Device and Method for Performing Open-Loop and Closed-Loop to Control of a Robot Manipulator

Abstract

The invention relates to a device and method for performing open-loop and closed-loop control of a robot manipulator which is driven by a number M of actuators ACTm and has an end effector. The invention comprises a first unit which registers and/or makes available an external force winder {right arrow over (F)}ext(t)={{right arrow over (f)}ext(t),{right arrow over (m)}ext(t)} acting on the end effector, a regulator which is connected to the first unit and to the actuators ACTm and which comprises a first regulator R1, which is a force regulator, and a second regulator R2 which is connected thereto and which is an impedance regulator, an admittance regulator, a position regulator or a cruise controller, wherein the regulator determines manipulated variables um(t) with which the actuators ACTm can be actuated in such way that when contact occurs with the surface of an object, the end effector acts on said object with a predefined force winder {right arrow over (F)}D(t)={{right arrow over (f)}D(t),{right arrow over (m)}D(t)}; where um(t)=um,R1(t)+um,R2(t), wherein the first regulator R1 is embodied and configured in such a way that the manipulated variable um,R1(t) is determined as a product of a manipulated variable um,R1(t)* and a function S(v(t)) or as a function S*(v(t), um,R1(t)*), where: um,R1(t)=S(v(t)) um,R1(t)* or um,R1(t)=S*(v*(t), um,R1(t)*); v(t)=v({right arrow over (F)}D(t), {right arrow over (R)}(t)); vε[va, ve], v*(t)=v*({right arrow over (F)}D(t), {right arrow over (R)}(t))=[v1*({right arrow over (F)}D(t), {right arrow over (R)}(t)), . . . , vQ*({right arrow over (F)}D(t), {right arrow over (R)}(t))].

Description

BACKGROUND

The invention relates to a device and method for performing open-loop and closed loop control of a robot manipulator, which is driven by a number M of actuators ACT_m and has an end effector, where m=1, 2, . . . , M. Further, the invention relates to a computer system having a data processing device, a digital storage medium, a computer program product and a computer program.

It is known that robot manipulators can exceed humans in the performance of handling tasks with respect to repeatable speed and precision. With respect to sensitive exertion of force and compliancy, humans, however, are still superior to a robot manipulator regarding tasks, which primarily becomes apparent in real applications, which require objects to be sensitively manipulated or assembled. The latter requires a complex coordination of contact forces and sequence of movements.

“Impedance control” of robot manipulators is known in this context. The concept of impedance control of robot manipulators aims at imitating human behavior by active control of a robot manipulator, e.g., based on an externally animated mass spring damper model.

Generally, an intended compliancy of robot manipulators can be generated either by active control, by inserting compliant components into the robot manipulator or a combination of both. It is further known that it is not possible to create an arbitrary Cartesian compliancy solely by means of uncoupled elastic joints (Albu-Schäffer, Fischer, Schreiber, Schoeppe, & Hirzinger, 2004), so that a passive compliancy of a robot manipulator always requires to be combined with an active control to avoid the problem. In doing so, inaccuracies in the object model/surface model can be avoided, defined powers can be exerted onto the environment, and/or objects can be manipulated.

Furthermore known is an “active interaction control”. An active interaction control can be divided into “direct” and “indirect” force control (Villani & De Schutter, 2008). Recently, such force regulators having variations of the virtual position were introduced (Lutscher & Cheng, 2014 and Lee & Huang, 2010). Furthermore known is a power, position and/or impedance control under predetermined mandatory conditions in different spaces (Borghesan & De Schutter, 2014).

Although significant progress has been made in the field of robot manipulator control, the following disadvantages continue to exist.

For example, a purely impedance controlled robot manipulator generates the desired forces either based on a pure feed forward control or based on a respective displacement of a virtually desired position of an effector of the robot manipulator. Therefore, this regulator class does not explicitly take into consideration external forces, which, however, is required if a predetermined force/torque of an effector of the robot manipulator is to be exerted onto an environment/object/work piece etc. with sufficient accuracy. Furthermore, the environment is required to be modelled with sufficient accuracy regarding its geometry and compliancy properties for this regulator approach to work. This, however, contradicts the fundamental idea of impedance control to work in an unmodeled environment.

If a predefined large force is exerted onto an object (environment) by means of the effector of the robot manipulator via feed forward control, it is furthermore disadvantageous for a pure impedance controlled robot manipulator that a potentially dangerous instantaneous and large movement is executed by the robot manipulator (with respect to the traveled effector path, speed, and acceleration) in case of occurrence of loss of contact between effector and object. This is, e.g., conditioned by a virtually desired position of the effector being far away from the actual position of the effector in case of loss of contact.

Furthermore known is a “pure force control” of robot manipulators. A force control of a robot manipulator presents the basics to exchange external forces sufficiently enough with the environment and thus facilitates an exact manipulation of objects or the surfaces thereof. Such ability is an essential necessity in industrial applications of robot manipulators. Thus, the rather unprecise impedance control is no alternative for force control. These problems have caused diverse approaches of the so-called hybrid position force control (Raibert & Craig, 1981). These hybrid position force controls are based on the idea to partition a so-called “task space” into complementary force and position spaces so that force or torque and movement can be exerted and controlled in their separate spaces.

A disadvantage of known hybrid force controls is that they have very low robustness with respect to loss of contact of the robot manipulator with an environment. Furthermore, an environment is required to be exactly modelled in this case, as well, to secure good control performance, which, however, seldom exists with sufficient quality.

To show the stability of such regulators, the environment is typically modelled as a simple spring damper system. An overview on various force regulators including comments on the stability analysis thereof can be found in (Zeng & Hemami, 1997). A very general critique on such regulators is specified in (Duffy, 1990), because a wrong selection of the metrics or the coordinate system is oftentimes made.

