Articulated robot modeling method, robot control device, and robot system

Abstract

To provide a modeling method of a joint robot, a robot control device and a robot system which can control the vibration suppression in a joint robot whose weight is reduced and which has the low rigidity.SOLUTION: A method performs modeling so as to be divided into a load side unit 21 in which an arm is modeled, a speed reducer unit 22 in which a speed reducer is modeled, a motor side unit 23 in which a motor is modeled and a base side unit 24 in which a base side that fixes the motor is modeled. In the load side unit 21, the load side acceleration αL is calculated via processing of subtracting the base side acceleration αb calculated by the base side unit 24 from the acceleration αL* calculated by using the torsional torque τs that is the torsional torque τs calculated and input in the speed reducer unit 22 and is calculated from the motor side speed ωm, the deceleration ratio Rg, the speed reducer torsional rigidity Ks and the speed reducer viscous friction coefficient Ds and the load side inertial moment JL.SELECTED DRAWING: Figure 4A

Description

[Technical Field]

[0001] The present invention relates to a modeling method for an articulated robot, a robot control device, and a robot system. [Background technology]

[0002] Articulated robots are used as industrial robots. The joint axis of a robot actuator is modeled as a two-inertia system having two inertia systems, one on the motor side and one on the load side, and one spring. The two-inertia system model includes a resonant frequency and an anti-resonant frequency, which causes problems with vibration in control systems that include these frequencies in the control band. On the other hand, when modeling both primary and secondary resonance, the system is modeled as a three-inertia system. For example, Non-Patent Document 1 proposes highly responsive force control by modeling a three-inertia system that focuses on the external force on the load side. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Akinori Yabuki, Kiyoshi Ohishi, Toshimasa Miyazaki, Yuki Yokokura, “Quick Reaction Force Control for Three-inertia Resonant System”, IEEJ Journal of Industry Applications, 2019, Volume 8, Issue 6, pp. 941-952 Summary of the Invention [Problem to be solved by the invention]

[0004] However, even if the conventional two-inertia system model or the above-mentioned three-inertia system model is used, it is difficult to suppress vibration in low-rigidity joint robots, which have been made lighter in recent years.

[0005] Therefore, an object of the present invention is to provide a modeling method for an articulated robot, a robot control device, and a robot system that are capable of controlling vibration suppression in a lightweight, low-rigidity articulated robot. [Means for solving the problem]

[0006] The first concept of the present invention is When modeling an articulated robot that transmits the driving force of a motor to an arm via a reducer, a load side unit modeled as the arm; a reducer unit that models the reducer; a motor-side unit that models the motor; a base unit that models the base side that fixes the motor; Divided into In the base side unit, a process of subtracting a first torque calculated using the base side speed and the base side viscous friction coefficient; a process of subtracting a second torque calculated using the integral value of the base side speed and the base side torsional rigidity; a process of subtracting a third torque input from the motor-side unit; and A process of subtracting the torsional torque input from the reduction gear unit Then, the base side moment of inertia is calculated and the base side acceleration is calculated. In the motor side unit, A process of adding motor torques; a process of inputting the product of the base-side speed and the motor-base-side viscous friction coefficient from the base-side unit and adding them up; a process of inputting a product value of the torsional torque and the reciprocal of the reduction ratio from the reduction gear unit and subtracting the product value; and A process of subtracting the product of the speed before subtraction of the base-side speed input from the base-side unit and the motor-side viscous friction coefficient when determining the motor-side speed output to the reducer unit. the third torque obtained through the above is output to the base-side unit, an acceleration is calculated from a calculation with a motor-side moment of inertia to calculate a speed, and a base-side speed input from the base-side unit is subtracted from the calculated speed to calculate a motor-side speed, In the reduction gear unit, a process of subtracting a load side speed input from the load side unit from a product value of the motor side speed input from the motor side unit and the reciprocal of the reduction ratio; A process of adding the product of the integral value of the value obtained by the subtraction and the torsional rigidity of the reducer; and The process of adding the product of the value obtained by subtraction and the viscous friction coefficient of the reducer the torsional torque is calculated by passing through the above-mentioned process, and the torsional torque is input to the load-side unit, and the product of the torsional torque and the reciprocal of the reduction ratio is output to the motor-side unit, In the load side unit, adding the torsional torque input from the reduction gear unit; A process of subtracting the product value of the load side speed output to the reducer unit and the load side viscous friction coefficient; and Subtracting torque generated on the load side and calculating the load side moment of inertia through the base side unit, and then subtracting the base side acceleration input from the base side unit to calculate the load side acceleration. This relates to a method for modeling an articulated robot.

