Master-slave system

Abstract

A master-slave system (1) according to the present invention includes at least one master displacement sensor (Pm.sub.1 to Pm.sub.3) for measuring a master displacement for a master robot, at least one slave displacement sensor (Ps.sub.1 to Ps.sub.3) for measuring a slave displacement for a slave robot, a master target displacement calculating device (2) for mapping the slave displacement and thereby obtaining a master target displacement which is a target value for the master displacement corresponding to the slave displacement, and a master actuator (Am.sub.1 to Am.sub.3) for generating a master driving force to position-control the master robot on the basis of the master target displacement and the master displacement. The mapping is predefined such that a set of master target displacements excludes a singular configuration for the master robot. The master-slave system (1) renders it possible to solve a singular configuration problem for both the master robot and the slave robot.

Claims

1. A master-slave system having a master robot and a slave robot and being subjected to bilateral control, the master robot being an admittance-type haptic device manipulated by an operator, the slave robot being at least electrically connected to the master robot and having portions at least other than the trunk operating mechanically independent of the master robot, the system comprising: at least one master actuator for generating a master driving force to position-control the master robot; at least one slave actuator for generating a slave driving force to control the slave robot in terms of driving force; at least one master displacement sensor for measuring a master displacement for the master robot; at least one slave displacement sensor for measuring a slave displacement for the slave robot; at least one operating force sensor for measuring a master operating force applied to the master robot by the operator; a master target displacement calculating device for mapping the slave displacement and thereby obtaining a master target displacement which is a target value for the master displacement corresponding to the slave displacement; and a slave target driving force calculating device for obtaining a slave target driving force which is a target value for the slave driving force, on the basis of the master operating force, wherein, the slave actuator is adapted to generate the slave driving force on the basis of the slave target driving force, whereas the master actuator is adapted to generate the master driving force on the basis of the master target displacement and the master displacement, thereby: (1) eliminating the need for a working force sensor adapted for the bilateral control and to measure a slave working force applied to the environment by the slave robot; and (2) allowing the operator to feel the sense of slave dynamics without feeling the sense of master dynamics, and the mapping by the master target displacement calculating device is predefined such that a set of master target displacements excludes a singular configuration for the master robot, thereby (3) allowing a singular configuration problem for both the master robot and the slave robot to be solved in the entire range of movement of the slave robot regardless of whether the slave robot and the master robot have the same structure or different structures.

2. The master-slave system according to claim 1, wherein, the master target displacement calculating device obtains the master target displacement corresponding to the slave displacement by calculating inverse kinematics of the master robot in a master joint coordinate system for the master robot, whereby, the positional control of the master robot by the master actuator is performed in the master joint coordinate system.

3. The master-slave system according to claim 2, wherein the master robot has a mechanism configured such that the inverse kinematics of the master robot is analytically calculated without requiring numerically iterative convergence calculation.

4. The master-slave system according to claim 3, wherein, the master robot has six or less degrees of freedom, among the six or less degrees of freedom, three consecutive degrees of freedom are permitted by three rotational joints constituting a single serial link mechanism, and rotation axes of the three rotational joints or extensions thereto cross one another at a point.

5. The master-slave system according to claim 1, wherein, the master robot is selected from among a plurality of master robots, the slave robot is selected from among a plurality of slave robots electrically connectable to any of the master robots, and the selected master robot and the selected slave robot are electrically connected to each other.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of a force-projecting type master-slave system according to the present invention.

(2) FIG. 2 is a control block diagram of the force-projecting type master-slave system according to the present invention.

(3) FIG. 3 is a schematic diagram showing an example of a master arm of the force-projecting type master-slave system according to the present invention.

(4) FIG. 4 is a schematic diagram showing an example of a master arm which is inappropriate as a master arm of the force-projecting type master-slave system according to the present invention.

MODE FOR CARRYING OUT THE INVENTION

(5) Hereinafter, embodiments of the present invention will be described with reference to the drawings.

(6) As shown in FIG. 1, a force-projecting type master-slave system 1 according to the present invention (more precisely, a master-slave system to which force-projecting bilateral control is applied) includes a master robot with a master arm M and a slave robot with a slave arm S, the master arm M and the slave arm S being provided at different positions on a trunk B and electrically connected to each other in a manner as will be described below. In the force-projecting type master-slave system 1, the master arm M is an admittance-type haptic device manipulated by an operator U.

