WO2006000092A1

WO2006000092A1 - Device comprising an elastic element with controllable dynamic behavior

Info

Publication number: WO2006000092A1
Application number: PCT/CA2005/000989
Authority: WO
Inventors: Pierre Marcotte
Original assignee: Pierre Marcotte
Priority date: 2004-06-25
Filing date: 2005-06-23
Publication date: 2006-01-05
Also published as: CA2471142A1

Abstract

A device for interacting with an object. The device comprises an elastic element comprising a mobile end part adapted for contacting the object. The device also comprises a sensor for sensing a contact load exerted by the object on the mobile end part and for generating a signal indicative of the contact load. The device further includes a load application unit coupled to the mobile end part, the load application unit being operative for applying a control load to the mobile end part in accordance with a control signal. The device also comprises a control unit coupled to the load application unit and the sensor. The control unit is operative for receiving the signal indicative of the contact load and generating the control signal based at least in part on the signal indicative of the contact load. In a non-limiting embodiment, the device is operable in one of an impedance control mode, a load control mode, and a position control mode. In the impedance control mode, the device is operative to cause the elastic element to exhibit a desired effective impedance. In the load control mode, the device is operative to cause the mobile end part to apply a desired contact load to the object. In the position control mode, the device is operative to cause the mobile end part to acquire a desired position.

Description

DEVICE COMPRISING AN ELASTIC ELEMENT WITH CONTROLLABLE DYNAMIC BEHAVIOR

Field of the invention

The present invention relates to a device comprising an elastic element and, more particularly, to a device comprising an elastic element with controllable dynamic behavior.

Background

A mechanical system is often modeled as a mass-spring-damper system and is made up of components having invariant characteristics. Such a system with invariable elasticity (stiffness) and damping characteristics results in a system with invariant dynamics. Therefore, for a given load applied to the system, the system's dynamic behavior will usually always be the same - in other words, the system's impedance remains constant. Generally, impedance of a mechanical system refers to a ratio between a function of a load applied to the system and a function of a position of the system.

When the impedance of a system does not meet specified requirements, some or all components of the system must be altered or replaced. The impedance of a given system cannot be easily modified to cope with varying needs or requirements. Moreover, such modification of impedance can rarely be done in real time.

In addition, a mass-spring-damper system is typically not designed for enabling position control or force control. Position and force control usually require different approaches involving motorization and gearing that frequently exhibit poor shock tolerance. Shock tolerance is sometimes required of a system due to unexpected or unpredictable high- force interactions that the system may have with its environment. Accordingly, there is a need for improvements directed to a device whose impedance can be modified without altering or replacing its components and, optionally, that can also enable force and/or position control while preserving good shock tolerance.

Summary of the invention

In accordance with a broad aspect, the invention seeks to provide a device for interacting with an object. The device comprises an elastic element comprising a mobile end part adapted for contacting the object. The device also comprises a sensor for sensing a contact load exerted by the object on the mobile end part and for generating a signal indicative of the contact load. The device further includes a load application unit coupled to the mobile end part, the load application unit being operative for applying a control load to the mobile end part in accordance with a control signal. The device also comprises a control unit coupled to the load application unit and the sensor. The control unit is operative for receiving the signal indicative of the contact load and generating the control signal based at least in part on the signal indicative of the contact load.

The contact load may be a contact force or a contact torque, and the control load may be a control force or a control torque.

In a non-limiting embodiment, the device is operable in one of an impedance control mode, a load control mode, and a position control mode. In the impedance control mode, the device is operative to cause the elastic element to exhibit a desired effective impedance. In the load control mode, the device is operative to cause the mobile end part to apply a desired contact load to the object. In the position control mode, the device is operative to cause the mobile end part to acquire a desired position.

These and other aspects and features of the present invention will now become apparent to those of ordinary skill in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying drawings. Brief description of the drawings

A detailed description of specific embodiments of the present invention is provided herein below, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 shows a device for interacting with an object, in accordance with a non-limiting embodiment of the present invention;

Figure 2 shows a block diagram representation of the device shown in Figure 1;

Figures 3A to 3C show different examples of implementation of an elastic element of the device shown in Figure 1 ;

Figure 4 shows a possible configuration of a mobile end part of the elastic element of the device shown in Figure 1 ;

Figure 5 shows a non-limiting example of implementation of a control unit of the device shown in Figure 1 ;

Figure 6 shows an example of a force balance model for the elastic element of the device shown in Figure 1 ;

Figure 7 shows an example of a control loop model usable by the control unit of the device shown in Figure 1 ;

Figure 8A shows an example of a plot of position over time for a given elastic element;

Figure 8B shows a plot of position over time for the given elastic element of Figure 8, wherein the given elastic element is used as the elastic element of the device shown in Figure 1 with the device operating in an impedance control mode; and Figures 8C and 8D show plots of measured position, predicted position, and predicted speed over time, respectively, for the elastic element of the device shown in Figure 1 with the device operating in an impedance control mode.

In the drawings, the embodiments of the invention are illustrated by way of examples. It is to be expressly understood that the description and drawings are only for the purpose of illustration and are an aid for understanding. They are not intended to be a definition of the limits of the invention.