[0007] The second concept of the present invention is When modeling an articulated robot that transmits the driving force of a motor to an arm via a reducer, a load side unit modeled as the arm; a reducer unit that models the reducer; a motor-side unit that models the motor; a base unit that models the base side that fixes the motor; Divided into In the base side unit, a process of subtracting a first torque calculated using the base side speed and the base side viscous friction coefficient; a process of subtracting a second torque calculated using the integral value of the base side speed and the base side torsional rigidity; a process of subtracting a third torque input from the motor-side unit; and A process of subtracting the torsional torque input from the reduction gear unit Then, the base side moment of inertia is calculated and the base side acceleration is calculated. In the motor side unit, A process of adding motor torques; a process of inputting the product of the base-side speed and the motor-base-side viscous friction coefficient from the base-side unit and adding them up; a process of inputting a product value of the torsional torque and the reciprocal of the reduction ratio from the reduction gear unit and subtracting the product value; and A process of subtracting the product of the speed before subtraction of the base-side speed input from the base-side unit and the motor-side viscous friction coefficient when determining the motor-side speed output to the reducer unit. the third torque obtained through the above is output to the base-side unit, an acceleration is calculated from a calculation with a motor-side moment of inertia to calculate a speed, and a base-side speed input from the base-side unit is subtracted from the calculated speed to calculate a motor-side speed, In the reduction gear unit, a process of subtracting a load side speed input from the load side unit from a product value of the motor side speed input from the motor side unit and the reciprocal of the reduction ratio; A process of adding the product of the integral value of the value obtained by the subtraction and the stiffness of the reducer; and The process of adding the product of the value obtained by subtraction and the viscous friction coefficient of the reducer the torsional torque is calculated by passing through the above-mentioned process, and the torsional torque is input to the load-side unit, and the product of the torsional torque and the reciprocal of the reduction ratio is output to the motor-side unit, In the load side unit, adding the torsional torque input from the reduction gear unit; A process of subtracting the product value of the load side speed output to the reducer unit and the load side viscous friction coefficient; and Subtracting torque generated on the load side The load side acceleration is calculated by passing through the above, and the base side speed input from the base side unit is calculated from the integral value of the load side acceleration. This relates to a method for modeling an articulated robot.

[0008] The third concept of the present invention is: an observer that estimates state quantities in an articulated robot that transmits a driving force of a motor to an arm via a reducer, the observer receiving a current input to the motor and an actual measured speed of the motor, and determining, as estimated values, an estimated torque generated on a base side that fixes the motor, an estimated speed generated on the base side, an estimated torsional torque of the reducer, and an estimated speed on a load side by a modeling method for the articulated robot; a state feedback control system that receives the reference speed of the motor, the measured speed of the motor, and the estimated values ​​obtained by the observer, and outputs the current; The present invention relates to a robot control device comprising:

[0009] The fourth concept of the present invention is the robot control device; the articulated robot; The present invention relates to a robot system having: [Effects of the Invention]

[0010] According to the present invention, when modeling an articulated robot that transmits the driving force of a motor to an arm via a reducer, the model is divided into a load-side unit that models the arm, a reducer unit that models the reducer, a motor-side unit that models the motor, and a base-side unit that models the base to which the motor is fixed.

