to small angle measurement precision errors, a deadband on the angle may be used. The deadband is an area of a sign range where no action on the system occurs. The movement device  22  may also be excited by small amplitude, high frequency unmodeled dynamics or it may be difficult for the control to manage high frequency oscillations. During oscillations, when the cable  26  is close to a vertical position, since the angle measurement often changes sign, it becomes difficult to suppress the oscillations. An algorithm, shown as an oscillation logic block  70 , is provided to compensate for high frequency oscillations, while keeping precision and performance to keep the cable  26  vertical. It should be appreciated that one of the signals may be, for example, θ 1 . For a small deadband, θ db1  is used to cope with precision errors of the angle measurements. Two other angles are defined, θ db2  and θ db3 . The signal θ p0  is determined in a deadband block  72  and expressed as follows: 
               θ     p   ⁢           ⁢   0       =     {         0           if   -     θ     db   ⁢           ⁢   1         &lt;   θ   &lt;     θ     db   ⁢           ⁢   1                   θ   -     θ     db   ⁢           ⁢   1                 if   ⁢           ⁢   θ     &gt;     θ     db   ⁢           ⁢   1                   θ   +     θ     db   ⁢           ⁢   1                 if   ⁢           ⁢   θ     &lt;     -     θ     db   ⁢           ⁢   1                         
and the signal θ p1  is determined in a deadband and saturation block  74  and expressed as follows:
 
     
       
         
           
             
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     The signal θ p0  then corresponds to the input angle signal above θ db1  while θ p1  corresponds to the input signal between θ db2  and θ db3 . In order to remove the high frequency oscillations from θ p1 , this signal is further processed. Because the natural and desired cable  26  position is vertical, a filtering algorithm may be used, as shown at  70  in  FIG. 6 . The absolute signal of θ p1  is determined in an absolute logic block  76  and then the absolute signal passes through a rate limiter block  78 . The rising limit is low and the falling limit is high, such that it takes time for the output signal to increase, filtering high frequency oscillations. However, the signal of the θ p1  can return to zero rapidly, avoiding a phase shift. This signal is then multiplied by the sign of θ p1 , stored in a sign block  82 . The resulting signal, can then optionally be slightly filtered with a usual low pass filter at a low pass block  80 , resulting in the signal θ p2 . Although, θ p0  and θ p2  can be used individually in the control, they can also be grouped as:
 
θ pf =θ p0 +θ p2  
 
     Referring to  FIGS. 5A-5C , a relation between the angles β i  and θ i  needs to be obtained. A unit vector e, is aligned with the cable  26  and the cable&#39;s  26  endpoint coordinates are [X S , Y S , Z S ] T . The cross product between e and unit vector [0 1 0] gives the normal to the plan σ 1  in which the cable  26  lies. The dot product of these results with the unit vector [1 0 0] leads to the angle θ 1  cosine. The angle θ 2  cosine is obtained similarly. Also, using the fact that X 2 +Y 2 +Z 2 =1: 
                 dynamical   ⁢           ⁢   cos   ⁢           ⁢     θ   1       =         1   -     X   s   2     -     Y   s   2             1   -     Y   s   2             ,       cos   ⁢           ⁢     θ   2       =         1   -     X   s   2     -     Y   s   2             1   -     X   s   2                   
The unit vector e coordinates are:
 
 X   S =sin θ 1  cos β 1  
 
 Y   S =sin β 1  
 
 Z   S =cos θ 1  cos β 1  
 
The correspondence is:
 
               cos   ⁢           ⁢     β   1       =       cos   ⁢           ⁢     θ   2           1   -       sin   2     ⁢     θ   1     ⁢     sin   2     ⁢     θ   2                           sin   ⁢           ⁢     β   1       =       cos   ⁢           ⁢     θ   1     ⁢   sin   ⁢           ⁢     θ   2           1   -       sin   2     ⁢     θ   1     ⁢     sin   2     ⁢     θ   2                   
Taking the derivatives of any questions of the previous equation leads to:
 
     
       
         
           
             
               
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     In the following, the equations of motion are first obtained with a complete model called coupled motion. Then, with simplifications, a simplified model is obtained. With reference to  FIGS. 1-4  and the parameters defined in  FIGS. 5A-5C , the measured variable from the cable angle sensors  24  are θ 1 , corresponding the first axis  52 , and θ 2 , corresponding to the second axis  54 . The equations of motion for the payload  12  position are:
 
 X   p   =X   C   +L   p  sin θ 1  cos β 1  
 
 Y   p   =Y   C   +L   p  sin β 1  
 
 Z   p   =L   p  cos θ 1  cos β 1  
 
where X p , Y p  and Z p  are the payload  12  center of mass  42  position in fixed coordinates, X C  and Y C  are the cart  28  coordinates in fixed coordinates, and L p  is the distance between the cable pivot point  60  and the payload  12  center of mass  42 . The potential energy is provided as follows:
 
 V=−mgL   p  cos β 1  cos θ 1  
 
where m is the payload  12  mass and the kinetic energy is expressed as:
 