Detailed description of embodiments

Figure 1 shows a device 10 for interacting with an object 16, in accordance with a non- limiting embodiment of the present invention. Figure 2 illustrates a block diagram representation of the device 10 shown in Figure 1. In this specific embodiment, the device 10 comprises an elastic element 12 comprising a mobile end part 14 adapted for contacting the object 16, a force sensor 18, a position sensor 20, an acceleration sensor 22, a force application unit 24, and a control unit 26.

As described below, these components interact so as to enable the device 10 to operate in one of an impedance control mode, a force control mode, and a position control mode. In the impedance control mode, the device 10 is operative to cause the elastic element 12 to exhibit a desired effective impedance. In the force control mode, the device 10 is operative to cause the mobile end part 14 to apply a desired contact force to the object 16. In the position control mode, the device 10 is operative to cause the mobile end part 14 to acquire a desired position.

The device 10 is usable in a wide range of applications including but not limited to robotics, automation, and actuation applications. For instance, the device 10 may be used as a variable mass-spring-damper system in applications such as: an automobile or other vehicle suspension wherein accurate dynamic control is an issue; a shock absorber wherein a mass is accelerated and decelerated (e.g. a hydraulic press); a shock absorber or propeller used as a gymnastics apparatus (e.g. in replacement of a trampoline); a robotic end effector or other robotic component interacting with its environment; an adjustable seat suspension; etc. It is to be understood that the above examples are in no way limiting and that various other applications are possible for the device 10 without departing from the scope of the invention.

With continued reference to Figure 1, the elastic element 12 is capable of deforming under application of a load and regaining its original configuration when the load is no longer applied. In the particular embodiment shown, the elastic element 12 comprises a spring 28 having an end portion that is fixedly connected to a base 30 of the device 10 and a bearing 32 which supports its mobile end part 14. The spring 28 may have any desired geometry and properties and may be made of materials such as steel, aluminum, other metals, polymers, composites, or any other suitable material. Advantageously, as shown in Figure 3A, the spring 28 may have an helicoidal and cylindrical configuration, mainly for efficiency and economic considerations. Alternatively, as shown in Figure 3B, the spring 28 may have a conical configuration for space economy and/or stability considerations, hi any event, due to its configuration and constituting materials, the elastic element 12 is characterized by certain stiffness (elasticity) and damping characteristics which are essentially invariable.

In the specific embodiment shown in Figure 1, the mobile end part 14 of the elastic element 12 is implemented as an output element, e.g. a plate or other suitable structure, which is adapted to enter into contact with the object 16. While in this non-limiting embodiment the mobile end part 14 is distinct from the spring 28, it is to be understood that, in other embodiments, the mobile end part 14 may be part of the spring 28, for instance, a portion of the last coil of the spring 28. For its part, the object 16 may be any conceivable object depending on which application the device 10 is used in. For instance, the object 16 may be: a road surface in an automotive suspension application; the moving mass in a hydraulic press application; a human body in a gymnastics apparatus application; a mechanical device or other component with which a robot interacts in a robotic application (e.g. an assembly operation); etc. It is to be understood that the above examples of the object 16 are in no way limiting and that the object 16 may be any conceivable object depending on which application the device 10 is used in. Although in the embodiment shown in Figure 1 the elasticity of the elastic element 12 is provided by a spring, it will be appreciated that the elasticity of the elastic element 12 may be provided in various other ways without departing from the scope of the invention. For instance, as shown in Figure 3C, the elastic element 12 may comprise a piece of elastic material shaped, for instance, as a prism with or without holes.

With continued reference to Figure 1, the force application unit 24 is coupled to the mobile end part 14 of the elastic element 12. The force application unit 24 is operative for applying a control force to the mobile end part 14 in accordance with a control signal. The control signal is generated by the control unit 26, as described below.

In this non-limiting embodiment, the force application unit 24 comprises an actuator 44 coupled to the base 30 as well as a transmission unit 46 coupled to the actuator 44 and the mobile end part 14 and in parallel with the elastic element 12. In a particular case, the actuator 44 is an electric motor such as the AKM41E motor model available from Kollmorgan, Inc., Wood Dale, Illinois, U.S.A.. The transmission unit 46 converts the output torque of the motor 44 into the control force applied to mobile end part 14. For example, the transmission unit 46 may comprise a rack and pinion arrangement, with the rack coupled to the mobile end part 14 and the pinion coupled to an output shaft of the motor 44. As another example, the transmission unit 46 may comprises a pulley and cable arrangement, with the pulley being driven by the motor 44 and the cable coupled to the mobile end part 14. Advantageously, in such an arrangement, the cable substantially shields the motor 44 from unidirectional shock loads and the elastic element 12 acts as a low pass filter to shock loads, thereby protecting the motor 44 from possible damage. It will be appreciated that various other implementations are possible for the transmission unit 46 without departing from the scope of the invention.

Although in the specific embodiment shown in Figure 1 the force application unit 24 uses a motor to apply the control force to the mobile end part 14 of the elastic element 12, it is to be understood that the force application unit 24 may use other types of actuators such as hydraulic, pneumatic, or electromechanical actuators, to apply the control force to the mobile end part 14.