[0011] In the base unit, the base speed and the base viscous friction coefficient D b and a process of subtracting the first torque calculated using the integral value of the base side speed and the base side torsional stiffness K b The base-side moment of inertia is calculated by subtracting the second torque calculated using the torque vector, the third torque input from the motor-side unit, and the torsional torque input from the reducer unit, and the base-side acceleration is calculated by calculating the base-side moment of inertia.

[0012] In the motor side unit, a third torque is calculated through the following processes: adding the motor torque; inputting the product of the base side speed and the motor base side viscous friction coefficient from the base side unit and adding it; inputting the product of the torsional torque and the inverse of the reduction ratio from the reducer unit and subtracting it; and subtracting the product of the speed before subtracting the base side speed input from the base side unit when calculating the motor side speed output to the reducer unit and the motor side viscous friction coefficient. This third torque is then output to the base side unit, and the acceleration is calculated from an operation with the motor side moment of inertia to calculate the speed. The motor side speed is then calculated by subtracting the base side speed input from the base side unit from this speed.

[0013] In the reducer unit, the torsional torque is calculated by the following processes: subtracting the load side speed input from the load side unit from the product of the motor side speed input from the motor side unit and the reciprocal of the reduction ratio; adding the product of the integral of the value obtained by this subtraction and the torsional stiffness of the reducer; and adding the product of the value obtained by this subtraction and the viscous friction coefficient of the reducer.The torsional torque is then input to the load side unit, and the product of the torsional torque and the reciprocal of the reduction ratio is output to the motor side unit.

[0014] In particular, in the first concept, the load side unit performs the following processes: adding the torsional torque input from the reducer unit; subtracting the product of the load side speed output to the reducer unit and the load side viscous friction coefficient; and subtracting the torque generated on the load side to calculate the load side moment of inertia.Then, the base side acceleration input from the base side unit is subtracted from this calculated value to calculate the load side acceleration.

[0015] This makes it possible to achieve vibration suppression control even in lightweight, low-rigidity joint robots by constructing a state disturbance observer as an observer and a state feedback control system based on a three-inertia system model.

[0016] Instead of subtracting the base-side acceleration input from the base-side unit, the load-side unit may calculate the load-side speed by subtracting the base-side speed input from the base-side unit from the integral of the load-side acceleration after it is calculated, as in the second concept. This is an equivalent alternative expression to the mathematical expression described in the first concept.

[0017] When modeling an articulated robot that transmits the driving force of a motor to an arm via a reducer, the description of motion according to the first concept may be used as a base and modified to resemble a description of motion according to the second concept, or the description of motion according to the first concept may be modified to resemble yet another description.

[0018] For example, instead of inputting the base side speed from the base side unit to the motor side unit, the base side acceleration calculated by calculation with the base side moment of inertia in the base side unit may be output to the motor side unit, and the base side acceleration input from the base side unit may be subtracted from the acceleration calculated by calculation with the motor side moment of inertia in the motor side unit, and the value obtained by this subtraction may be integrated to calculate the motor side speed.

[0019] Furthermore, if some viscous friction coefficients do not significantly affect the calculation results, they may be set to zero. [Brief explanation of the drawings]