             T   =         1   2     ⁢     M   x     ⁢       X   .     c   2       +       1   2     ⁢     M   y     ⁢       X   .     c   2       +       1   2     ⁢     m   (         X   .     p   2     +       Y   .     p   2     +       Z   .     p   2                   
where M X  is the cart  28  mass in the X direction and M Y  is the cart  28  mass in the Y direction. One should note that the cable  26  mass was neglected. The equations of motion are obtained from the previous two equations and the Lagrange method as follows:
 
 F   X   =M   x   {umlaut over (X)}   c   +m ( {umlaut over (X)}   c   +{umlaut over (L)}   p  cos β 1  sin θ 1   −L   p  sin β 1  sin θ 1 {umlaut over (β)} 1   −L   p  cos β 1  sin θ 1 {dot over (β)} 1   2   −L   p  cos β 1  sin θ 1 {dot over (θ)} 2 +2 cos β 1  cos θ 1   {dot over (L)}   p {dot over (θ)} 1 −2 L   p  sin β 1  cos θ 1 {dot over (β)} 1 {dot over (θ)} 1 −2 {dot over (L)}   p {dot over (β)} 1  sin β 1  sin θ 1   +L   p  cos θ 1  cos β 1 {umlaut over (θ)} 1 )
 
 F   Y   =M   y   Ÿ   c   +m ( Ÿ   c +2 {dot over (L)}   p {dot over (β)} 1  cos β 1   −L   p {dot over (β)} 1   2  sin β 1   +L   p  cos β 1 {umlaut over (β)} 1   +{umlaut over (L)}   p  sin β 1 )
 
 F   L   =m ( {umlaut over (X)}   c  cos β 1  sin θ 1   +{umlaut over (L)}   p   +Ÿ   c  sin β 1   −L   p {dot over (β)} 1   2   −L   p {dot over (θ)} 1   2  cos 2 β 1   −g  cos β 1  cos θ 1 )
 
 F   Z =0= M   z   {umlaut over (Z)}   c   +m ( {umlaut over (Z)}   c   +L  cos θ 1 {dot over (θ)} 1   2   +L  sin θ 1 {umlaut over (θ)} 1   +L  cos θ 2 {dot over (θ)} 2   2   +L  sin θ 2 {umlaut over (θ)} 2   +g )
 
 F   θ1 =0= m ( L{umlaut over (θ)}   1   +{umlaut over (x)}  cos θ 1   +g  sin θ 1 +2 {dot over (L)}   p {dot over (θ)} 1  cos β 1 −2 L   p {dot over (θ)} 1 {dot over (β)} 1  sin β 1 ) L  cos β 1  
 
 F   β1 =0= m ( L   p {umlaut over (β)} 1   +L   p   ÿ  cos β 1   −{umlaut over (x)}  sin β sin θ+2{dot over (β)} 1   {dot over (L)}+L   p {dot over (θ)} 1   2  cos β 1  sin β 1   +mg  sin β 1  cos θ 1 ) L   p  
 
     One should note that similar equations could be found with the other angle representation as (θ 2 , β 2 ). Additionally, the coupling between angles θ 1  and θ 2  is negligible for relatively small angles and angular velocities. Thus, motion along the X axis  19  and Y axis  17  will be treated separately, as described below. 
     With only one degree-of-freedom and a small rotation rate, where θ refers to θ 1  or θ 2 , while the other angle remains fixed, equations of motion are as follows:
 
 F= ( M+m ) {umlaut over (x)}+m{umlaut over (θ)}L  cos θ− mL{dot over (θ)}   2  sin θ+ m{umlaut over (L)}  sin θ+2 m{dot over (θ)}{dot over (L)}  cos θ
 
τ=0=( {umlaut over (x)}  cos θ+ g  sin θ+ L{umlaut over (θ)}+ 2 {dot over (L)}{dot over (θ)} ) mL  
 
which can be simplified to the pendulum equations for constant cable  26  length L as follows:
 
 F= ( M+m ) {umlaut over (x)}+m{umlaut over (θ)}L  cos θ− mL{dot over (θ)}   2  sin θ
 
τ=0=( {umlaut over (x)}  cos θ+ g  sin θ+ L{umlaut over (θ)} ) mL  
 
where M is the mass of the cart  28  and m is the mass of the payload  12 . Assuming small angles and a slowly varying vertical translation and neglecting {dot over (θ)} 2 , the equations can be linearized as follows:
 
 F= ( M+m ) {umlaut over (x)}+m{umlaut over (θ)}L  
 
0= {umlaut over (x)}+gθ+L{umlaut over (θ)} 
 
where L is considered constant over a time step and also corresponds to L p .
 