(7) The master arm M and the slave arm S respectively have a grip G, which serves as an operating end, and a working end d at one end, and are joined at the other end to different positions on the trunk B. Moreover, each of the master arm M and the slave arm S has two links and also has a joint (e.g., a rotational joint) at each of the end connected to the grip G or the working end d, the other end connected to the trunk B, and the connection between the links. Accordingly, each of the master arm M and the slave arm S has three degrees of freedom.

(8) Provided at these joints are master displacement sensors Pm.sub.1, Pm.sub.2, and Pm.sub.3, slave displacement sensors Ps.sub.1, Ps.sub.2, and Ps.sub.3, master actuators Am.sub.1, Am.sub.2, and Am.sub.3, and slave actuators As.sub.1, As.sub.2, and As.sub.3. In addition, the grip G is provided with an operating force sensor F.sub.m. Further, the force-projecting type master-slave system 1 includes a positional control system PC.sub.m, a master target displacement calculating device 2, a driving force control system FC.sub.s, and a slave target driving force calculating device 3, as shown in FIG. 1.

(9) Herein, the master arm M, the master displacement sensors Pm.sub.1, Pm.sub.2, and Pm.sub.3, the master actuators Am.sub.1, Am.sub.2, and Am.sub.3, the operating force sensor F.sub.m (or the grip G), and the positional control system PC.sub.m are included in the master robot, and the slave arm S, the slave displacement sensors Ps.sub.1, Ps.sub.2, and Ps.sub.3, the slave actuators As.sub.1, As.sub.2, and As.sub.3, and the driving force control system FC.sub.s are included in the slave robot.

(10) The operating force sensor F.sub.m is provided in the master arm M, and measures a master operating force f.sub.m from the operator U. The master displacement sensors Pm.sub.1, Pm.sub.2, and Pm.sub.3 are provided at the joints of the master arm M, and measure master displacements q.sub.m and x.sub.m. Moreover, the slave displacement sensors Ps.sub.1, Ps.sub.2, and Ps.sub.3 are provided at the joints of the slave arm S, and measure slave displacements q.sub.s and x.sub.s.

(11) The master target displacement calculating device 2 calculates master target displacements, which are target values for the master displacements q.sub.m and x.sub.m, on the basis of the measured slave displacements q.sub.s and x.sub.s. Moreover, the slave target driving force calculating device 3 calculates a slave target driving force, which is a target value for a slave driving force .sub.s to be described later, on the basis of the measured master operating force f.sub.m.

(12) The slave actuators Ps.sub.1, Ps.sub.2, and Ps.sub.3 are provided at the joints of the slave arm S, and generate the slave driving force .sub.s through the slave driving force control system FC.sub.s on the basis of the slave target driving force, whereby the slave arm S is controlled in terms of driving force. On the other hand, the master actuators Am.sub.1, Am.sub.2, and Am.sub.3 are provided at the joints of the master arm M, and generate a master driving force .sub.m on the basis of the master displacements q.sub.m and x.sub.m and the master target displacements, whereby the master arm M is position-controlled. More specifically, the master actuators Am.sub.1, Am.sub.2, and Am.sub.3 generate the master driving force .sub.m through the positional control system PC.sub.m, such that the deviation between a signal from each of the master displacement sensors Pm.sub.1, Pm.sub.2, and Pm.sub.3 and a signal from the master target displacement calculating device 2 is 0.

(13) In this manner, in the force-projecting type master-slave system 1, the slave actuators As.sub.1, As.sub.2, and As.sub.3, which generate the slave driving force .sub.s, control the slave arm S in terms of driving force, whereas the master actuators Am.sub.1, Am.sub.2, and Am.sub.3, which generate the master driving force .sub.m, position-control the master arm M.

(14) FIG. 2 represents the above configuration in a control block diagram. In FIG. 2, the master robot includes the master arm M, the master displacement sensors Pm.sub.1, Pm.sub.2, and Pm.sub.3, the master actuators Am.sub.1, Am.sub.2, and Am.sub.3, the operating force sensor F.sub.m (or the grip G), and the positional control system PC.sub.m. Also, the slave robot includes the slave arm S, the slave displacement sensors Ps.sub.1, Ps.sub.2, and Ps.sub.3, the slave actuators As.sub.1, As.sub.2, and As.sub.3, and the driving force control system FC.sub.s.