[0020] [Figure 1] FIG. 1 is a schematic diagram of an articulated robot to be modeled in an embodiment of the present invention. [Figure 2] FIG. 2 shows a rotated version of a three-inertia system model for a modeling method according to an embodiment of the present invention. [Figure 3] FIG. 3 is a diagram showing a linear version of a three-inertia system model relating to a modeling method according to an embodiment of the present invention. [Figure 4A] FIG. 4A is a block diagram of a three-inertia system model for explaining a modeling method according to an embodiment of the present invention. [Figure 4B] FIG. 4B is a block diagram of a three-inertia system model different from that of FIG. 4A. [Figure 4C] FIG. 4C is a block diagram of a three-inertia system model different from those in FIGS. 4A and 4B. [Figure 5] FIG. 5 is a block diagram of a robot system including a robot control device according to an embodiment of the present invention. [Figure 6A] FIG. 6A is a block diagram showing a conventional two-inertia system model that models the articulated robot shown in FIG. [Figure 6B] FIG. 6B is a block diagram showing a conventional three-inertia system model that models the articulated robot shown in FIG. [Figure 7] FIG. 7 is a diagram showing frequency characteristics from a current command to a motor-side speed, which are obtained using a two-inertia system model. [Figure 8] FIG. 8 is a diagram showing the results of state feedback control for a two-inertia system. [Figure 9] Figure 9 shows the frequency characteristics from the current command to the load side acceleration, measured by attaching acceleration sensors capable of acquiring DC components to the tip position and the fixed side position of the motor to be controlled in the articulated robot shown in Figure 1. [Figure 10] Fig. 10 shows the frequency characteristics from the current command to the fixed-side position of the motor, measured by attaching acceleration sensors capable of acquiring DC components to the tip position and the fixed-side position of the motor to be controlled in the articulated robot shown in Fig. 1. [Figure 11] FIG. 11 is a diagram showing the simulation results of the frequency characteristics from the current command to the motor-side speed response, among the simulation results in the three-inertia system according to the embodiment of the present invention. [Figure 12] FIG. 12 is a diagram showing the simulation results of the frequency characteristics from the current command to the load side acceleration response, among the simulation results in the three-inertia system according to the embodiment of the present invention. [Figure 13] FIG. 13 is a diagram showing the simulation results of the frequency characteristics from the current command to the base-side acceleration response, among the simulation results in the three-inertia system according to the embodiment of the present invention. [Figure 14] FIG. 14 shows the simulation results of a state feedback speed controller based on a conventional two-inertia system model and a state feedback speed controller based on a three-inertia system model according to an embodiment of the present invention, where FIG. 14(a) relates to the motor side speed and FIG. 14(b) relates to the load side speed. [Figure 15] FIG. 15 is a diagram showing experimental results of state feedback speed control based on a three-inertia system model according to an embodiment of the present invention. [Figure 16] FIG. 16 shows the experimental results of state feedback speed control based on a three-inertia system model according to an embodiment of the present invention, with FIGS. 16(a) to 16(e) respectively relating to the motor-side speed (actual measured value), load-side speed (estimated value of the state disturbance observer), base-side speed (estimated value of the state disturbance observer), torsional torque (estimated value of the state disturbance observer), and base-side torque (estimated value of the state disturbance observer). DETAILED DESCRIPTION OF THE INVENTION

[0021] [Articulated robot to be modeled] FIG. 1 is a schematic diagram of an articulated robot to be modeled in an embodiment of the present invention. As shown in FIG. 1, the articulated robot 1 is, for example, a six-axis articulated robot, and is configured to include, from bottom to top, a swing axis, a lower arm axis, an upper arm axis, a wrist rotation axis, a wrist bending axis, and a wrist turning axis. That is, from bottom to top, the S axis, L axis, U axis, R axis, B axis, and T axis are arranged, and are also called the first axis, second axis, third axis, fourth axis, fifth axis, and sixth axis from bottom to top. An example of modeling three axes will be described below.

[0022] [Three-inertia system model] FIG. 2 is a diagram showing a rotational version of a three-inertia system model relating to a modeling method according to an embodiment of the present invention. It is a diagram showing a three-inertia system model relating to a modeling method according to an embodiment of the present invention. The three-inertia system model is divided into a controlled object side 11 that rotates due to a motor 10 and a fixed side 12 to which the controlled object shaft is fixed. As shown in FIGS. 4A to 4C , the three-inertia system model is modeled by dividing the controlled object side 11 into a load side unit 21, a reducer unit 22, and a motor side unit 23, and dividing the fixed side 12 into a base side unit 24. That is, the model is divided into a load side unit 21 that models an arm, a reducer unit 22 that models a reducer, a motor side unit 23 that models the motor 10, and a base side unit 24 that models the base to which the motor is fixed.