     The movement mechanism may be operated in a cooperation mode allowing the operator  33  to operate the movement device  22  by placing their hands  35  directly on the payload  12 . The movement mechanism allows the operator  33  to impart an angle to the cable  26  by pushing the payload  12 , and this angle is measured by the sensors  64  as a rotation (θ 1  and θ 2 ) of the first and second curved elements  36 ,  38  about the respective first and second axes  52 ,  54 . The control system moves the cart  28  in response to the angle θ 1  and θ 2  of the cable  26  measured by the sensors  64  to keep the cable  26  vertical. Thus, the cart  28  moves in the direction desired by the operator  33 , while controlling any sway of the cable  26 , resulting in assistance to the operator  33  in moving the payload  12  in the X and Y directions. Additionally, since the controller  32  ensures that the cable  26  remains vertical, the operator  33  is not required to manually stop the load, since the control system manages itself to stop the payload  12 . An autonomous mode, where the payload  12  position is prescribed, while reducing cable  26  sway, may also be desired. 
     The force F required for an operator  33  to move the payload  12  would be reduced because a measure of the imparted angle(s) θ 1  and θ 2  of the first and second curved elements  36 ,  38  about the respective first and second axes  52 ,  54  can be precisely and accurately measured. This results in a system that moves along the corresponding X axis  19  and/or Y axis  17 . 
     The controller  32  includes a control block  86 , shown in  FIG. 7 , which is configured to operate for cooperative motion or autonomous motion. Using only the last equation above, the cart  28  acceleration is considered as the input. The payload  12  and cart  28  mass do not need to be known. The following equations are therefore obtained in a Laplace domain as follows:
 
 {umlaut over (X)} ( s )+ g θ( s )+ s   2   Lθ ( s )=0
 
The state-space representation is as follows:
 
   {dot over (x)}     s   =A   s     x     s   +B   s   u   s  
 
 y   s   =C   s     x     s   +D   s   u   s  
 
where y S  the output vector,  x   S  is the state vector, u s  is the input scalar, A S  is an n×n state matrix, B S  is an n×m input matrix, C S  is a p×n output matrix, D S  is a p×m feed through matrix and where n is the number of states, m is the number of inputs and p is the number of outputs. Here,  x   S =[x {dot over (x)} θ {dot over (θ)}] T  and u S ={umlaut over (x)}, with
 
               A   s     =         [         0       1       0       0           0       0       0       0           0       0       0       1           0       0           -   g     L         0         ]     ⁢           ⁢   and   ⁢           ⁢     B   s       =     [         0           1           0               -   1     L           ]             
The above equation, obtained from the Laplace domain, is used, where u={umlaut over (x)}, the control law is u S =K R e, where:
 
                 K   R     =         ⌊           K   x           K   v           -     K   θ             -     K     θ   ⁢           ⁢   p               ⌋     ⁢           ⁢   and   ⁢           ⁢   e     =     [             x   d     -   x                   x   .     d     -     x   .                   θ   d     -   θ                   θ   .     d     -     θ   .             ]         ,         
where {dot over (x)} d , θ d , and {dot over (θ)} d  equal zero.
 
     Referring again to the control logic block of  FIG. 7 , the input, u S , is the acceleration of the cart  28 , and because controlling acceleration is not practical, velocity control is used in the cooperation mode and position control is used in the autonomous mode. The output of the latter lower level controller block  88  is shown as u 2  in  FIG. 7 . 
     In the cooperation mode, the state space controller block  90  output of  FIG. 7  is obtained as a discrete velocity with a zero-order-hold integration, as follows:
 
 {umlaut over (x)}   d(k)   =u=K   r   e  
 
 {dot over (x)}   d(k)   ={dot over (x)}   d(k-1)   +{umlaut over (x)}   d(k)   T   S  
 
Likewise, in the autonomous mode, the state space controller block  90  output of  FIG. 7  is obtained as a position by integrating once more, as follows:
 
 x   d(k)   =x   d(k-1)   +{dot over (x)}   d(k-1)   T   S +0.5 {umlaut over (x)}   d(k)   T   S   2  
 
     One should note that the measured velocity could be used in the preceding equations instead of the last time step desired value. This integration method is used to achieve acceleration control in an admittance control scheme. The desired acceleration is then obtained by using velocity or position control, which is more practical. It is also possible to additionally use computed torque control using the previous force equations. Although the payload  12  and cart  28  mass would then be required, an approximation is sufficient since feedback control is also used. Additionally, the payload  12  and cart  28  mass are not required in order to adapt the state space controller block  90  gains to varying parameters. Additionally, a limit and saturation block  92  may be used for virtual walls and to limit velocity and acceleration of the cart  28 . 
     In the cooperation mode, since there is no reference position, K x  is set to zero. The control gain K θp , i.e., gain on the angular velocity signal, can be optionally used, depending on the angle derivative signal quality. An adaptive controller  32 , based on pole placement and state space control may be used. The pole of the system may be obtained by:
 
det[s1−A+BK r ]
 
leading to the equation:
 
                   s   3     ⁢   L     +       s   2     ⁡     (         K   θ     ⁢   p     +       K   v     ⁢   L       )       +     s   ⁡     (     g   +     K   θ       )       +       K   v     ⁢   g       L         
where K θ  and K θp  are assumed negative.
 