(15) The force-projecting type master-slave system 1 according to the present invention is different from the basic force-projecting type master-slave system proposed in Patent Document 1 by the present inventor, in terms of computation by the master target displacement calculating device 2. More specifically, the master target displacement calculating device 2 of the force-projecting type master-slave system 1 according to the present invention obtains a master target displacement x.sub.md corresponding to the slave displacement x.sub.s using a mapping , which is predefined such that a set of master target displacements x.sub.md excludes a singular configuration for the master robot.

(16) The force-projecting bilateral control according to the present invention uses a master control law, for example, as represented by the following expression, in place of the master control law (18).
[Expression 29]
.sub.m=J.sub.m.sup.TK.sub.p(x.sub.mdx.sub.m)(29)
As for the slave control law, on the other hand, the aforementioned slave control law (19) is used without modification.

(17) Furthermore, in the force-projecting bilateral control according to the present invention, the master target displacement calculating device 2 uses a mapping as defined below. First, assuming that a set X.sub.m in a master operation domain is such that X.sub.m x.sub.m, and a set X.sub.s in a slave work domain is such that X.sub.sx.sub.s, a mapping between these sets is defined as shown below.
[Expression 30]
: X.sub.s.fwdarw.X.sub.m(30)
Furthermore, each set X.sub.mS in the vicinity of all singular configurations within the master operation domain is assumed to be such that X.sub.mSX.sub.m. In this case, the mapping is set such that the following expression is established for the image X.sub.md=((X.sub.s)x.sub.md of the set X.sub.s under the mapping .
[Expression 31]
X.sub.mdX.sub.m and X.sub.mdX.sub.mS=(31)

(18) The mapping thus defined renders it possible to obtain the master target displacement x.sub.md=(x.sub.s) which corresponds to the slave displacement x.sub.s, so as to avoid the vicinity of the singular configuration for the master robot. In addition, this renders it possible to solve the singular configuration problem for both the master robot and the slave robot.

(19) The set X.sub.mS in the vicinity of the singular configuration depends on the mechanism of the master robot, and therefore, upon implementation, it is necessary to specifically define the mapping for each master robot, but expectedly, in most cases, it is sufficient to simply use a mapping obtained by adding a translation (or an offset) of x.sub.mdo to the scale transformation x.sub.md=S.sub.px.sub.s, as represented by the following expression, set x.sub.mdo as a position corresponding to the vicinity of the center of the master operation domain, and set the scale ratio S.sub.p low to such a degree that the master target displacement x.sub.md does not contain the vicinity of the singular configuration.
[Expression 32]
x.sub.md=(x.sub.s)=S.sub.px.sub.s+x.sub.mdo(32)

(20) In the case where the simple mapping represented by Expression (32) does not suffice, it is simply required to define the mapping by a linear transformation, including a simple scale transformation (i.e., scaling) and a translation combined with rotation and shearing of a so-called affine transformation. In addition, the mapping can also be defined by a projective transformation or an appropriate nonlinear transformation.

(21) Non-Patent Document 4 describes on pp. 78-85 an approach of correlating a master operation domain and a slave work domain in a double-structure master-slave system, but this approach is a method for allowing the directions of movement of the master and the slave in different shapes to roughly match each other approximately in the entire range of movement, and cannot solve the singular configuration problem as can the present invention.

(22) The positional control of the master robot has been described above as being performed in the work coordinate system in accordance with the master control law (29), but by using the inverse kinematics of the master robot, the positional control can be performed, for example, in a master joint coordinate system in accordance with the following master control law (33).
[Expression 33]
.sub.m=K.sub.p(q.sub.mdq.sub.m)(33)
The master joint displacement q.sub.m and its target value, master target joint displacement q.sub.md, are as shown below. Note that the master joint displacement q.sub.m is equivalent to the posture of the master robot, and therefore, will also be referred to herein as the posture q.sub.m.
[Expression 34]
q.sub.m=.sub.m.sup.1(x.sub.m)(34)
[Expression 35]
q.sub.md=.sub.m.sup.1(x.sub.md)=.sub.m.sup.1((x.sub.s))(35)
In Expressions (34) and (35), .sup.1 is a nonlinear function representing the inverse kinematics of the master robot. As described earlier, in the present invention, the mapping p is defined so as to cover the entire slave work domain X.sub.s while avoiding the singular configuration for the master robot, and therefore, the inverse kinematics .sub.m.sup.1((x.sub.s)) always has a solution.