SUMMARY

It is the object of the invention to specify a device and a method for performing open-loop closed-loop control of a robot manipulator which is driven by a number M of actuators ACT_m having an end effector, where m=1, 2, . . . , M, which avoid the above mentioned disadvantages to a large extent. In particular, larger movements of the robot manipulator after loss of contact with an object of the end effector are to be avoided.

The invention becomes apparent from the features of the independent claims. Advantageous further developments and embodiments are subject of the dependent claims. Further features, application possibilities and advantages of the invention will become apparent from the following description as well as the explanation of exemplary embodiments of the invention, which are illustrated in the figures.

According to a first aspect, the object is solved by means of a device for performing open-loop and closed-loop control of a robot manipulator, which is driven by a number M of actuators ACT_m, having an end effector, where m=1, 2, . . . , M. The term “actuators” is to be understood broadly. It comprises, e.g., electric motors, linear motors, multiphase motors, Piezo actuators, etc.

The device further comprises a first unit, which registers and/or makes available an external force winder {right arrow over (F)}_ext(t)={f_ext(t),{right arrow over (m)}_ext(t)}, acting on the end effector, where {right arrow over (f)}_ext(t):=external force acting on the end effector and {right arrow over (m)}_ext(t):=external torque acting on the end effector. To do so, the first unit advantageously has a sensor system to register the external force winder {right arrow over (F)}_ext(t)={{right arrow over (f)}_ext(t),{right arrow over (m)}_ext(t)} and/or an estimator to estimate the external force winder {right arrow over (F)}_ext(t)={{right arrow over (f)}_ext(t),{right arrow over (m)}_ext(t)}. The sensor system advantageously comprises one or more force sensors and/or torque sensors. The estimator advantageously comprises a processor to run a program to estimate the force winder {right arrow over (F)}_ext(t).

Furthermore, the suggested device comprises a regulator connected with the first unit and the actuators ACT_m. The regulator, in turn, comprises a first regulator R1, which is a force regulator, and a second regulator R2 connected thereto, which is an impedance regulator, an admittance regulator, a position regulator, a cruise controller or a combination thereof, wherein the regulator determines manipulated variables u_m(t), with which the actuators ACT_m can be actuated in such way that when contact occurs with the surface of an object, the end effector acts on said object with a predefined force winder formula {right arrow over (F)}_D(t)={{right arrow over (f)}_D(t),{right arrow over (m)}_D(t)}, where:

u _m(t)=u_m,R1(t)+u_m,R2(t),  (1)

with {right arrow over (f)}_D(t):=predetermined power; {right arrow over (m)}_D(t):=predetermined torque, u_m,R1(t):=ratio of manipulated variables of the first regulator R1, and u_m,R2(t):=ratio of manipulated variables of the second regulator R2 and t:=time. The predefined force winder {right arrow over (F)}_D(t) results from the object presented to the robot.

In doing so, the first regulator R1 is embodied and configured in such way that the manipulated variable u_m,R1(t) is determined as a product of a manipulated variable u_m,R1(t)* and a function S(v(t)) or as a function S*(v*(t), u_m,R1(t)*), where:

u _m,R1(t)=S(v(t))·u_m,R1(t)*  (2a)

u _m,R1(t)=S*(v*(t),u_m,R1(t)*)  (2b)

v(t)=v({right arrow over (F)}_D(t),{right arrow over (R)}(t))  (3a)

v*(t)=v*({right arrow over (F)}_D(t),{right arrow over (R)}(t))=[v₁*({right arrow over (F)}_D(t),{right arrow over (R)}(t)), . . . ,v_Q*({right arrow over (F)}_D(t),{right arrow over (R)}(t))]v*(t)=[v₁*(t),v₂*(t), . . . ,v_Q*(t)]  (3b)

v(t)ε[v_a,v_e]  (4a)

v ₁*(t)ε[v_1a,v_1e],v₂*(t)ε[v_2a,v_2e], . . . ,v_Q*(t)ε[v_Qa,v_Qe]  (4b)

with: u_m,R1*(t):=a manipulated variable determined by the first regulator R1 to generate the predefined force winder {right arrow over (F)}_D(t); {right arrow over (R)}(t):=a regulator difference made available by the regulator, S(v(t)):=a monotonically decreasing function of v(t), which depends on {right arrow over (F)}_D(t) and {right arrow over (R)}(t), S*(v*(t), u_m,R1(t)*):=a function, for which the influence of u_m,R1(t)* is basically monotonically decreasing in each of the Q individual components [v₁*(t), v₂*(t), . . . , V_Q*(t)], [v_a, v_e]:=a predefined definition area of the variable v(t), and [v_1a, v_1e], [v_2a, v_2e], . . . , [v_Qa, v_Qe] a component-wise definition area of the vector quantity v*(t) of the dimension Q.

Thus, in one alternative the invention features the ratio of the manipulated variables of force regulator R1 u_m,R1(t), which is determined conventionally, being multiplied with a monotonically decreasing function S(v(t))=S(v({right arrow over (F)}_D(t), {right arrow over (R)}(t))) (so-called “shaping function”), which altogether causes that, when contact loss with an environment of the end effector occurs, larger movements of the robot manipulator can be excluded. The “shaping” effect can also be achieved in one alternative, if u_m,R1(t) is determined as a function S*(v(t), u_m,R1(t)*). In doing so, “shaping” effects according to the invention are achieved for all those configurations of the force regulator, which cannot be represented mathematically as a product of a manipulated variable u_m,R1(t)* and a function S(v(t)). For example, individual components of a PID regulator can have different, respectively monotonically decreasing shaping function S*₁(v*₁(t)), S*₂(v*₂(t)), . . . .