     The transfer function from angle θ to an angle initial condition θ 0  is as follows: 
     
       
         
           
             
               
                 
                   θ 
                   0 
                 
                 ⁡ 
                 
                   ( 
                   
                     s 
                     + 
                     
                       K 
                       v 
                     
                   
                   ) 
                 
               
               ⁢ 
               
                 L 
                 s 
               
             
             
               
                 
                   s 
                   3 
                 
                 ⁢ 
                 L 
               
               + 
               
                 
                   s 
                   2 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         K 
                         θ 
                       
                       ⁢ 
                       p 
                     
                     + 
                     
                       
                         K 
                         v 
                       
                       ⁢ 
                       L 
                     
                   
                   ) 
                 
               
               + 
               
                 s 
                 ⁡ 
                 
                   ( 
                   
                     g 
                     + 
                     
                       K 
                       θ 
                     
                   
                   ) 
                 
               
               + 
               
                 
                   K 
                   v 
                 
                 ⁢ 
                 g 
               
             
           
         
       
     
     The poles may be placed to the following:
 
( s+p   1 )( s   2 +2ζ 1 ω n1 +ω n1   2 )
 
     In a first method, K v  and K θ  are used, which leads to the following: 
               K   v     =       p   1     +     2   ⁢     ζ   1     ⁢     ω     n   ⁢           ⁢   1                           g   L     +       K   θ     L       =       ω     n   ⁢           ⁢   1     2     +     2   ⁢     ζ   1     ⁢     ω     n   ⁢           ⁢   1       ⁢     p   1                           K   v     ⁢   g     L     =       p   1     ⁢     ω     n   ⁢           ⁢   1     2             
and then, the following are used:
 
               p   1     =       2   ⁢   g   ⁢           ⁢     ζ   1     ⁢     ω     n   ⁢           ⁢   1             -   g     +       ω     n   ⁢           ⁢   1     2     ⁢   L                       K   v     =         p   1     ⁢     ω     n   ⁢           ⁢   1     2     ⁢   L     g                   K   θ     =       (       ω     n   ⁢           ⁢   1     2     -     g   L     +     2   ⁢   ζ   ⁢           ⁢     ω     n   ⁢           ⁢   1       ⁢     p   1         )     ⁢   L                   where   ⁢           ⁢     ω     n   ⁢           ⁢   1         ≥       g   L             
and ζ are design parameters. The control gains are thus obtained. The transfer function zero influences the response, but without practical effect, since it is relatively high, ω n1  is chosen very close to
 
                 g   L       ,         
but not too close to avoid numerical problems.
 
     The control scheme is then used with these gains to manage the cooperation with the operator  33 , while stabilizing the cable  26 . 
     In a second method, K v , K θ , and K θp  are used, which leads to the following: 
     
       
         
           
             
               
                 K 
                 v 
               
               + 
               
                 
                   K 
                   
                     θ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     p 
                   
                 
                 L 
               
             
             = 
             
               
                 p 
                 1 
               
               + 
               
                 2 
                 ⁢ 
                 
                   ζ 
                   1 
                 
                 ⁢ 
                 
                   ω 
                   
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 g 
                 L 
               
               + 
               
                 
                   K 
                   θ 
                 
                 L 
               
             
             = 
             
               
                 ω 
                 
                   n 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 2 
               
               + 
               
                 2 
                 ⁢ 
                 
                   ζ 
                   1 
                 
                 ⁢ 
                 
                   ω 
                   
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 ⁢ 
                 
                   p 
                   1 
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 
                   
                     K 
                     v 
                   
                   ⁢ 
                   g 
                 
                 L 
               
               = 
               
                 
                   p 
                   1 
                 
                 ⁢ 
                 
                   ω 
                   
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   2 
                 
               
             
           
         
       
     
     The second method allows the poles to remain constant. Using the gain K θp  allows the cart  28  to move in regards to the angles θ 1  and θ 2  and angular velocity. The following is then obtained: 
               p   1     =       -     g   ⁡     (       K     θ   ⁢           ⁢   p       -     2   ⁢     ζω     n   ⁢           ⁢   1       ⁢   L       )           L   ⁡     (       -   g     +       ω     n   ⁢           ⁢   1     2     ⁢   L       )                       K   v     =         p   1     ⁢     ω     n   ⁢           ⁢   1     2     ⁢   L     g                   K   θ     =       (       ω     n   ⁢           ⁢   1     2     -     g   L     +     2   ⁢     ζω     n   ⁢           ⁢   1       ⁢     p   1         )     ⁢   L               where                 ω     n   ⁢           ⁢   1       ≥       g   L         ,         
ζ, and K θp  are design parameters. The control gains are thus obtained. The transfer function zero influences the response, but without practical effect since it is relatively high, ω n1  is chosen very close to
 
                 g   L       ,         
but not too close to avoid numerical problems.
 
     The control scheme is then used with these gains to manage the cooperation with the operator  33 , while stabilizing the movement device  22 . 
     Neglected terms from the complete model as {dot over (L)}, {dot over (β)}, {dot over (θ)} 2  and viscous friction can be compensated for, for example, with gains K θ  and K θp  by considering the terms constant over a time step, similarly as with the lengths L of the cable  26 . 
     Control gains may also be heuristically modified from the computed gains. Additionally, control gains on θ p0  and θ p2  and their derivatives may be different from each other. 
     In the autonomous mode, K x  is used to control the cart  28  position. The control gain K θp  can be optionally used. An adaptive controller  32  based on pole placement and state space control using K θp  is provided. Similar to the cooperation mode, the system poles are: 
                   s   4     ⁢   L     +       s   3     ⁡     (         K   θ     ⁢   p     +       K   v     ⁢   L       )       +       s   2     ⁡     (     g   +     K   θ     +       K   x     ⁢   L       )       +     s   ⁡     (       K   v     ⁢   g     )       +       K   x     ⁢   g       L         
where K θ  and K θp  are assumed to be negative.
 