With continued reference to Figure 1, the force sensor 18 is operative for sensing a contact force exerted by the object 16 on the mobile end part 14 and for generating a signal indicative of the contact force. The contact force is the force applied by the object 16 on the mobile end part 14 (or, equivalently, the force applied by the mobile end part 14 on the object 16) when the object 16 contacts the mobile end part 14. As shown in Figure 4, in this specific embodiment, the force sensor 18 comprises a load cell 34 positioned at the mobile end part 14 between a contact plate 35 and a structure 36 and connected to a signal transducer 38 for amplifying and filtering the signal generated by the load cell 34 in response to contact of the mobile end part 14 with the object 16. One suitable type of load cell is a force sensing high impedance load cell 9212 model, available from Kistler, Inc., Winterthur, Switzerland. While the signal transducer 38 is shown as being distinct from the load cell 34, it is to be understood that, in certain embodiments, the functionality of the signal transducer 38 may be accomplished by the load cell 34 itself. It is also to be understood that, generally, various types of technologies may be used for the force sensor 18, including piezocrystal and strain gauge technologies, without departing from the scope of the invention.

Continuing with Figure 1, the position sensor 20 is operative for generating a signal indicative of a position of the mobile end part 14 of the elastic element 12 relative to a reference point of the device 10 such as the base 30. In this specific embodiment, the position sensor 20 comprises a rotary position transducer operative for detecting an angular position of the shaft of the motor 44 and for generating a signal indicative of that angular position. Knowledge of the angular position of the shaft of the motor 44 enables the position of the mobile end part 14 to be determined. One suitable type of rotary position transducer is a DM6814 transducer model available from RTD Embedded Technologies Inc., State College, Pennsylvania, U.S.A.. In other embodiments, the position sensor 20 may comprise a linear position transducer coupled to the mobile end part 14 of the elastic element 12 and a fixed point of the device 10 such as the base 30. It will be appreciated that various other types of components may be used to implement the position sensor 20 without departing from the scope of the invention. With continued reference to Figure 1, the acceleration sensor 22 is operative for generating a signal indicative of an acceleration of the mobile end part 14 of the elastic element 12. As shown in Figure 4, in this specific embodiment, the acceleration sensor 22 comprises an accelerometer 40 positioned in the structure 36 and connected to a signal transducer 42 for amplifying and filtering the signal generated by the accelerometer 40. One suitable type of accelerometer is a 8305A10M7SP1M model, available from Kistler, Inc., Winterthur, Switzerland. While the signal transducer 42 is shown as being distinct from the accelerometer 40, it is to be understood that, in certain embodiments, the functionality of the signal transducer 42 may be accomplished by the accelerometer 40 itself. It is also to be understood that, generally, various types of technologies may be used for the acceleration sensor 22, including capacitive acceleration transducer technologies, without departing from the scope of the invention.

Although in the particular embodiment shown in Figure 1 the device 10 includes the acceleration sensor 22, it is to be understood that, in other embodiments, the acceleration sensor 22 may be omitted. For instance, in some embodiments, an indication of an acceleration of the mobile end part 14 of the elastic element 12 may be obtained based on the second derivative of the position of the mobile end part 14 with respect to time (or, in an embodiment in which a velocity of the mobile end part 14 is measured, based on the first derivative of the velocity of the mobile end part 14 with respect to time).

Continuing with Figure 1 , in this particular embodiment, the control unit 26 is coupled to the force sensor 18, the position sensor 20, the acceleration sensor 22, and the force application unit 24. The control unit 26 is operative for receiving the signal indicative of the contact force from the force sensor 18, the signal indicative of the position of the mobile end part 14 from the position sensor 20, and the signal indicative of the acceleration of the mobile end part 14 from the acceleration sensor 22 (or deriving an indication of that acceleration based on the signal indicative of the position of the mobile end part 14). Based at least in part on these signals and on which mode of operation the device 10 is in (i.e. the impedance control mode, the force control mode, or the position control mode, described below), the control unit 26 is operative for generating the control signal transmitted to the force application unit 24 for controlling the control force applied by the force application unit 24 to the mobile end part 14 of the elastic element 12.

In some embodiments, certain functionality of the control unit 26 may be implemented as pre-programmed hardware or firmware elements (e.g., application specific integrated circuits (ASICs), electrically erasable programmable read-only memories (EEPROMs), etc.), or other related components. In other embodiments, the control unit 26 may comprise an arithmetic and logic unit (ALU) having access to a code memory (not shown) which stores program instructions for the operation of the ALU in order to implement the functionality and execute the various processes and functions described above. The program instructions may be stored on a medium which is fixed, tangible and readable directly by the control unit 26, (e.g., removable diskette, CD-ROM, ROM, or fixed disk), or the program instructions may be stored remotely but transmittable to the control unit 26 via a modem or other interface device (e.g., a communications adapter) connected to a network over a transmission medium. The transmission medium may be either a tangible medium (e.g., optical or analog communications lines) or a medium implemented using wireless techniques (e.g., microwave, infrared or other transmission schemes).

Figure 5 illustrates a non-limiting example of implementation of the control unit 26. In this particular example, the control unit 26 comprises an input/output (I/O) module 50 and a processing unit 52 coupled to the I/O module 50. A computer 54 is adapted for communicating with the processing unit 52.