[0023] The three-inertia system model shown in Fig. 2 has a motor-side moment of inertia J m and the load moment of inertia J L and the base side moment of inertia J b The inertia mass is g In Figure 2, the radius of the small gear is R g The motor 10 and the load side moment of inertia J are controlled by the reducer 13, which is virtually configured by a gear having a radius twice that of the motor 10. L The inertia of the load is J LThe torsional stiffness of the reducer K is between the inertia body and the output side of the reducer. s and the viscous friction coefficient D of the reducer s Each mechanical element is virtually connected in parallel, and the moment of inertia on the base side J b The base side torsional stiffness K is between the inertia body and the base. b and the base side viscous friction coefficient D b The mechanical elements are virtually connected in parallel, and the motor 10 has a motor-side moment of inertia J m The viscous friction coefficient D on the motor side between the inertia body m1 and the base side moment of inertia J b The viscous friction coefficient D between the inertia body and the motor base side m2 The load side has a viscous friction coefficient D L In the drawings, the letter "L" is replaced with a lowercase "l."

[0024] In the three-inertia system model shown in Fig. 2, the load moment of inertia J L The position, velocity, and acceleration of the inertial body are θ L , ω L , α L The position, velocity, and acceleration on the motor shaft side are respectively θ m , ω m , α m The position, velocity, and acceleration of the motor fixed shaft are respectively θ b , ω b , α b Let's say.

[0025] In the three-inertia system model, the gear on the output side of the reducer and the moment of inertia J b A first bearing 14, which serves as a fulcrum on the output side of the reducer, is virtually connected between the inertial body of the motor and the rotation shaft of the motor or the gear on the input side of the reducer and the base side inertia moment J b A second bearing 15 is virtually connected between the inertial body.

[0026] Load moment of inertia J L A torsional torque τ is generated between the inertia body and the output side of the reducer. soccurs, and the base side moment of inertia J b The torsional torque τ between the inertia body and the base b For example, the q-axis current i q By flowing, the torque constant is K t Then, the motor 10 has a motor torque K t i q Then, the motor torque is increased by the reducer 13 to reduce the load side inertia moment J L The inertial body rotates. The moment of inertia of the load side is J L When the inertial body rotates, the base-side inertia moment J b Rotation occurs around the inertial body of the load. L A torsional torque τ is generated between the inertia body and the output side of the reducer. s When this occurs, the moment of inertia J m The inertial body of the base begins to rotate with a time lag due to the influence of its inertia and the viscous friction coefficient, and the meshing between the input side and the output side of the reducer 13 becomes the fulcrum, and the base side inertia moment J b This accelerates the inertial body of the base side, J b A torsion occurs between the inertial body and the base, and a torsional torque τ b occurs.

[0027] FIG. 3 is a diagram showing a linear version of a three-inertia system model according to a modeling method according to an embodiment of the present invention. In FIG. 3, the reducer is composed of a link 13A. The motor-side moment of inertia J m The inertial body of the base side moment of inertia J b The motor slides on the inertial bodies, both of which are connected to the link 13A. One end of the link 13A is connected to the motor-side inertial moment J m The other end of the link 13A is connected to the inertial body of the base side with a moment of inertia J b The link 13A is connected to the inertia body at a reduction ratio R g At the point (fulcrum) where it is externally divided into and 1, the base side moment of inertia J b On the opposite side of the inertia body of the load, the moment of inertia J LThe inertia body of the link 13A is connected to the load side with a moment of inertia J L Between the inertial body and the reducer torsional stiffness K s and the viscous friction coefficient D of the reducer s The mechanical elements are virtually connected in parallel. The moment of inertia on the base side is J b and the load moment of inertia J L Each inertial body has a load-side viscous friction coefficient D L The moment of inertia on the base side is J b The inertial body has a base side torsional stiffness K between the fixed system and the inertial body. b and the base side viscous friction coefficient D b The mechanical elements are virtually connected in parallel. The moment of inertia on the motor side is J m The inertial body of the motor has a torsional viscous friction coefficient D between the motor and the fixed system. m1 and the base side moment of inertia J b The viscous friction coefficient D between the inertia body and the base side of the motor m2 It has the following characteristics.