     There is a compromise between the cart  28  position trajectory and the cable  26  oscillation cancellation. In regards to the equations, this is due to the transfer function zeros. 
     Pole placement is used using the characteristic equation:
 
( s+p   1 ) 2 ( s   2 +2ζ 1 ω n1 +ω n1   2 )
 
     Equaling the previous equations for the system poles and pole placement provides: 
                 2   ⁢     ζ   1     ⁢     ω     n   ⁢           ⁢   1         +     2   ⁢           ⁢     p   1         =       K   v     +       K     θ   ⁢           ⁢   p       L                       ω     n   ⁢           ⁢   1     2     +     4   ⁢     ζ   1     ⁢     ω     n   ⁢           ⁢   1       ⁢     p   1       +     p   1   2       =         K   θ     L     +     K   x     +     g   L                       2   ⁢     ω     n   ⁢           ⁢   1     2     ⁢     p   1       +     2   ⁢     ζ   1     ⁢     ω     n   ⁢           ⁢   1       ⁢     p   1   2         =         K   v     ⁢   g     L                     ω     n   ⁢           ⁢   1     2     ⁢     p   1   2       =         K   x     ⁢   g     L           
and then the following are used:
 
where
 
               ω     n   ⁢           ⁢   1       ≥       g   L             
and ζ are design parameters and p 1  is heuristically chosen to be equal to ω n1  as to lie on the same circle as the other poles. It is a design choice to use two complex poles and two equal real poles as other choices are possible. The state space controller gains to adapt are thus obtained. The transfer function zero influence the response but without practical effect since it is relatively high. A value of ω n1  is chosen very close to
 
                 g   L       ,         
but not too close to avoid numerical problems.
 
     
       
         
           
             
               K 
               x 
             
             = 
             
               
                 
                   ω 
                   
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   2 
                 
                 ⁢ 
                 
                   p 
                   1 
                   2 
                 
                 ⁢ 
                 L 
               
               g 
             
           
         
       
       
         
           
             
               K 
               v 
             
             = 
             
               
                 2 
                 ⁢ 
                 
                   ω 
                   
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 ⁢ 
                 
                   p 
                   1 
                 
                 ⁢ 
                 
                   L 
                   ⁡ 
                   
                     ( 
                     
                       
                         ω 
                         
                           n 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       + 
                       
                         
                           ζ 
                           1 
                         
                         ⁢ 
                         
                           p 
                           1 
                         
                       
                     
                     ) 
                   
                 
               
               g 
             
           
         
       
       
         
           
             
               K 
               θ 
             
             = 
             
               
                 ( 
                 
                   
                     ω 
                     
                       n 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     2 
                   
                   + 
                   
                     4 
                     ⁢ 
                     
                       ζ 
                       1 
                     
                     ⁢ 
                     
                       ω 
                       
                         n 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                     
                       p 
                       1 
                     
                   
                   + 
                   
                     p 
                     1 
                     2 
                   
                   - 
                   
                     K 
                     x 
                   
                   - 
                   
                     g 
                     L 
                   
                 
                 ) 
               
               ⁢ 
               L 
             
           
         
       
       
         
           
             
               K 
               
                 θ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 p 
               
             
             = 
             
               
                 ( 
                 
                   
                     2 
                     ⁢ 
                     
                       ζ 
                       1 
                     
                     ⁢ 
                     
                       ω 
                       
                         n 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       p 
                       1 
                     
                   
                   - 
                   
                     K 
                     v 
                   
                 
                 ) 
               
               ⁢ 
               L 
             
           
         
       
     
     One should note that the operator  33  can still push the payload  12  in autonomous mode. The cart  28  position will move in the direction desired by the operator  33 , while be attracted to its reference position and cancelling oscillations of the movement device  22 . Depending on the control gains, it will be more or less easy to move the cart  28  away from its reference position. Referring to  FIG. 7 , the control block  86  will then be used with these gains to manage autonomous and cooperation with the operator  33 , while stabilizing the movement device  22 . 
     Neglected terms from the complete model as {dot over (L)}, {dot over (β)}, {dot over (θ)} 2  and viscous friction can be compensated for, for example, with gains K θ  and K θp  by considering the terms constant over a time step, similarly as with the cable  26  length L. 
     Control gains can also be heuristically modified from the computed gains. Additionally, control gains on θ p0  and θ p2  and their derivatives can be different from one another. 
     When switching between the modes, i.e., cooperation mode, autonomous mode, stopping, and the like, rude acceleration and jerk profile may be required. The most frequent abrupt profile happens when switching modes when the cable  26  angles θ 1  and θ 2  are non-zero. “Bumpless” transfer or smooth transfer between modes may be achieved. In one embodiment, the last control input is memorized or observed. In another embodiment, the measured velocity is memorized when the mode switch happens. In the cooperation mode, the output bumpless velocity is as follows:
 