The function S(v(t)) preferably has a value domain of [1, 0], wherein in case of contact of the end effector with the environment (normal operation) S(v(t))=1. If loss of contact of the end effector with the environment occurs, then a large negative deviation {right arrow over (R)}(t)) occurs at the regulator. S(v(t)) is preferably actuated such that the larger the negative deviation {right arrow over (R)}(t)) and the larger the force winder {right arrow over (F)}_D(t) to be applied by the end effector, the faster the function v(t) decreases from One to Zero. This is applicable analogously to S*(v*(t)).

A further development of the proposed device is characterized in that—in case that the object (with which the end effector is in contact and onto which it exerts the force winder {right arrow over (F)}_D(t)) is elastic and its surface is flexible—the regulator takes into consideration predefined elasticity properties of the object when determining the manipulated variables u_m(t).

A further development of the proposed device is characterized in that a second unit is present, which serves as energy storage for passivation of the regulator and stores energy T1 coming from the regulator according to a predefined energy storage dynamic and delivers energy T2 to the regulator, wherein the second unit and the regulator form a closed loop, and an initialization of the unit with energy T0 depends on a determined or predefined expenditure of energy E_Expenditure to perform a current task of the robot manipulator. In doing so, energy E stored by the second unit can be a virtual or a physical energy. In the first case, the virtual energy is only an operand. In the second case, the energy is a physical energy (e.g., electrical energy), wherein the second unit comprises a corresponding physical energy storage (e.g., a battery). The second case of the further development facilitates not only an improved, i.e., passivated open-loop and closed-loop control of the robot manipulator, but also simultaneously a decrease of the expenditure of energy during operation of the robot manipulator.

An upper energy limit G1 is defined advantageously for the above further development, wherein the second unit is embodied and configured such that: E≦G1 is always true for the energy E stored in the second unit. Furthermore advantageously defined is a lower energy limit G2, with: 0<G2<G1, and the second unit is embodied such that, if: G2<E≦G1 is true for the energy E stored in the second energy unit, the second unit is coupled to the regulator, and if E≦G2 is true, the second unit is uncoupled from the regulator.

A further aspect of the invention relates to a robot having a robot manipulator, which is driven by a number M of actuators ACT_m, having an end effector, which has a device as explained herein, where m=1, 2, . . . , M.

A further aspect of the invention relates to a method for performing open-loop and closed loop control of a robot manipulator, which is driven by a number M of actuators ACT_m, having an end effector, where m=1, 2, . . . , M, having the following steps: Registering and/or making available an external force winder {right arrow over (F)}_ext(t)={{right arrow over (f)}_ext(t), {right arrow over (m)}_ext(t)} acting on the end effector, where {right arrow over (f)}_ext(t):=external force acting on the end effector; {right arrow over (m)}_ext(t):=external torque acting on the end effector; by means of a regulator, which comprises a first regulator R1, which is a force regulator, and a second regulator R2 connected therewith, which is an impedance regulator, an admittance regulator, a position regulator, a cruise controller or a combination thereof, determining manipulated variables u_m(t), with which the actuators ACT_m are actuated in such way that when contact occurs with a surface of an object, the end effector acts on said object with a predefined force winder {right arrow over (F)}_D(t)={{right arrow over (f)}_D(t),{right arrow over (m)}_D(t)}; where:

u _m(t)=u_m,R1(t)+u_m,R2(t),  (1)

where {right arrow over (f)}_D(t):=predefined force; {right arrow over (m)}_D(t):=predefined torque, u_m,R1(t):=ratio of manipulated variables of the first regulator R1, and u_m,R2(t):=ratio of manipulated variables of the second regulator R2, wherein the first regulator R1 is embodied and configured in such way that the manipulated variable u_m,R1(t) is determined as a product of a manipulated variable u_m,R1(t)* and a function S(v(t)) or as a function S*(v*(t), u_m,R1(t)*), where:

u _m,R1(t)=S(v(t))·u_m,R1(t)*  (2a)

u _m,R1(t)=S*(v*(t),u_m,R1(t)*)  (2b)

v(t)=v({right arrow over (F)}_D(t),{right arrow over (R)}(t))  (3a)

v*(t)=v*({right arrow over (F)}_D(t),{right arrow over (R)}(t))=[v₁*({right arrow over (F)}_D(t),{right arrow over (R)}(t)), . . . ,v_Q*({right arrow over (F)}_D(t),{right arrow over (R)}(t))]v*(t)=[v₁*(t),v₂*(t), . . . ,v_Q*(t)]  (3b)

v(t)ε[v_a,v_e]  (4a)

v ₁*(t)ε[v_1a,v_1e],v₂*(t)ε[v_2a,v_2e], . . . ,v_Q*(t)ε[v_Qa,v_Qe]  (4b)

where: u_m,R1*(t):=is a manipulated variable determined by the first regulator R1 to generate the predefined force winder {right arrow over (F)}_D(t); {right arrow over (R)}(t):=is a provided negative deviation of the regulator, S(v(t)):=is a monotonically decreasing function of v(t), which is dependent on {right arrow over (F)}_D(t) and {right arrow over (R)}(t), S*(v*(t), u_m,R1(t)*):=is a function, where the influence of u_m,R1(t)* is generally monotonically decreasing in each of the Q individual components [v₁*(t), v₂*(t), . . . , V_Q*(t)], [v_a, v_e]:=is a predefined definition area of the variable v(t), and [v_1a, v_1e], [v_2a, v_2e], . . . , [v_Qa, v_Qe] is a component-wise definition area of the vector quantity v*(t) of dimension Q.

Preferably, predefined elasticity properties of the object will be taken into consideration for the method by the regulator during the determination of the manipulated variables u_m(t), in case the object is elastic and thus its surface is flexible.