The I/O module 50 is adapted for receiving the signals generated by the force sensor 18, the position sensor 20, and the acceleration sensor 22 and for converting these signals into digital format. For instance, the I/O module 50 may comprise an analog-to-digital (AfD) converter for conversion of the received signals into digital format. The I/O module 50 is also adapted for releasing the control signal to be transmitted to the force application unit 24 (in the example shown, the control signal is released to an amplifier 57 that amplifies the signal which is then applied to the actuator 44). The I/O module 50 may include a digital-to-analog (D/A) converter for releasing the control signal in an analog format.

The processing unit 52 is operative to sample data from the I/O module 50 at a certain rate, for instance, 1 kHz, process the sampled data, and generate (in digital form) the control signal to be transmitted to the force application unit 24 via the I/O module 50. The processing unit 52 is programmed to generate the control signal based on the data sampled from the I/O module 50 and on which mode of operation the device 10 is in. In a specific embodiment, the processing unit 52 may be implemented by an embedded PC programmed, for example, via coding in C++. One type of suitable embedded PC is a IB 104+ model available from IBT Technologies, Inc., St-Laurent, Quebec, Canada.

The computer 54 includes a user interface having a display for displaying data obtained based on signals provided by the force sensor 18, the position sensor 20, and the acceleration sensor 22 as well as data elements associated with the mode of operation the device 10 is in. The user interface also has an input device such as a keyboard that enables entering of commands or data elements which may be required by the processing unit 52 in generating the control signal. Although shown as distinct components in Figure 5, it is to be understood that, in some embodiments, the functionality of the computer 54, the processing unit 52, and the I/O module 50 may be integrated in a single component.

Thus, as mentioned above, based at least in part on signals received from the force sensor 18, the position sensor 20, and the acceleration sensor 22 as well as on which mode of operation the device 10 is in (i.e. the impedance control mode, the force control mode, or the position control mode), the control unit 26 is operative for generating the control signal transmitted to the force application unit 24 for controlling the control force applied by the force application unit 24 to the mobile end part 14 of the elastic element 12. Operation of the control unit 26 in each of the impedance control mode, the force control mode, and the position control mode will now be described.

I. Impedance control mode

Generally, impedance of the elastic element 12 refers to a ratio between a function of a load applied to the elastic element 12 and a function of a position of a reference point of the elastic element 12 such as a point on the mobile end part 14. In this particular case, assume that the elastic element 12 may be modeled as a second order system with a lump mass M , stiffness K and a damping!? , and on which the object 16 applies the contact force u_c(t), which acts on the mobile end part 14 that has a position q(t)\ M q + Bq + Kq(t) = u_c(t) The Laplace transform of this equation yields an equation expressed in the domain of the complex variables :

which can be expressed as a ratio of two complex expressions:

This ratio defines the mechanical impedance Z of the elastic element 12.

Note that the above impedance equation may be rewritten as: Z{s) = M(S² + 2ζω_ns + ω² )

where ω_n = J^Λ_r is the undamped natural frequency of the elastic element 12 and

the damping ratio of the elastic element 12.

The impedance is said to be constant if coefficients M, B, and K (or equivalentlyM, ω_n, and ζ ) are constant in time.

In the impedance control mode, the device 10 is operative to cause the elastic element 12 to exhibit a desired effective impedance Z_d , i.e. to exhibit a desired dynamic behavior. More particularly, the control unit 26 generates the control signal that is transmitted to the force application unit 24 such that the control force applied by the force application unit 24 to the mobile end part 14 combined with the contact force u_c applied by the object 16 to the mobile end part 14 results in the elastic element 12 exhibiting a desired effective impedance Z_d . That is, by controllably applying the control force to the mobile end part 14, the elastic element 12 exhibits a desired effective impedance Z_d which is different from the impedance Z that the elastic element 12 exhibits without application of the control force. In other words, for a given contact force u_c, the elastic element 12 behaves dynamically differently depending on the control force applied by the force application unit 24.

The desired effective impedance Z_d may be specified in terms of various parameters. For example, the desired effective impedance Z_d may be specified in terms of an indication of a desired effective stiffness K₁, and an indication of a desired effective damping i?_rf for the elastic element 12. The indication of the desired effective stiffness^ may be the desired effective stiffness K_d itself or parameters from which the desired effective stiffness K_d is derivable. Similar comments apply for the indication of the desired effective damping l?_rf . As another example, the desired effective impedance Z_d maybe specified in terms of an indication of a desired effective undamped natural frequency ω_{n d} and an indication of a desired effective damping coefficient^ for the elastic element 12. The indication of the desired effective undamped natural frequency ω_nd may be the desired effective undamped natural frequency ω_Hrf itself or parameters from which the desired effective undamped natural frequency ω_nd is derivable. Similar comments apply for the indication of the desired effective damping coefficient £_rf . As yet another example, the desired impedance Z_d may be specified in terms of an indication of desired effective polesr_lrf andr_2rf of the impedance function, i.e. desired roots of the characteristic equation forming the denominator of the impedance function (assuming a second order system model). The indication of desired effective poles r_u andr_2(/may be the desired effective poles r_]d and r_2d themselves or parameters from which the desired effective poles r_λd and r_2d are derivable. It is to be understood that the above examples of parameters which may be used to define the desired effective impedance Z_d are not exhaustive and that various other parameters may be used to define the desired effective impedance Z_d without departing from the scope of the invention. The parameters defining the desired effective impedance Z_rf may be provided to the control unit 26 in various manners. For example, the parameters defining the desired effective impedance Z₁, may be provided to the control unit 26 via transmission of data regarding the parameters from the computer 54, e.g. by a user entering data regarding the parameters using the computer 54. As another example, the parameters defining the desired effective impedance Z_d may be stored in a memory of the control unit 26 and computationally used by the control unit 26 in response to a certain condition being satisfied. For instance, when the control unit 26 determines that the certain condition is satisfied (e.g. it receives a signal indicating that the elastic element 12 should now exhibit the desired effective impedance Z₁, ), the control unit 26 uses the parameters defining the desired effective impedance Z_d to generate the control signal transmitted to the force application unit 24 which applies the control force to the mobile end part 14 such that the elastic element 12 exhibits the desired effective impedance Z_d .