 v   DesBumpl   =a   bt   v   mem +(1 −a   bt ) v   des  
 
     The variable a bt  is reinitialized at 1 when a mode switch happens and is then multiplied by b bt  at each time step. At first v DesBumpl  is then equal to the measured velocity (v mem ) and after some time, depending on parameter b bt , a bt  goes to 0 and v DesBumpl  to v des . The goal is to go from the present velocity as the mode switch moment (v mem ) to the desired velocity (v des ) in a smooth filtered way. For the autonomous mode, the desired position is first reset to the measured position and the desired bumpless velocity is integrated to obtain a new desired position respecting this velocity. Further smoothing may also be possible by considering the acceleration in the mode switch. 
     In addition to the movement in the X direction and Y direction, the payload  12  may also be moved in a vertical direction, i.e., in the Z direction. In order to control the vertical movement of the cable  26 , a winch  94 , in combination with a load cell  96  (or force sensor), and an accelerometer  97  may be used. The winch  94  may use a DC motor with a pulley to roll the cable  26  and thus change the length L of the cable  26 . The accelerometer  97  may be placed in line with the cable  26 , near the attachment point  84  of the payload  12 . 
     In order for the operator  33  to be able to apply forces anywhere on the payload  12 , vertical cooperation must be obtained. More specifically, vertical cooperation is movement of the payload  12  in the vertical direction. To achieve vertical cooperation, the load cell  96  is placed in line with the cable  26 , before the payload  12 . A signal of the load cell  96  depends on the inertial effects of the load. This signal is: 
                     f     1   ⁢           ⁢   cell       =       ⁢       f   H     +     m   (           X   ¨     c     ⁢   cos   ⁢           ⁢     β   1     ⁢   sin   ⁢           ⁢     θ   1       +       L   ¨     p     -       L   p     ⁢       β   .     1   2       -       L   p     ⁢       θ   .     1   2     ⁢     cos   2     ⁢     β   1       +         Y   ¨     c     ⁢   sin   ⁢           ⁢     β   1       -                         ⁢       g   ⁢           ⁢   cos   ⁢           ⁢     β   1     ⁢   cos     -     g   ⁢           ⁢   cos   ⁢           ⁢     β   1     ⁢   cos   ⁢           ⁢     θ   1         )               =       ⁢       f   H     +     ma   p                   
where f H  is the operator  33  force and a p  is the payload  12  acceleration:
 
 a   p =( {umlaut over (X)}   c  cos β 1  sin θ 1   +{umlaut over (L)}   p   −L   p {dot over (β)} 1   2   −L   p {dot over (θ)} 1   2  cos 2 β 1   +Ÿ   c  sin β 1   −g  cos β 1  cos θ 1 )
 
     In order to estimate the payload  12  mass or the operator  33  force, the dynamical effects must be compensated for in the control. Some methods compensating for the dynamical effects may include the individual compensation method, the fusion method, the accelerator method, and the like. 
     The individual method is used to compute each term of the previous equation individually. The estimation is then:
 
 â   pi =( {umlaut over (X)}   c  cos β 1  sin θ 1   +{umlaut over (L)}   p   −L   p {dot over (β)} 1   2   −L   p {dot over (θ)} 1   2  cos 2 β 1   +Ÿ   c  sin β 1   −g co β   1  cos θ 1 )
 
where â pi  is the payload acceleration estimation with the individual method.
 
     From the previous equation, several measures are needed. The cable angle θ 1  and θ 2  (from which β 1  and β 2  are deduced), are obtained with the cable angle sensor, as explained previously. The cable angular velocity {dot over (θ)} 1  and {dot over (θ)} 2 , (from which {dot over (β)} 1  and {dot over (β)} 2  are deduced), are obtained from the cable angle derivatives (done here with the Kalman filter). However, rate gyroscopes could also be placed on the cable angle sensor shafts. The cable length L c  is obtained with a position sensor on the winch  94  motor shaft (done here with a potentiometer and an incremental encoder, which are fused together). The cable length L c  is the length between the cable pivot point  60  and the payload attachment point  84 . The payload  12  position, L p , is obtained with:
 
 L   p   =L   c +δ cm  
 
where δ cm  is an approximation of the payload  12  center of mass from the payload  12  attachment point  84 . The cable vertical acceleration, {umlaut over (L)} p , is obtained from a fusion from the desired acceleration and the cable length L measure second derivative. One of these two signals could also be used directly. A rotational accelerometer or a gyroscope could also be placed on the winch  94  motor shaft. The gyroscope signal should be derived to obtain the angular acceleration. From this, the measure of the cable vertical acceleration can be obtained. The cart acceleration, {umlaut over (X)} C  and Ÿ C , is obtained from a fusion from the desired acceleration and the cable length L measure second derivative. One of these two signals could also be used directly. The cart acceleration may also be obtained by placing a rotational accelerometer or a gyroscope (derivative) on the motor shafts. Linear accelerometers could also be placed on the cart  28 . The acceleration â pi  is then obtained by inputting all of these measures and estimations into the previous equation.
 