(23) The master control law (29) uses the Jacobian matrix J.sub.m(q.sub.m) for positional control in the work coordinate system, and therefore, the gain J.sub.m.sup.TK.sub.p for displacement error in the work coordinate system changes depending on the posture q.sub.m of the master robot. That is, a gain appropriate for a posture might not be appropriate for another posture. On the other hand, in the case of the master control law (33), the gain K.sub.p for displacement error in the master joint coordinate system is a constant independent of the posture q.sub.m of the master robot, and therefore, system stability is expected to be enhanced.

(24) The inverse kinematics .sub.m.sup.1((x.sub.s)) in the master control law (33) has been described as always having a solution, but the solution is not always analytically derivable. In particular, it is often the case that the inverse kinematics of a link mechanism having a number of degrees of freedom does not have a general analytical solution. In the case where there is no analytical solution, it is necessary to derive a solution through a numerical solution method, i.e., numerically iterative convergence calculation by a computer, but such calculation imposes an extremely high burden on the control system.

(25) However, for example, mechanisms of most industrial robot arms are devised such that solutions can be analytically derived without using a numerical solution method. In this regard, Non-Patent Document 10 indicates that the general solution to inverse kinematics can be analytically derived so long as the robot to be controlled satisfies the following two conditions:

(26) i) the number of degrees of freedom of the robot is six or less; and

(27) ii) among the six or less degrees of freedom, three consecutive degrees of freedom are permitted by three or more rotational joints constituting a single serial link mechanism, and the rotation axes of the three rotational joints or their extensions cross one another at a point.

(28) Accordingly, in the present invention also, the master robot is provided as such a mechanism, so that the solution to the inverse kinematics .sub.m.sup.1((x.sub.s)) in the master control law (33) can be analytically derived, and the positional control of the master robot can be performed in a fast and simple manner in accordance with the master control law (33).

(29) In conventional master-slave systems not being of the force-projecting type, the slave robot is position-controlled, and therefore, to enhance system stability using inverse kinematics and also achieve fast and simple control, the slave robot is preferably structured with analytically derivable inverse kinematics such that the above conditions i) and ii) are satisfied. However, the slave robot is primarily required to have working performance to achieve its tasks, and there is difficulty in having the structure intended to both realize required working performance and allow analytical derivation of inverse kinematics. In this regard, the master robot is simply required to have a structure that can be readily manipulated by a human, and therefore, it is relatively easy to provide a structure that allows analytical derivation of inverse kinematics and is superior in operability.

(30) FIG. 3 shows an example of a master robot (master arm M) which satisfies the conditions i) and ii). As shown in the figure, the master arm M includes six rotational joints indicated at 1 to 6, and therefore, has six degrees of freedom. Moreover, among the rotational joints 1 to 6, the three consecutive rotational joints 4 to 6 constitute a serial link mechanism, and further, an extension to the rotation axis of the rotational joint 4 and an extension to the rotation axis of the rotational joint 6 cross each other at a point on the rotation axis of the rotational joint 5.

(31) Note that, for example, the rotational joints 1, 2, and 4 cannot be said to be consecutive. Also, for example, the rotational joints 1, 2, and 3 are consecutive but their rotation axes (or extensions thereto) do not cross one another at a point.

(32) FIG. 4 shows an example of a master robot (master arm M) which does not satisfy the conditions i) and ii). As shown in the figure, the master arm M has eight degrees of freedom permitted by seven rotational joints indicated at 1 to 3 and 5 to 8 as well as one prismatic joint indicated at 4, and therefore, does not satisfy the condition i). Moreover, the master arm M has three sets of three consecutive rotational joints (1 to 3, 5 to 7, and 6 to 8), but none of the sets includes joints whose rotation axes (or extensions thereto) cross one another at a point. Accordingly, the master arm M dose not satisfy the condition ii) either.

(33) The force-projecting type master-slave system according to the present invention may be a master-slave system constructed by electrically connecting one master robot selected from among a plurality of master robots and one slave robot selected from among a plurality of slave robots that can be electrically connected to any of the master robots. As described above, the master robot is required to have operability, whereas the slave robot is required to have workability, and if the above configuration is provided, it is possible to use a preferable master robot (i.e., the user's own preferred master robot) and also change the slave robots to choose from, depending on tasks, resulting in such advantages as rendering it possible to shorten the period of training for acquiring skills and also to deal with a wide variety of tasks which cannot be completed simply by changing an end effector provided at the working end of the slave robot.