Furthermore preferably, a second unit exists, which serves as energy storage for passivation of the regulator, and which stores energy T1 coming from the regulator and delivers energy T2 to the regulator according to predefined energy storage dynamics, wherein the second unit and the regulator form a closed loop and an initialization of the unit with an energy T0 depends on a determined or predefined expenditure of energy E_Expenditure for implementation of a current task of the robot manipulator.

Advantages and preferred further developments of the suggested method result from an analogous and mutatis mutandis application of the above explanations regarding the suggested device.

A further aspect of the invention relates to a computer system having a data processing device, wherein the data processing device is designed such that a method as explained above is run on the data processing device.

A further aspect of the invention relates to a digital storage medium having electronically readable control signals, wherein the control signals can interact with a programmable computer system such that a method as explained above is run.

A further aspect of the invention relates to a computer program product having program code which is stored on a machine-readable carrier for implementation of the method as explained above if the program code is run on a data processing device.

A further aspect of the invention relates to a computer program having program codes to implement the method, as explained above, if the program runs on a data processing device. To do so, the data processing device can be designed as any computer system known in the art.

The suggested device and the suggested method for performing open-loop and closed loop control of a robot manipulator having an end effector, which is driven by a number M of actuators ACT_m, where m=1, 2, . . . , M is therefore based on a robust, passive-based approach by combination of force control with impedance control (cf. FIG. 1) and with energy tanks. The invention facilitates acceptance of arbitrary passive environments and thus has no necessity for variations of the virtually desired position, which have a rather non-robust behavior. The invention allows for a robust, compliant and stable manipulation of an environment by a robot manipulator without having to choose between force or impedance control. Furthermore, the described inherent disadvantage of force and impedance control is avoided and the advantages of force control and impedance control are combined, as best as possible. In particular, dangerous movements of the robot manipulator, which are caused by loss of contact of the end effector with the environment, are avoided.

The following explanations explain the invention in detail with respect to the following topics: A) robot modelling, B) regulator design, C) stabilization of losses of contact, and D) handling of flexible and strongly compliant objects.

A Robot Modelling

A1 Rigid Body Dynamics

The known dynamics of a robot manipulator having n joints (degrees of freedom, DOF) is given by:

M(q){umlaut over (q)}+C(q,{dot over (q)}){dot over (q)}+g(q)=τ_m+τ_ext  (5)

where qεRⁿ is the joint position. The mass matrix is given by M(q)εR^n×n, the Coriolis and centrifugal vector by C(q,{dot over (q)}){dot over (q)}εRⁿ, and the gravitation vector by g(q) εRⁿ. The control input of the system is the motor torque τ_m εRⁿ, where τ_ext εRⁿ comprises all externally engraved torques. In doing so, friction is neglected to simplify the illustration. External forces in the Cartesian space are given by vector F_ext:=(f_ext^T,m_ext^T)^T εR⁶, which represents a force-torque vector. Said vector can be depicted by means of the transposed Jacobian matrix J^T(q) into external joint torques by means of τ_ext=J^T(q)F_ext.

A2 Dynamics of Flexible Joints

For lightweight design robot manipulators or those with springs in the joints, assumption (5) is not sufficiently exact to be able to describe the inherent dynamics which is created by the presence of flexible structures such as the transmission. Therefore, the (reduced) model for robot manipulators having elastic joints is assumed for such structures (Spong, 1987)

M(q){umlaut over (q)}+C(q,{dot over (q)}){dot over (q)}+g(q)=τ_J+τ_ext  (6)

B{umlaut over (θ)}+τ _J=τ_m  (7)

τ_J=K(θ−q)  (8)

where θεRⁿ is the motor position. Equations (6) and (7) each describe the output side and driving end dynamics. Equation (8) couples (6) and (7) by means of the joint torque τ_J εRⁿ, which is assumed as linear spring torque. This can be readily expanded to non-linear joint springs by a person skilled in the art. In doing so, the damping in the joints can be neglected since the expansion is trivial and is therefore not taken into consideration, herein. The matrices KεR^n×n and BεR^n×n are both constant, positive defined diagonal matrices, which each describe the stiffness of the joints and inertia of the motor. The output side and driving end dynamics are not taken into consideration, herein, either.

B Regulator Design

B1 Cartesian Impedance Regulator

A stable impedance control of robot manipulators having elastic joints can be achieved by means of a skillful passivation of the system. This is achieved, e.g., in that the position feedback takes place as function of θ instead of θ and q. To do so, q is replaced by its statistic equivalent q(θ)−ζ⁻¹(θ), which is numerically achieved by means of a contraction with the implicit function ζ(q_e)=q_e+K⁻¹ g(q_e), wherein q_e is the output side position of the equilibrium point. Under weak assumptions, q(θ) can be used as estimator for q. Reference is made to (Albu-Schäffer, Ott, & Hirzinger, A Unified Passivity-based Control Framework for Position, Torque and Impedance Control of Flexible Joint Robots, 2007) for more details on the implicit function ζ as well as to the underlying theory. The passivity-based mathematical control law of impedance control for robot manipulators having flexible joints can now be formulated as follows:

τ_mi=−J^T(q)(K_x{tilde over (x)}(q(θ))+D_x{dot over (x)})  (9)

{tilde over (x)}(θ)={tilde over (x)}(q(θ))=f(q(θ))−x_s=x(σ)−x_s  (10)

B2 Cartesian Force Regulator

The regulator design is based on a Cartesian force regulator:

τ_mf=J^T(q)((K_p−I)(F_ext(t)−F_d(t))+K_d({dot over (F)}_ext(t)−{dot over (F)}_d(t))K_i∫₀^tF_ext(t)−F_d(t)dσ)  (11)

where K_d εR^6×6 and K_i εR^6×6 are each diagonal, positive definite matrices for the differential and integral ratio of the regulator. IεR^6×6 describes the identity matrix, and the matrix K_p εR^6×6 is selected such that K_p−I is also diagonal and positive definite. The desired force F_d:=(f_d^T,m_d^T)^T applied onto the environment is predefined by the user or a corresponding planer. Furthermore defined be: h_i (F_ext(t),t):=K_i∫₀^tF_ext(t)−F_d(t)−F_d(t)dσ, to improve subsequent readability. F_ext can either be obtained by means of a force sensor or by means of an observer (Haddadin, Towards Safe Robots: Approaching Asimov's 1st Law, 2013). If the force regulator is to be applied to a rigid robot, τ_m=τ_mf is inserted into (5) and into (7) for robots with flexible joints.

B3 Unified Force and Impedance Regulator

The simple combination of the above force and impedance regulator leads to the following mathematical control law:

τ_m=−J^T(q)((K_p−I)(F_ext(t)−F_d(t))+K_d({dot over (F)}_ext(t)−{dot over (F)}_d(t))+K_ih_i+K_x{tilde over (x)}(q(θ))+D_x{dot over (x)}).  (12)

Stability, however, cannot be guaranteed by such law. Therefore, the regulator is required to be augmented with an energy tank (cf. FIG. 2), so that the passivity and therefore, in turn, the stability of the system is warranted. Thus, a new mathematical control law is created:

τ_m=−J^T(q)(γK_d({dot over (F)}_d(t)−{dot over (F)}_ext(t))−ωx_t+K_x{tilde over (x)}(q(θ))+D_x{dot over (x)}),  (13)

where x_t is the condition of the energy tank, and co is defined by

$\begin{array}{cc}\omega =\frac{\alpha }{x_t}\left(K_pF_d+\left(1-\gamma \right)K_d\left({\stackrel{.}{F}}_d\left(t\right)-{\stackrel{.}{F}}_{\mathrm{ext}}\left(t\right)\right)-K_ih_i\right).& \left(14\right)\end{array}$

The dynamics of the energy tank can be described by:

$\begin{array}{cc}{\stackrel{.}{x}}_t=\frac{\beta }{x_t}\left({\stackrel{.}{x}}^TD_x\stackrel{.}{x}+\gamma {\stackrel{.}{x}}^TK_d\left({\stackrel{.}{F}}_d\left(t\right)-{\stackrel{.}{F}}_{\mathrm{ext}}\left(t\right)\right)\right)+u_t& \left(15\right)\end{array}$

The input of the energy tank is described herein as u_t. The binary scalars α,β,γ always guarantee the stability of the entire system.

B4 Task-Based Initialization

To calculate the task energy, the statistical balance of forces f_I|=x=xw+f_d=f_W is used, where f_I=K_x,t(p−p_s) and f_W=K_W,t(p_w−p_w,0) are each the forces for the impedance stiffness and the counterforce of the environment. The counterforce, which is generated by means of a surface of an object, is modelled herein as a linear function in the stiffness without taking the dampening into consideration. By solving for p_w, the position of the surface is obtained, after the force was regulated. The required work to move this surface can be calculated as:

$\begin{array}{cc}{E}_T={\int }_0^t\frac{1}{2}{\left(p_W\left(\sigma \right)-p_{W,0}\right)}^TK_{w,t}\left(p_W\left(\sigma \right)-p_{W,0}\right)d\sigma & \left(16\right)\end{array}$

Herein, only the translational energy is taken into consideration. Of course, an expansion for rotational cases is required, which is readily possible for the person skilled in the art.

For the specific control case f_d=konst., the task energy is calculated as:

$\begin{array}{cc}{E}_T=\frac{1}{2}{\left(p_W-p_{W,0}\right)}^TK_{w,t}\left(p_W-p_{W,0}\right)& \left(17\right)\end{array}$

The task energy is initialized accordingly.

C Stabilization of Losses of Contact

The stability of performing open-loop and closed-loop control of the robot manipulator is warranted for any conceivable cases, but this does not automatically mean that the robot manipulator performs exclusively secure movements. An unexpected loss of contact of the end effector with a surface of an object would still cause the robot having the robot manipulator to try to regulate a force until the energy tank is empty. Depending on the remaining energy in the energy tank, this can also cause large, fast and particularly undesired movements of the robot manipulator.

To avoid this, it could be suggested that the regulator is simply deactivated as soon as contact is no longer detected between the end effector and the environment/the object. This, however, causes an undesired switching behavior based on, e.g., sensor noise.

To avoid this, a robust position-based method is suggested herein, which uses a regulator-forming function S(v):=ρ(ψ), which is integrated into the regulator. Herein, it is as follows:

ρ(ψ)=(ρ_t(ψ),ρ_t(ψ),ρ_r(ψ),ρ_r(ψ),ρ_r(ψ),ρ_r(ψ))^T

and consists of a translational and a rotational ratio, each defined as:

${\rho }_t\left(\psi \right):=\{\begin{array}{cc}1& \mathrm{falls}f_d^{T}\Delta p\ge 0\\ \frac{1}{2}\left[1+\cos \left(\frac{\psi -\Delta p}{d_{\max }}\pi \right)\right]& \begin{array}{c}\mathrm{falls}f_d^{T}\Delta p<0\bigwedge \psi \in \\ \left[\Delta p,\Delta p+d_{\max }\right]\end{array}\\ 0& \mathrm{sonst}\end{array}\mathrm{and}{\rho }_r\left(\psi \right):=\{\begin{array}{cc}1& \mathrm{falls}m_d^{T}\Delta k_0\Delta k_v\ge 0\\ \frac{1}{2}\left[1+\cos \left(\frac{\psi -\Delta \varphi }{{\varphi }_{\max }}\pi \right)\right]& \begin{array}{c}\mathrm{falls}m_d^{T}\Delta k_0\Delta k_v<\\ 0\bigwedge \psi \in \left[\Delta \varphi ,\Delta \varphi +{\varphi }_{\max }\right]\end{array}\\ 0& \mathrm{sonst}\end{array}.\mathrm{falls}=\mathrm{if}\mathrm{sonst}=\mathrm{otherwise}$

The function ρ(ψ) in this example corresponds to the above function S(v). ψ corresponds to the regulator deviation {right arrow over (R)}(t).