Thus, based on signals received from the force sensor 18, the position sensor 20, and the acceleration sensor 22 as well as on the indication of a desired effective impedance Z_d , the control unit 26 generates the control signal transmitted to the force application unit 24 such that the control force applied by the force application unit 24 to the mobile end part 14 of the elastic element 12 results in the elastic element 12 exhibiting the desired effective impedance Z_d . For instance, assuming that the desired effective impedance Z_d is defined in terms of a desired effective stiffness K_d and a desired effective damping B_d for the elastic element 12, even though its configuration and constituting materials are such that it has the stiffness K and the damping B , the elastic element 12 behaves dynamically as if it has the desired effective stiffness^, and the desired effective damping B_d (which are respectively different from the stiffness K and the damping B ).

Figures 6 and 7 illustrate an example of a model that may be used by the control unit 26 to generate the control signal transmitted to the force application unit 24 for applying the control force to the mobile end part 14 of the elastic element 12 so as to achieve the desired effective impedance Z₁, . It is to be understood that the following model is presented for illustrative purposes only and that various other models may be used without departing from the scope of the invention.

As shown in Figure 6, a force balance on the elastic element 12 of mass M may be expressed as: M q = u{t)+ u_exl{t) (1) where q is the position second time derivative, i.e. the acceleration, t time, u{t) the control force applied by the force application unit 24 to the mobile end part 14, and u_exl it) comprises other forces applied on the elastic element 12, such as the spring force, the friction force, etc.

With additional reference to Figure 7, there is shown a theoretical control loop 60 including a plant model 62 and a control law 64. The control law 64 is shown as a function of its variables (constant parameters are presented below) as: u(t) = u{q{t), q_d (0, a{t),

u{t - T)) (2)

where q(t) is the position vector *«^' q_d(t) is the desired position vector H,d M)

α(/)the acceleration, u_c{t) the contact force, and u(t - T) the previous control force, T being the sampling time interval. Equation (2) is developed below.

The external force u_exl{t) comprises the contact force w_c (J) and other forces Δ(t) such as the spring force, the friction force, the force due to gravity, and non-modeled phenomena:

In order to develop a control law suited for software implementation, equation (1) is rewritten as a function of the desired acceleration q_d as: "W = -^) + Mq_d (4) where the desired acceleration q^' _d is obtained from the desired impedance: «_c(0 = M q_d - B_d{q_d -q)- K_d{q_d(t)-q{t)) (5) where B_d and K_d are the desired damping and stiffness of the elastic element 12, respectively. Assuming that the control is not constrained, and assuming that the system parameters M and u_exl(t) of equation (1) correspond to the control law parameters of equation (4), then equations (4) and (1) yields:

i.e., the actual acceleration q behaves like the desired acceleration q^' _d to create an impedance control effect according to equation (5).

From equation (4), the external force u_exl (t) may be approximated from the previous computation as: "«,(') ^« uJ$ -T) = M q(t -f)- u(t -T) (7) where T is the sample time, as previously mentioned. To implement the control law, we replace u_exl{t) in equation (4) with equation (7): u(t) = u{t -T)-M q(t -T) + M q_d (8)

Now, the desired acceleration q^' _d from equation (5): M q_d + B_dq + K_d q{t) = B_d q_d + K_d q_d{t)+ u_c{t) (9)

As previously mentioned, the Laplace transform of a second order equation may be expressed as:

where ζ and ω_n are the damping coefficient and the undamped natural frequency, respectively. Comparing equation (11) to the characteristic equation of equation (10) yields:

~ = 2ζ ω_n M K , ^{( 12}>

and replacing coefficients of equations (10) and (12), and adding appropriate subscripts, yields: q* + 2ζ_dω_ad q + ω]_d q{t) = 2ζ_dω_ndq_d + ω]_dq_d {ή + ^ (13) M which may be expressed as:

g_{d +} 2ζ_dω_ιld q + ω_n ² _d q{ή = ^J^ (14)

where u_d (t) is:

«_</ (0 = uM)+ M(2ζ_dω_ndq_d + ω_Λ ²q_d(ή) (15)

The desired acceleration q_d from equation (13):

h = 2ζ_dω_nd(q_d -q)+ a>l_d(q_d(t)-q(t))+ aM (16) M in equation (8) yields:

u{t) = u{t -T)-M q{t -T)+ M [2ζ_dω_nd{q_d -q)+ ωl_d{q_d{t)-q{t))}₊ u_c{t) ^{(1 ?)} which is the specific equation suited for implementation in the control unit 26, providing a continuous time expression of equation (2).