     The cable vertical acceleration {umlaut over (L)} p  and the cart acceleration {umlaut over (X)} C  and Ÿ C  are obtained by fusing the desired acceleration with the position measure second derivative. Using the desired acceleration alone may be inexact, while the position measure second derivative is known to be very noisy. However, fusing the signals can take advantage of both by using Kalman filtering. 
     A third order acceleration model is used: 
             A   =     [         1         T   s           0.5   ⁢           ⁢     T   s   2               0       1         T   s             0       0       1         ]             B=[ 0 0 0] T      C=[ 1 0 0] T    
to find the state estimate {circumflex over (x)} i (k):
 
 {circumflex over (x)}   i ( k )= [ê   i ( k ) {dot over (ê)}   i ( k ) {umlaut over (ê)}   i ( k )] T  
 
     The acceleration estimation is then reconstructed with:
 
 {circumflex over (q)}   i   =q   di   +ê   i  
 
 {dot over ({circumflex over (q)})}   i   ={dot over (q)}   di   +{dot over (ê)}   i  
 
 {umlaut over ({circumflex over (q)})}   i   ={umlaut over (q)}   di   {umlaut over (ê)}   i  
 
where {circumflex over (q)} i , {dot over ({circumflex over (q)})} i , and {umlaut over ({circumflex over (q)})} i  are respectively the position, velocity, and acceleration final estimation.
 
     This leads to a more precise estimation than if the Kalman filter was applied directly to the signal q i . More specifically, the error signal has less amplitude and bandwidth than the joint signal so that it is easier to obtain a signal of quality, while reducing filtering drawbacks. By way of a non-limiting example, if the filter parameters are set to high filtering values, the estimation will be closed to the desired movement instead of being close to zero with a filter directly on the joint signal. 
     For the cart acceleration, the idea is similar, but is more complex. More specifically, in X and Y cooperation mode, the desired velocity and acceleration are known, but not the desired position. It is not desirable to integrate the desired velocity to obtain the desired position since it would drift with time. The error is then defined as:
 
 e   i   ={dot over (q)}   di   −{dot over (q)}   i  
 
and filtered with a Kalman second order model velocity model. The variable q i  can be inputted directly or after being slightly filtered as with a third order Kalman filter acceleration model. Joint acceleration is then reconstructed as with the cable vertical acceleration.
 
     The individual method has the advantage of having no drift, contrarily to the accelerometer method, and the dynamical effect estimation can be accurate, since it can be done at the payload center of mass position. 
     One should note that the individual and fusion method could be used not only for a suspended cable but also for other mechanisms, such as an articulated mechanism, and the like. 
     In the fusion method, the accelerometer and the individual method are fused to seize the advantages of each method, as shown at  100  in  FIG. 10 . The acceleration at the accelerometer position, L a , is first obtained independently by the accelerometer and by the individual method. The corresponding individual terms and the accelerometer are fused at this position depending on the confidence of each term. With the corrected individual terms obtained in output, the acceleration is computed at the payload center of mass. The fusion at the accelerometer position is done here with linear data reconciliation with the equality:
 
 E   1   +E   2   +E   3   +E   4   =E   5  
 
where
 
 E   1   ={umlaut over (L)}   a  
 
 E   2   =−L   a {dot over (β)} 1   2   −L   a {dot over (θ)} 1   2  cos 2 β 1  
 
 E   3   =−g  cos β 1  cos θ 1  
 
 E   4   ={umlaut over (X)}   c  cos η 1  sin θ 1   +Ÿ   c  sin β 1  
 
 E   5   =a   acc  
 
where a acc  is an accelerometer signal and E 1  to E 4  are obtained with the individual method (L a  is known from the cable length L and the distance from the accelerometer and the cable end point).
 
     Using the Lagrangian method, the criteria is: 
             J   =           (         E   ^     1     -     E     1   ⁢           ⁢   m         )     2       σ     E   ⁢           ⁢   1     2       +         (         E   ^     2     -     E     2   ⁢           ⁢   m         )     2       σ     E   ⁢           ⁢   2     2       +         (         E   ^     3     -     E     3   ⁢           ⁢   m         )     2       σ     E   ⁢           ⁢   3     2       +         (         E   ^     4     -     E     4   ⁢           ⁢   m         )     2       σ     E   ⁢           ⁢   4     2       +         (         E   ^     5     -     E     5   ⁢           ⁢   m         )     2       σ     E   ⁢           ⁢   5     2       +       λ   T     ⁡     (         E   ^     1     +       E   ^     2     +       E   ^     3     +       E   ^     4     -       E   ^     5       )               
where Ê 1  is a given effect final estimation, E im  is the given effect input measure or initial estimation and σ Ei , are confidence terms. The solution is given by:
 
 E   out   =E   in   −W   −1   H   T ( HW   −1   H   T ) −1   HE   in  
 
where
 
 E   in   =[E   1m   E   2m   E   3m   E   4m   E   5m ] T  
 
 E   out   =[Ê   1   Ê   2   Ê   3   Ê   4   Ê   5 ] T  
 
 H=[ 1111−1]
 
     
       
         
           
             W 
             = 
             
               diag 
               ( 
               
                 
                   1 
                   
                     σ 
                     
                       E 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
                 , 
                 
                   1 
                   
                     σ 
                     
                       E 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
                 , 
                 
                   
                     1 
                     
                       σ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                   . 
                   