[0028] As shown in Figure 3, the load moment of inertia J L The position, velocity, and acceleration of the inertial body are θ L , ω L , α L and the moment of inertia on the motor side J m The position, velocity, and acceleration of the inertial body are θ m , ω m , α m and the moment of inertia on the base side J b The position, velocity, and acceleration of the inertial body are θ b , ω b , α b In the figure, φ corresponds to the motor position (rotation angle).

[0029] Load moment of inertia J L A torsional torque τ is generated between the inertia body and the link 13A. s occurs, and the base side moment of inertia J b There is a torsional torque τ between the inertia body and the base. b The moment of inertia on the motor side Jm and the base side moment of inertia J b Between each inertial body and the motor torque K t i q Then, the moment of inertia J of the link 13A on the motor side is m A torsional torque τ is applied to one end of the inertial body. m The moment of inertia J of the base side of the link 13A b The other end of the inertial body is subjected to a torsional torque τ b This results in the load moment of inertia J L A torsional torque τ is applied to the inertial body of s At the fulcrum of link 13A, the load moment of inertia J L Torsional torque τ from the inertial body s occurs in the opposite direction. Load moment of inertia J L Torque τ on the inertial body L The moment of inertia on the load side, J L When the inertial body of is displaced (rotated), the moment of inertia J b The load-side viscous friction coefficient D between the inertia body L3 This causes a misalignment, which results in the base side inertia moment J b2 A torsion occurs between the inertial body and the base, and a torsional torque τ b occurs.

[0030] 4A is a block diagram of a three-inertia system model for explaining a modeling method according to an embodiment of the present invention. L (t) is the load side speed ω L (t) - Motor speed ω m Velocity ω calculated by (t) s (t) is the motor side speed ω m (t) is the base side speed ω b Here, t indicates a certain time, and the initial value of t=0 (for example, zero) is assumed to be given. According to the three-inertia system model shown in FIG. 4A, the load-side unit 21 has an acceleration α L * (t+Δt) is the acceleration αm * (t+Δt) is the base side acceleration α b (t+Δt) is then calculated as follows:

[0031] In addition, acceleration α L * (t+Δt) to acceleration α L * (t+iΔt), acceleration α m * (t+Δt) to acceleration α m * (t+2Δt), base side acceleration α b (t+Δt) to base side acceleration α b (t+2Δt) are calculated, and by repeating this, the acceleration α L * , acceleration α m * and base side acceleration α b is required.

[0032] In the base side unit 24, the base side moment of inertia J b The base acceleration α b * (t+Δt) is calculated, and then the base speed ω is calculated by time integration. b (t+Δt) is calculated. The base side moment of inertia J b The torque calculated as follows is calculated through the following process: In the first process in the base-side unit 24, the base-side speed ω b (t) and the base side viscous friction coefficient D b In the second process in the base-side unit 24, the first torque τ1 calculated using the base-side speed ω b (t) integral value and base side torsional stiffness K b In a third process in the base-side unit 24, a third torque τ3 input from the motor-side unit 23 is subtracted. In a fourth process in the base-side unit 24, a torsional torque τ sThe order of processing does not matter. In other words, the base side inertia moment J b The torque calculated is the first torque τ1, the second torque τ2, the third torque τ3, and the torsional torque τ s The torsional torque τ can be calculated by subtracting the sum of the two. When calculating the sum, several processes can be combined. b is calculated as the subtraction of the sum of the first torque τ1 and the second torque τ2.

[0033] In the motor-side unit 23, the third torque τ3 to be input to the base-side unit 24 is calculated through the following process. The first process in the motor-side unit 23 is to calculate the motor torque K t i q The second process in the motor-side unit 23 is to add the base-side speed ω b (t) and the viscous friction coefficient D on the motor base side m2 The product of these values ​​is input from the base side unit 24 and added. The third process in the motor side unit 23 is to calculate the torsional torque τ s and the reciprocal of the reduction ratio R g -1 The fourth process in the motor-side unit 23 is to subtract the product of the motor-side speed ω m The base speed ω input from the base unit 24 when (t) is calculated b Velocity ω before subtracting (t) m * (t) and the viscous friction coefficient D on the motor side m1 The order of the processes does not matter. In other words, the third torque τ3 input to the base side unit 24 is the product of the motor torque K t i q ω b (t) + Motor base side viscous friction coefficient D m2 × Base speed ω b (t) + torsional torque τ s × Reciprocal of reduction ratio R g -1 +Motor side viscous friction coefficient D m1 ×speed ω m *(t). In this case, several processes may be combined.