The discrete time control law is obtained from equation (17) as:

(18) where k is the discrete time variable:

The floor(») function corresponds to the Matlab (version 6.1.0.450 Release 12.1) floor(») function, Matlab being a software product of Matworks, Inc., Natick, Massachusetts, U.S.A.. For practical reasons, the time delay T in equation (17) may be generalized in equation (2) as the following variable u_{del τ} :

which has to be fine tuned to optimize performance. Advantageously, equation (18) may be implemented in the control law 64 as follows:

«[* + !_ = -u_m/[k] + M [2ζ_dωJsAk +

^{(21 )}

In this example, the variables related to external forces u_exl are grouped as equation (22), prior to be filtered through a 2^nd order butterworth numerical filter with a cut off frequency at 30Hz, yielding u_{exl f} . Similarly, the acceleration q may be replaced with ά _f , a filtered value of the measure obtained from the acceleration sensor 22 (or the second derivative over time of the position as detected by the position sensor 20), and the contact force w_cmay be replaced with its filtered value u_cf . Note that variables s_d and p_d are equivalent to variables q_d and q_d , respectively.

Regarding the position q and speed q , although measures p and 5 can be obtained directly from the position sensor 20' s signal and its time derivative, respectively, it will be appreciated that prediction estimators p and s such as:

p[k + l]

+ I^< _Pι (p, [k]- p[k^'ύ (23)

s[k + \] = Φ₂,p[k) + Φ₂₂s[k] + ^u_d[k] + L_p2 (_P/ [k]- p[k]) (24)

can also be used. Such position and speed estimators require only a position measure P_j (here provided by the position sensor 20 and in some cases being filtered). Coefficients φ_t of equations (23) and (24) can be obtained from equation (25): φ_u = e"^τ i cosbT - sinbT φ_u =e"^rUsinbTJ

φ₂₂ = e^πT\ cosbT + ~ sin bT while coefficients γ\ and γ₂' can be obtained from equation (26)

where parameters a and b are computed from the desired damping factor ζ_d , and the system natural frequency ω_nd :

Parameters L_p] and L_p2 can be tuned according to following equations: L_pt = a_lp + 2e^aT cosbT (28) L₁₁-, = — ^l- — [(- b + 2a cos bT sin bT + 2b cos² bτ)e"^τ + (a sin bT + b cos bT)a_{t p} +ba_ϋ e^'aT _/onx sin bT (29) where estimator poles (re. coefficients a_Op, a_ip of equations (28) and (29)) should be selected to generate a dynamic 2 to 6 times faster than the controller:

Here ω_{n p} and ζ _p represent the estimator natural frequency and damping, respectively. Equation (21) along with equations (23) and (24) provide the control law 64 suited for implementation in the control unit 26. Based on this model, the control unit 26 is operative to generate the control signal for causing the force application unit 24 to apply the control force u{t) to the mobile end part 14 of the elastic element 12 such that the elastic element 12 exhibits the desired effective impedance Z .

As an example of the impedance control mode, Figure 8 A shows a given spring with an elasticity (stiffness) K of 682 N/m while oscillating naturally (without any control) at a frequency ω_n of approximately 4.5 Hz. When used as the elastic element 12 of the non- limiting embodiment shown in Figure 1 , this spring under impedance control mode behaves differently. One example of induced behavior or controlled impedance of this elastic element 12 is shown in Figure 8B, which illustrates a response of the elastic element 12 to a -10 N impact occurring at 0.845 seconds and released 2 seconds later. It is observed that, under impedance control, the elastic element 12 behaves as if it has a desired effective elasticity K_d of approximately 213 N/m (compared to the actual elasticity K of 682 N/m). It is also observed that the elastic element 12 behaves as if it has a desired effective damping ratio ζ_Λ of approximately 0.7 (compared to the actual damping ratio ζ which is well below 0.7) and a desired effective frequency ω_nd of approximately 1.5 Hz (compared to the actual frequency co_noi 4.5 Hz). It will thus be appreciated that, in the impedance control mode, the elastic element 12 behaves as if it has a desired effective impedance Z_d which is different from its actual impedance. Z (in other words, for a given contact load, the elastic element 12 behaves dynamically differently depending on the control force applied by the force application unit 24).

In addition, Figures 8C and 8D respectively illustrate position p and speed s sampled data from estimators in relation to the example shown in Figure 8B. Figure 8C plots the position p_j obtained from the encoder (solid line) and the position p predicted by the estimator (dashed line), while Figure 8D plots the predicted speed? . As previously discussed, no measured speed data is required due to use of the estimators.