(34) The above configuration is suitable for use in, for example, a master-slave system serving as a surgical robotic system. As for the master, a surgeon can select a well-adjusted master robot in accordance with his/her body size, skills, and preferences, and as for the slave, a suitable one for the operative procedure can be selected from among a wide variety of slave robots prepared in advance. Moreover, the above configuration is also suitable for the case where it is desired for one master robot to selectively operate either a small slave robot such as a surgical robot or a large slave robot such as a power-amplifying robot.

(35) In the case of the conventional master-slave systems with the singular configuration problem, it is necessary to address the singular configuration problem for each combination of the master robot and the slave robot, and therefore, it is extremely difficult to construct a master-slave system by connecting a master robot and a slave robot, each being selected at will, as described above, from among a plurality of master robots or a plurality of slave robots.

(36) However, since the force-projecting type master-slave system according to the present invention renders it possible to solve the singular configuration problem for both the master robot and the slave robot, it is rendered possible to readily construct a master-slave system including an arbitrary combination of a master robot and a slave robot, simply by manually or automatically defining a mapping based on information held in the master robot and the slave robot when the master robot and the slave robot are selected and connected, the slave robot holding information regarding the entire range of movement (or the entire work domain), i.e., information regarding sets X.sub.s in the slave work domain, the master robot holding information regarding the entire range of movement (or the entire operation domain) as well as information regarding the vicinity of singular postures, i.e., information regarding sets X.sub.m in the master operation domain and information regarding sets X.sub.mS in the vicinity of all singular configurations in the master operation domain. Note that the defining of the mapping can be readily automated, for example, by a method which can adjust S.sub.p and x.sub.mdo in Expression (32).

(37) [Points to be Noted]

(38) The terms master robot and slave robot are used herein for convenience, but the present invention is not necessarily limited only to the application to typical and orthodox robots. The master-slave system and the bilateral control are expected to be used in a wide variety of applications, and the present invention can be applied to any electrical master-slave systems. For example, any systems called X-by-Wire are electrical master-slave systems. Accordingly, in the case where the bilateral control is used not only in master-slave robotic systems but also in X-by-Wire systems for vehicles, airplanes, vessels, and any other types of operable machine, the present invention can be applied without modification.

(39) The terms displacement and position herein are intended to mean a generalized displacement and encompass a position and a posture in translation and rotation. Similarly, the term force is intended to mean a generalized force and encompass a translational force and a rotational force (or torque).

(40) The specific control laws for various types of bilateral control are mere examples for the sake of explanation, and higher-level control laws can be used so long as the purpose of control remains the same. For example, proportional control is used as the positional control law, but it is understood that high-level control such as PID control, proxy-based sliding mode control, which is an extended version of the PID control (see Non-Patent Document 11), or a further extended version thereof as described in Patent Document 2, can also be used.

(41) The operating force sensor does not have to be a hardware force sensor, and may be a means for estimating an operating force on the basis of a current from an electromagnetic actuator or a pressure from a hydro-pneumatic actuator or may be a means for estimating an operating force using an observer or suchlike on the basis of, for example, a signal from a displacement sensor.

(42) In the force-projecting bilateral control, the result of operation is presented as displacement information, using a wide frequency range from DC at lower limit to about hundreds of Hz to 1 kHz at upper limit. The result of operation does not have to be presented by one type of actuator, and may be presented by a plurality of actuators capable of presenting different frequency ranges from each another. Conceivable examples of a combination of such actuators include a combination of large and small motors (i.e., a so-called macro-micro system) and a combination of a motor in charge of a low-frequency range and an oscillator, a speaker, a voice coil motor, or the like in charge of a high-frequency range.

DESCRIPTION OF THE REFERENCE CHARACTERS

(43) 1 master-slave system

(44) 2 master target displacement calculating device

(45) 3 slave target driving force calculating device

(46) M master arm

(47) S slave arm

(48) F.sub.m operating force sensor

(49) FC.sub.s driving force control system

(50) PC.sub.m positional control system

(51) Am.sub.1 to Am.sub.3 master actuator

(52) As.sub.1 to As.sub.3 slave actuator

(53) Pm.sub.1 to Pm.sub.3 master displacement sensor

(54) Ps.sub.1 to Ps.sub.3 slave displacement sensor