[0034] The motor-side unit 23 outputs the third torque τ3 calculated as described above to the base-side unit 24. The third torque τ3 and the motor-side moment of inertia J m From the calculation, the acceleration α m * (t+Δt) is calculated, and then the velocity ω m * (t+Δt) is calculated, and the speed ω m * The base-side velocity ω input from the base-side unit 24 from (t+Δt) b Subtract (t+Δt) to obtain the motor speed ω m (t+Δt) is calculated.

[0035] In the reduction gear unit 22, a torsional torque τ s The first process of the speed reducer unit 22 is to calculate the motor-side speed ω m (t) and the reciprocal of the reduction ratio R g -1 From the product of these values, the load side speed ω L The second process of the speed reducer unit 22 subtracts the value {ω m (t) × R g -1 -ω L (t)} and the time integral value of the reducer torsional stiffness K s The third process of the speed reducer unit 22 is to add the product value of the value {ω m (t) × R g -1 -ω L (t)} and the viscous friction coefficient D s The product values ​​of these are added together. The order of the second process of the speed reducer unit 22 and the third process of the speed reducer unit 22 does not matter.

[0036] In the reduction gear unit 22, the torsional torque τ sis input to the load side unit 21, and a torsional torque τ s and the reciprocal of the reduction ratio R g -1 The product value of these is output to the motor-side unit 23.

[0037] In the load side unit 21, the load side moment of inertia J L The load side acceleration α L * (t+Δt) is calculated, and then the load speed ω L (t+Δt) is calculated. Load moment of inertia J L The torque calculated as follows is calculated through the following process: In the first process in the load side unit 21, the torsional torque τ s In the second process in the load side unit 21, the load side speed ω L (t) and the load side viscous friction coefficient D L In the third process in the load side unit 21, the product value of the torque τ generated on the load side is subtracted. L The order of processing does not matter. In other words, the load side moment of inertia J L The torque calculated as follows is the torsional torque τ s - Load side viscous friction coefficient D L ×Load side speed ω L (t)-Torque τ generated on the load side L In this case, several processes may be combined.

[0038] In this way, the base speed ω b (t) is input from the base side unit 24 to the motor side unit 23, and the base side acceleration α b (t+Δt) is input to the load side unit 21, and the torsional torque τ s is input from the reduction gear unit 22 to the base side unit 24, and the motor base side viscous friction coefficient D m2 and base speed ω b The product of this and (t) is input from the base side unit 24 to the motor side unit 23, and the base side unit 24 calculates the base side speed ω b(t) to the base side torsional stiffness K b Using the base side acceleration α b Therefore, it is possible to consider the effect of the reaction force from the base caused by the base being pushed out by the motor's rotational torque, and the rotation of the load inertia body around the base inertia body caused by the reducer.

[0039] Figure 5 is a block diagram of a robot system including a robot control device according to an embodiment of the present invention. The robot system 30 is composed of a robot 31 and a robot control device 32. As shown in Figure 2, the robot 31 may be any articulated robot that transmits the driving force of a motor 10 to an arm via a reducer 13, and includes, for example, a vertical articulated robot.

[0040] The robot control device 32 includes an observer (state disturbance observer) 33 that estimates the state quantity of the articulated robot, and a state feedback control system 34. The observer 33 estimates the q-axis current i q and motor speed ω m and the estimated torque ^τ generated on the base side where the motor is fixed. b and the estimated velocity ^ω generated on the base side b and the estimated torsional torque ^τ of the reducer s and the estimated speed of the load side ^ω L and the estimated load torque ^τ L and the motor side estimated speed ^ω m is estimated using the modeling method for articulated robots described above.