II. Force control mode

In the force control mode, the device 10 is operative to cause the mobile end part 14 of the elastic element 12 to apply a desired contact force u_{c d} to the object 16. More particularly, the control unit 26 generates the control signal that is transmitted to the force application unit 24 such that the control force applied by the force application unit 24 to the mobile end part 14 results in the mobile end part 14 applying a desired contact force u_{c d} to the object 16.

An indication of the desired contact force u_{c d} is provided to the control unit 26. For example, the indication of the desired contact force u_{c d} may be the desired contact force u_{c d} itself or parameters from which the desired contact force u_{c d} is derivable. The indication of the desired contact force u_{c d} may be provided to the control unit 26 in various manners as mentioned previously in connection with provision of parameters defining the desired effective impedance Z₁, in the impedance control mode.

With renewed reference to the non-limiting model shown in Figure 7, in the force control mode, the variables of the control law 64 are replaced withe^), the force error, as follows: u(t) = u(e_f {ή) (31) e_f {t) = u_{c d} {ή- u_c{t) (32) where u_{c d} (t) and u_c(t)aτe the desired contact force and the measured contact force, respectively. In a specific example, the control law (31) is a proportional-integral- derivative control (PlD): u(t)= Pe_f(t) + I Je, dt + De _f (33) The corresponding discrete time control law may be expressed as follows:

u[k] = K_pe_f [k]+ lih K_d (e_f [k]-e_f[k~\]) (34)

Parameters K , K₁ , and K_d are constant values corresponding toP, I , and D parameters. It will be appreciated by those skilled in the art that various tuning procedures can be effected to set the K _p, K₁ , and A^ parameters.

Equation (34) provides the control law 64 suited for implementation in the control unit 26. Based on this model, the control unit 26 is operative to generate the control signal for causing the force application unit 24 to apply the control force u{t) to the mobile end part 14 of the elastic element 12 such that the mobile end part 14 applies a desired contact force u_{c d} to the object 16.

III. Position control mode

In the position control mode, the device 10 is operative to cause the mobile end part 14 to acquire a desired position p_d relative to a reference point of the device 10 such as the base 30. More particularly, the control unit 26 generates the control signal that is transmitted to the force application unit 24 such that the control force applied by the force application unit 24 to the mobile end part 14 results in the mobile end part 14 acquiring a desired position p_d .

An indication of the desired position p_d is provided to the control unit 26. For example, the indication of the desired position p_d may be the desired position p_d itself or parameters from which the desired position p_d is derivable. The indication of the desired position p_d may be provided to the control unit 26 in various manners as mentioned previously in connection with provision of parameters defining the desired effective impedance Z_d in the impedance control mode.

With renewed reference to the non-limiting model shown in Figure 7, in the position control mode, the variables of the control law 64 are replaced withe_p(/), the position error, as follows: u(t) = u(e_p{ή) (35)

where p_d (t) and p(t) are the desired position and the measured position, respectively.

In a specific example, the control law (35) is a proportional-integral-derivative control (PID):

The corresponding discrete time control law may be expressed as follows:

u[k] = K_pe_p[k] + K∑e_p]i] + K, (e_p[k]-e_p[k -$ (38) ι=0

Equation (38) provides the control law 64 suited for implementation in the control unit 26. Based on this model, the control unit 26 is operative to generate the control signal that is transmitted to the force application unit 24 such that the control force u{t) applied by the force application unit 24 to the mobile end part 14 results in the mobile end part 14 acquiring a desired position p_d .

It will thus be appreciated that the device 10 enables a variation of the impedance of the elastic element 12, which would otherwise be fixed due to its configuration and constituting materials, in a particularly effective and efficient manner. In particular, the effective impedance of the elastic element 12 maybe varied while the device 10 is in use or operation, something that is not possible with other devices which require a replacement of one or more components in order to effect an impedance variation. Furthermore, the device 10 enables, via switching of the control law applied by the control unit 26, two alternate control modes for position and force control.

While in the above-described embodiments of the device 10 deformation of the elastic element 12 is associated with linear displacements of the mobile end part 14 of the elastic element 12, it is to be understood that, in other embodiments, the device 10 may be adapted such that deformation of the elastic element 12 is associated with rotation or angular displacements of the mobile end part 14 of the elastic element 12. For instance, in some embodiments, the elastic element 12, which may comprise a torsion spring or a piece of elastic material that is torsionally deformable, deforms when the mobile end part 14 experiences an angular displacement due to application of a contact torque to the mobile end part 14. In such embodiments, the force application unit 24 would be replaced by a torque application unit operative for applying a control torque to the mobile end part 14 in accordance with the control signal generated by the control unit 26. Also, the force sensor 18 would be replaced by a torque sensor for sensing a contact torque exerted by the object 16 on the mobile end part 14 and for generating a signal indicative of the contact torque. Similarly, the position sensor 20 and acceleration sensor 22 would be adapted to provide to the control unit 26 indications of the angular position and angular acceleration of the mobile end part 14, respectively. Thus, generally, a "contact load" exerted by the object 16 on the mobile end part 14 can be either a contact force or a contact torque; a "load application unit" can be either a force application unit or a torque application unit; and a "control load" can be either a control force or a control torque.

Although specific embodiments have been illustrated, this was for the purpose of describing, but not limiting, the invention. Various modifications will become apparent to those skilled in the art and are within the scope of the present invention, which is defined more particularly by the attached claims.