A robot posture x:=(p^T,φ^T)^T consists of a translational ratio p and a suitable rotational representation, such as, e.g., an Euler angle φ.

Δp=p_s−p is the given vector, which points from the end effector to the virtually desired position and F_d:=(f_d^T,m_d^T)^T is the given desired 6-dimensional force winder (cf. FIG. 2). As soon as Δp and f_d include an angle larger than 90° the regulator should be deactivated.

To warrant a smooth transition, an interpolating function ρ_t (ψ) is selected, which interpolates in a user-defined region d_max. For rotational ratio ρ_r(ψ), quaternions are actuated as nonsingular representation. The unit quaternion k=(k₀,k_v) indicates the current orientation and the quaternion k_s=(k_0,s,k_v,s) the desired orientation.

The rotational error is then defined as Δk:=k⁻¹k_s and Δφ:=2 arccos(Δk₀). The user-defined region, which represents a robustness, can be indicated by an angle φ_max, which represents a relationship with a scalar component of the quaternion by means of φ_max:=2 arccos(k_0,max). From the point of view of stability analysis, this shaping function can be interpreted as a shaping of ω, which only scales the force regulator of the combined force and impedance regulator. Therefore, ω can be newly defined as ω_φ:=ρ(ψ) ω and the stability is warranted, again. The multiplication of ρ(ψ) is done component-wise, herein.

D) Handling of Flexible and Strongly Compliant Objects

If a position-based method is used for control, as introduced in the previous chapter, it must be taken into consideration that soft and deformable materials require a specific handling. To take into consideration a planning of the virtually desired position without compliancy or deformation of the environment, in some circumstances causes the problem that the force regulator is involuntarily deactivated or scaled. This is conditioned by the fact that, currently, based on compliancy, another current position exists as compared to without the presence of compliancy. Therefore, a corrective virtually desired position x′_d=(p′_d^T,φ′_d^T)^T is introduced to adjust the virtually desired position of the regulator for such flexible and strongly compliant materials. K_mat hereafter indicates the assumed (but not necessarily known) stiffness of the surface or object to be treated. A quasi-static mathematical correction law therefore is:

$\begin{array}{cc}\left(\begin{array}{c}{p}_d^{\prime }\\ {\varphi }_d^{\prime }\end{array}\right)=\left(\begin{array}{c}{p}_d\\ {\varphi }_d\end{array}\right)-{\left[\begin{array}{cc}{K}_{\text{?},\max }& K_{\text{?},\mathrm{mat}}\\ K_{\mathrm{rt},\mathrm{mat}}& K_{r,\mathrm{mat}}\end{array}\right]}^{-1}\left(\begin{array}{c}{f}_d\\ m_d\end{array}\right)\text{?}\text{indicates text missing or illegible when filed}& \left(18\right)\end{array}$

or, more briefly, x′_d=x_d−K_mat⁻¹F_d. It can be discerned that the virtually desired position is displaced such that the deviation caused by the soft-elastic material is corrected, accordingly (cf. FIG. 4). Of course, the environmental stiffness must be known or at least estimated for this approach. From equation (18) however, it follows intuitively, that for K→∞ the previous case is achieved. Of course, the law can also be extended in such way that a dampening of the environment is also taken into consideration. This however, aggravates the calculation.

REFERENCES

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Further advantages, features and details result from the following description, in which —under reference to the drawing, if required—at least one exemplary embodiment is described in detail. Same, similar and/or identically functioning components are indicated with the same reference numerals.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIGS. 1a-c show a conceptionally simplified diagram to illustrate a suggested hybrid regulator having an impedance regulator and a force regulator;

FIG. 2 shows a model system illustration for performing open-loop and closed loop control of a robot manipulator, which interacts with the environment;

FIG. 3a shows a schematized illustrated impedance controlled robot manipulator having an end effector EFF and a predefined translational robustness region d_max;

FIG. 3b shows a regulator shaping function ρ(ψ)=S(v(t)) for the translational case;

FIG. 4 shows a graph for deformation of elastic material by means of applied pressure of the end effector in the translational case;

FIG. 5 shows a schematized flow chart of a suggested device; and

FIG. 6 shows a schematized flow chart of a suggested method.

DETAILED DESCRIPTION

FIG. 1 shows a conceptionally simplified diagram to illustrate a suggested hybrid regulator having an impedance regulator and a force regulator. Dampers are not shown for reasons of clarity. FIG. 1a shows a pure impedance controlled robot manipulator having an end effector EFF. The impedance control is indicated by the illustrated spring. FIG. 1b shows a pure force regulated robot manipulator having an end effector EFF, which presses with a predefined force F_d against an object surface (shaded line). FIG. 1c shows a combination of the force regulator and the impedance regulator according to the invention from FIG. 1a and FIG. 1b.