                     1 
                     
                       σ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         4 
                       
                     
                   
                   . 
                   
                     1 
                     
                       σ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         5 
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Then, with Ê 1  to Ê 4 , the payload acceleration estimation is computed: 
                 a   ^       p   ⁢           ⁢   f       =         E   ^     1     +         E   ^     21     ⁢       L   p       L   a         +       E   ^     3     +       E   ^     4             
where â pf  is the payload acceleration estimation with the fusion method at  100  in  FIG. 10 .
 
     Referring now to  FIG. 8 , a general scheme of the fusion method is shown. 
     It would also be possible to add other accelerometers (or fuse only accelerometers) or other sensors and fuse them with the same technique by slightly modifying the above vectors or to use fusion with Kalman filtering, and the like. It should be appreciated that the individual method and the fusion method may also be used with other mechanisms, such as an articulated mechanism, and the like. 
     The mass of the payload  12  may also be monitored for reasons which include, but are not limited to knowing if the device is loaded or if the mass exceeds the payload limit, and the like. This information could also be used in the position or velocity control to enhance the performances. It may also be used to estimate the payload mass prior to entering a float mode  102 . More specifically, the mass will be needed to estimate the applied human force, as will be explained in more detail below. If, for example, the estimate is {circumflex over (m)}=F lcell /g (or a filtered version of this), the mass would have to be still with a right cable for the estimation to be accurate, which is not useful in practice. The mass is then found with a filtered version {circumflex over (m)}=F lcell /â pf . (or an identification technique) where â pf  is the fusion method estimation, as provided above. 
     The human force estimation is used in a float mode at  102  in  FIGS. 9 and 10 . Prior to entering this float mode  102 , the payload mass is determined at  103 , as was explained in the previous section. The human force is deduced at  105  from the following equation:
 
 {circumflex over (f)}   H   =F   lcell   −{circumflex over (m)}   0   â   pf  
 
where â pf  is the payload acceleration estimation, as described above and the fusion method, F lcell  is the load cell  96  signal and {circumflex over (m)} 0  is the payload mass estimation prior to entering float mode. The estimated human force signal can be treated in different ways. First of all, a deadband can be applied to cope with estimation errors:
 
               f   out     =     {         0           if   ⁢           -     F   dband       &lt;     F   in     &lt;     F   dband                   f   in     -     f   dband               if   ⁢           ⁢     F   in       &gt;     F   dband                   f   in     +     f   dband               if   ⁢           ⁢     F   in       &lt;     -     F   dband                       
Where F dband  is a deadband to be defined.
 
     The signal can also be low pass filtered, before and after the deadband. The effect is different and is a design parameter. 
     The compensation of the dynamical effects and the deadband can also be a function of each individual dynamical effect. This can be used to reduce noise in the compensation and/or add a deadband for a given dynamical effect only if this effect is present. This is useful if the deadband must be high, due to high uncertainties. 
     The absolute signal is slightly filtered to remove high frequency noise. A rate limiter is then applied, which allows the signal to raise rapidly, but to decrease much more slowly to keep the effect a given time. By way of a non-limiting example, if the signal only passes temporarily to zero, the signal is then converted from zero to one here heuristically with an exponential function, such as:
 
1− e   a     e     w     e    
 
where w e  is the processed signal, and a e  is a design parameter. The given dynamical effect deadband and/or compensation is then multiplied by this value. For example, if the total uncertainty is 20 newtons (N) because four effects each have an uncertainty of 5N, and only one effect is present, as the cable vertical acceleration, the deadband could be set to only 5N instead of 20N. The deadband is raised only if other effects are present. This must be well tuned so it remains intuitive to the operator.
 
     Prior to entering the float mode  102 , the payload mass is estimated, as described above, and is frozen to this value called {circumflex over (m)} 0 . While in the float mode  102 , the human force is estimated and processed, as also described above. This estimation is sent to an admittance controller  98  at  107  which computes a command  99  to be sent to the mechanism  22  at  109 . The general float mode process is shown in  FIG. 9 . 
     Referring now to  FIG. 10 , a more detailed control scheme is shown. A PID controller is used as the position controller. The payload  12  mass estimation could also be used to enhance the control performances. 
     The admittance controller  98  accepts a force as an input, which is measured, and reacts with a displacement, i.e., position or velocity, in the vertical direction at output at  104 . This displacement output, i.e., position, velocity, and acceleration, are processed to saturation and limits at  106  and the output displacements, i.e., position, velocity, and acceleration, are sent to the position controller at  110 . The trajectory to be followed by the mechanism  22  can be prescribed as a desired trajectory. Position control is used since dynamical effects, such as gravity, are permanently acting on the load. 
     Referring again to  FIG. 10 , a control scheme is shown at  108 . A PID controller is used as the position controller at  110 . The payload  12  mass estimation could also be used to enhance the control performances. 
     While the best modes for carrying out the disclosure have been described in detail, those familiar with the art to which this disclosure relates will recognize various alternative designs and embodiments for practicing the disclosure within the scope of the appended claims.