Claims

Claims:

1. A device for interacting with an object, said device comprising: an elastic element comprising a mobile end part adapted for contacting the object; a sensor for sensing a contact load exerted by the object on said mobile end part and for generating a signal indicative of the contact load; a load application unit coupled to said mobile end part, said load application unit being operative for applying a control load to said mobile end part in accordance with a control signal; and a control unit coupled to said load application unit and said sensor, said control unit being operative for: receiving the signal indicative of the contact load; and generating the control signal based at least in part on the signal indicative of the contact load.

2. A device as claimed in claim 1, wherein said control unit is operative for generating the control signal further based at least in part on an indication of a desired effective impedance for said elastic element.

3. A device as claimed in claim 2, wherein the indication of the desired effective impedance for said elastic element comprises at least two of: an indication of a desired effective stiffness for said elastic element; an indication of a desired effective damping for said elastic element; - an indication of a desired effective undamped natural frequency for said elastic element; an indication of a desired effective damping ratio for said elastic element; an indication of a first desired effective pole of a characteristic equation modeling said elastic element; - an indication of a second desired effective pole of the characteristic equation modeling said elastic element.

4. A device as claimed in claim 2, wherein said control unit is operative for obtaining the indication of the desired effective impedance for said elastic element.

5. A device as claimed in claim 4, wherein said control unit is operative for obtaining the indication of the desired effective impedance for said elastic element based at least in part on user input at a user interface.

6. A device as claimed in claim 4, wherein said control unit comprises a memory, said control unit being operative for obtaining the indication of the desired effective impedance for said elastic element from said memory.

7. A device as claimed in claim 1, wherein said sensor is a first sensor, said device further comprising a second sensor for generating a signal indicative of a position of said mobile end part, said control unit being coupled to said second sensor, said control unit being operative for generating the control signal further based at least in part on the signal indicative of the position of said mobile end part.

8. A device as claimed in claim 7, wherein said control unit being operative for generating the control signal further based at least in part on the signal indicative of the position of said mobile end part comprises said control unit being operative for deriving an indication of an acceleration of said mobile end part and using the indication of the acceleration of said mobile end part in generating the control signal.

9. A device as claimed in claim 1, wherein said sensor is a first sensor, said device further comprising: a second sensor for generating a signal indicative of a position of said mobile end part; - a third sensor for generating a signal indicative of an acceleration of said mobile end part; wherein said control unit is coupled to said second sensor and said third sensor, said control unit being operative for generating the control signal further based at least in part on the signal indicative of the position of said mobile end part and the signal indicative of the acceleration of said mobile end part.

10. A device as claimed in claim 1, wherein said control unit is operative for generating the control signal further based at least in part on an indication of a desired contact load to be exerted by said mobile end part on the object.

1 1. A device as claimed in claim 1, wherein said device is operable in either of an impedance control mode and a load control mode: in the impedance control mode, said control unit is operative for generating the control signal further based at least in part on an indication of a desired effective impedance for said elastic element; and in the load control mode, said control unit is operative for generating the control signal further based at least in part on an indication of a desired contact load to be exerted by said mobile end part on the object.

12. A device as claimed in claim 11, wherein the indication of the desired effective impedance for said elastic element comprises at least two of: - an indication of a desired effective stiffness for said elastic element; an indication of a desired effective damping for said elastic element; an indication of a desired effective undamped natural frequency for said elastic element; an indication of a desired effective damping ratio for said elastic element; - an indication of a first desired effective pole of a characteristic equation modeling said elastic element; an indication of a second desired effective pole of the characteristic equation modeling said elastic element.

13. A device as claimed in claim 1, wherein said sensor comprises a load cell positioned at said mobile end part.

14. A device as claimed in claim 9, wherein said first sensor comprises a load cell positioned at said mobile end part and said third sensor comprises an accelerometer positioned at said mobile end part.

15. A device as claimed in claim 1 , wherein said load application unit comprises an actuator coupled to said control unit and a transmission unit coupled to said actuator and said mobile end part, said actuator being operative to interact with said transmission unit to apply the control load to said mobile end part in accordance with the control signal.

16. A device as claimed in claim 15, wherein said actuator is a motor.

17. A device as claimed in claim 15, wherein the contact load is a contact force and the control load is a control force, said transmission unit comprising a pulley coupled to said actuator and adapted to be driven by said actuator, and a cable coupled to said pulley and said mobile end part.

18. A device as claimed in claim 15, wherein the contact load is a contact force and the control load is a control force, said transmission unit comprising a rack and pinion arrangement coupled to said actuator and said mobile end part.

19. A device as claimed in claim 1, wherein said elastic element comprises a spring.

20. A device as claimed in claim 19, wherein said mobile end part is a structure coupled to an end portion of said spring.

21. A device as claimed in claim 1, wherein said elastic element comprises a piece of elastic material.

22. A device as claimed in claim 21 , wherein said mobile end part is a structure coupled to an end portion of said piece of elastic material.

23. A device as claimed in claim 1 , wherein the contact load is a contact force and the control load is a control force.

24. A device as claimed in claim 1 , wherein the contact load is a contact torque and the control load is a control torque.