FIG. 2 shows a model system illustration for performing open-loop and closed loop control of a robot manipulator according to the invention having an end effector, which interacts with an environment/object/workpiece. Represented as function blocks are the environment (=: “environment”), which interacts with the robot manipulator (=: “rigid body dynamics”) and the actuators (=: “motor dynamics”). The control and regulation of the actuators is implemented by means of a regulator (=: “force/impedance regulator”), to which an energy tank (=: “energy tank”) can be coupled. The connections and feedback connections of the blocks, which are interconnected with one another, are shown with the corresponding in/outputs and exchanged quantities. By decoupling of the regulator from the energy tank in case of violation of the passivity of the regulator, feedback of the external forces is annulled.

FIG. 3a shows a schematized illustrated impedance controlled robot manipulator having an end effector EFF and a predefined translational robustness region d_max. Δp=p_s−p indicates the vector, which points from the end effector position p to a set point p_s, wherein f_d indicates the predefined force winder.

FIG. 3b shows a regulator shaping function ρ(ψ)=S(v(t)) for the translational case. More detailed illustrations regarding the function ρ(ψ) can be found in the above description (cf. Part: “C Stabilization of losses of contact”).

FIG. 4 shows a graph for deformation of elastic material by means of applied pressure of the end effector EFF in the translational case, which illustrates in the above description in more detail (cf. Part “D Handling of flexible and strongly complaint objects”).

FIG. 5 shows a schematized flow chart of a suggested device for performing open-loop and closed loop control of a robot manipulator, which is driven by a number M of actuators ACT_m, having an end effector, where m=1, 2, 3. The device comprises a first unit 101, which registers and/or makes available a force winder {right arrow over (F)}_ext(t)={{right arrow over (f)}_e, (t),{right arrow over (m)}_ext(t)} acting on the end effector, where {right arrow over (f)}_ext(t):=external force acting on the end effector; {right arrow over (m)}_ext(t):=external torque acting on the end effector; a regulator 102, which is connected with the first unit 101 and the actuators ACT_m, which comprises a first regulator R1, which is a force regulator, and a second regulator R2 connected therewith, which is an impedance regulator, wherein the regulator 102 determines manipulated variables u_m(t), by means of which the actuators ACT_m can be actuated in such way that when contact occurs with the surface of an object, the end effector acts on said object with a predefined force winder {right arrow over (F)}_D(t)={{right arrow over (f)}_D(t),{right arrow over (m)}_D(t)}; wherein: u_m(t)=u_m,R1(t)+u_m,R2(t), where: {right arrow over (f)}_D(t):=predefined force; {right arrow over (m)}_D(t):=predefined torque, u_m,R1(t):=ratio of manipulated variables of the first regulator R1, and u_m,R2(t):=ratio of manipulated variables of the second regulator R2, wherein the first regulator R1 is embodied and configured such that the manipulated variable u_m,R1(t) is determined as a product of a manipulated variable u_m,R1(t)* and a function S(v(t)), wherein: u_m,R1(t)=S(v(t)) u_m,R1(t)*, v(t)=v({right arrow over (F)}_D(t), {right arrow over (R)}(t)),vε[v_a, v_e], where: u_m,R1*(t):=a manipulated variable determined by the first regulator R1 to generate the predefined force winder {right arrow over (F)}_D(t), {right arrow over (R)}(t):=a provided negative deviation of the regulator 102, S(v(t)):=a monotonically decreasing function of v(t), which depends on {right arrow over (F)}_D(t) and {right arrow over (R)}(t), and [v_a, v_e]:=a predefined definition area of the variable v(t).

FIG. 6 shows a schematized flow chart of a suggested method for performing open-loop and closed loop control of a robot manipulator, which is driven by a number M of actuators ACT_m, having an end effector, where m=1, 2, . . . , M. The method comprises the following steps. In a first step 201, a registering and/or making available of an external force winder {right arrow over (F)}_ext(t)={{right arrow over (f)}_ext(t),{right arrow over (τ)}_ext(t)} acting on the end effector takes place, where: {right arrow over (f)}_ext(t):=external force acting on the end effector; {right arrow over (m)}_ext(t):=external torque acting on the end effector. A determining of manipulated variables u_m(t), by means of which actuators ACT_m are actuated such that, the end effector in case of contact with a surface of an object acts on said object with a predefined force winder {right arrow over (F)}_D(t)={{right arrow over (f)}_D(t),{right arrow over (m)}_D(t)}, takes place in a second step 202 by means of a regulator 102, which comprises a first regulator R1, which is a force regulator, and a second regulator R2 connected therewith, which is an impedance regulator; wherein: u_m(t)=u_m,R1(t)+u_m,R2(t), wherein: {right arrow over (f)}_D(t):=predefined force; {right arrow over (m)}_D(t):=predefined torque, u_m,R1(t):=ratio of manipulated variables of the first regulator R1, and u_m,R2(t):=ratio of manipulated variables of the second regulator R2, wherein the first regulator R1 determines the manipulated variable u_m,R1(t) as product of a manipulated variable u_m,R1(t)* and a function S(v(t)), wherein: u_m,R1(t)=S(v(t)) u_m,R1(t)*, v(t)=v({right arrow over (F)}_D(t), {right arrow over (R)}(t)), and vε[v_a, v_e], where: u_m,R1*(t):=a manipulated variable determined by the first regulator R1 for generation of the predefined force winder {right arrow over (F)}_D(t), {right arrow over (R)}(t):=a provided negative deviation of the regulator 102, S(v(t)):=a monotonically decreasing function of v(t), which depends on {right arrow over (F)}_D(t) and {right arrow over (R)}(t), [v_a, v_e]:=a predefined definition area of the variable v(t).

Although the invention was illustrated and explained in more detail by preferred exemplary embodiments, the invention is not limited by the disclosed examples, and other variations can be derived therefrom by the person skilled in the art without leaving the scope of protection of the invention. It is therefore understood, that a plurality of variation possibilities exists. It is also understood, that exemplary stated embodiments do indeed represent mere examples, which are not to be interpreted in any way as limitation of, e.g., the scope of protection, the application possibilities or the configuration of the invention. Rather, the previous description and the description of the figures enable the person skilled in the art to specifically implement the exemplary embodiments, wherein the person skilled in the art can implement various changes with the knowledge of the disclosed idea of the invention, for example with respect to the function or arrangement of individual elements mentioned in an exemplary embodiment, without leaving the scope of protection, which is defined by the claims and their legal equivalences, such as the further explanation in the description.

Claims

1. A device for performing open-loop and closed loop control of a robot manipulator having an end effector, which is driven by a number M of actuators ACTm, where m=1, 2, . . . , M, comprising: a first unit, which registers and/or makes available an external force winder{right arrow over (F)}ext(t)={{right arrow over (f)}ext(t),{right arrow over (m)}ext(t)} acting on the end effector, where:{right arrow over (f)}ext(t):=external force acting on the end effector;{right arrow over (m)}ext(t):=external torque acting on the effector;a regulator R1 connected with the first unit and the actuators ACTm, which comprises a first regulator R1, which is a force regulator, and a second regulator R2 connected therewith, which is an impedance regulator, an admittance regulator, a position regulator or a cruise control, wherein the regulator determines manipulated variables um(t), by means of which the actuators ACTm can be actuated in such way that when contact occurs with the surface of an object, the end effector acts on said object with a predefined force winder {right arrow over (F)}D(t)={right arrow over (f)}D(t),{right arrow over (m)}D(t)}; wherein, um(t)=um,R1(t)+um,R2(t),  (1)where:{right arrow over (f)}D(t):=predefined force;{right arrow over (m)}D(t):=predefined torque,um,R1(t):=ratio of manipulated variables of the first regulator R1, andum,R2(t):=ratio of manipulated variables of the second regulator R2

2. The device according to claim 1, wherein, in case that the object is elastic and its surface is flexible, the regulator takes into consideration predefined elasticity properties of the object when determining the manipulated variables n um(t).

3. The device according to claim 1, wherein a second unit is present, which serves as energy storage for passivation of the regulator, and which stores energy T1 coming from regulator according to predefined energy storage dynamics, and delivers energy T2 to the regulator, wherein the second unit and the regulator form a closed-loop, and an initialization of the second unit with an energy T0 depends on a determined or predefined expenditure of energy EExpenditure to implement a current task of the robot manipulator.

4. The device according to claim 3, wherein the stored energy E is a virtual or a physical energy.

5. The device according to claim 3, wherein an upper energy limit G1 is defined, and the second unit is embodied and configured such that E≦G1 is always true for the energy E stored in the second unit.

6. The device according to claim 5, wherein a lower energy limit G2 is defined as: 0<G2<G1, and the second unit is embodied such that, if: G2<E≦G1 is true for the energy E stored in the second energy unit, the second unit is coupled to the regulator, andE≦G2 is true for the energy E stored in the second energy unit, the second unit is uncoupled from the regulator.

7. The device according to claim 1, wherein the first unit has as sensor system to register the external force winder {right arrow over (F)}ext(t)={{right arrow over (f)}ext(t),{right arrow over (m)}ext(t)} and/or an estimator to estimate the external force winder {right arrow over (F)}ext(t)={{right arrow over (f)}ext(t),{right arrow over (m)}ext(t)}.

8. A robot having a robot manipulator driven by a number of M actuators ACTm having an end effector, which has a device according to claim 1, where m=1, 2, . . . , M.

9. A method for open-loop and closed-loop control of a robot manipulator driven by a number of M actuators ACTm, having an end effector, where m=1, 2, . . . , M, with the following steps: registering and/or making available an external force winder{right arrow over (F)}ext(t)={{right arrow over (f)}ext(t),{right arrow over (m)}ext(t)} acting on the end effector, where:{right arrow over (f)}ext(t):=external force acting on the end effector;{right arrow over (m)}ext(t):=external torque acting on the end effector;by means of a regulator, which comprises a first regulator R1, which is a force regulator, and a second regulator R2 connected therewith, which is an impedance regulator, an admittance regulator, a position regulator or a cruise controller, determining manipulated variables um(t), by means of which the actuators ACTm are actuated such that when contact occurs with the surface of an object, the end effector acts on said object with a predefined force winder {right arrow over (F)}D(t)={{right arrow over (f)}D(t),{right arrow over (m)}D(t)}; where, um(t)=um,R1(t)+um,R2(t),  (1)where:{right arrow over (f)}D(t):=predefined force;{right arrow over (m)}D(t):=predefined torque,um,R1(t):=ratio of manipulated variables of the first regulator R1, andum,R2(t):=ratio of manipulated variables of the second regulator R2,

10. The method according to claim 9, wherein, in case the object is elastic and therefore its surface is flexible, the regulator takes into consideration predefined elasticity properties of the object when determining the manipulated variables um(t).

11. The method according to claim 9wherein a second unit is present, which serves as energy storage for passivation of the regulator, and which stores energy T1 coming from the regulator according to predefined energy storage dynamics, and delivers energy T2 to the regulator, wherein the second unit and the regulator form a closed-loop, and an initialization of the second unit with an energy T0 depends on a determined or predefined expenditure of energy EExpenditure to implement a current task of the robot manipulator.

12. A computer system, having a data processing device, wherein the data processing device is designed such that a method according to claim 9 is run on the data processing device.

13. A digital storage media having electronically readable control signals, wherein the control signals can interact with a programmable computer system in such way that a method according to claim 9 is run.

14. A computer program product having a program code stored on a machine-readable carrier to implement the method according to claim 9, if the program code is run on a data processing device.