[0041] The state feedback control system 34 calculates the reference speed ω of the motor. m ref and the measured motor speed ω m and each estimated value obtained by the observer 33 (estimated torque ^τ generated on the base side that fixes the motor b , the estimated velocity ^ω occurring on the base side b , the estimated torsional torque ^τ of the reducer s , the estimated speed of the load side ^ω L ) is input, and the q-axis current i qis output. The motor reference speed ω m ref The actual speed of the motor is ω m The difference between these is integrated and K i multiplied by 1, and subtract the value obtained by inputting the estimated value above to obtain the current i q is calculated and input to the robot 31.

[0042] The state equations are shown as (1a) to (1e), where s is the Laplace operator.

number

[0043]

number

[0044]

number

[0045]

number

[0046] Here, the numerical values ​​of each parameter are roughly as follows: [Table 1]

[0047] Here, since the controllability matrix Gc has a full rank, state feedback control is possible based on the three-inertia system model according to the embodiment of the present invention. Furthermore, the three-inertia system model differs from conventional models for base vibration.

[0048] Usually, the torsional torque τ s and load side speed ω LSince it is not possible to use a sensor to detect this, the state quantities required for state feedback are estimated using a state disturbance observer. The state disturbance observer based on the three-inertia system model according to the embodiment of the present invention is observable because the observability matrix G0 has a full rank. Therefore, the state disturbance observer and state feedback control system can be configured using equation (1).

[0049] The embodiment of the present invention is not limited to the above. For example, in the load side unit 21, the base side acceleration α b Instead of subtracting (t+Δt), the load side acceleration α L * After the load side acceleration α L * The integral value of ω L * The base-side velocity ω input from the base-side unit 24 is b By subtracting (t+Δt), the load speed ω L Alternatively, (t+Δt) may be calculated. This is an equivalent expression of the mathematical expression described in the block diagram shown in Figure 4A. The following description will be given with reference to Figure 4B.

[0050] 4B is a block diagram of a three-inertia system model different from that shown in FIG. 4A. In the configuration shown in FIG. 4A, a base-side moment of inertia J b The base side acceleration α calculated by b (t+Δt) is input, and the load side moment of inertia J L Acceleration α calculated by dividing L * (t+Δt) to base side acceleration α b (t+Δt) is subtracted, and the load side acceleration α after subtraction L (t+Δt) is integrated over time to obtain the load speed ω L (t+Δt) is calculated.

[0051] In contrast, in FIG. 4B, the base-side moment of inertia J b The base acceleration α is calculated by the following calculation: b (t+Δt) is further integrated over time to obtain the base velocity ω b (t+Δt) is calculated and output to the load side unit 21. Meanwhile, in the load side unit 21, the load side moment of inertia J L The load side acceleration α calculated by the calculation L * (t+Δt) is integrated over time to obtain the velocity ω L * (t+Δt) is calculated, and the base-side speed ω b (t+Δt) is subtracted to obtain the load speed ω L (t+Δt) is calculated.

[0052] When modeling an articulated robot that transmits the driving force of a motor to an arm via a reducer, the model is not limited to the matters described with reference to Figures 4A and 4B, and may be modified, for example, as described with reference to Figure 4C.

[0053] 4C is a block diagram of a three-inertia system model different from those of FIGS. 4A and 4B. In the embodiment shown in FIG. 4A, the base-side moment of inertia J b The base side acceleration α calculated by b The base speed ω is calculated by integrating (t+Δt) over time. b (t+Δt) is output to the motor-side unit 23, and the motor-side unit 23 outputs an acceleration α m * The velocity ω is calculated by integrating (t+Δt) over time. m * From the input base speed ω b Subtract (t+Δt) to obtain the motor speed ω m (t+Δt) is calculated.

[0054] In contrast, in the embodiment shown in FIG. 4C, the base-side moment of inertia J b The base acceleration α is calculated by b(t+Δt) is calculated and output to the motor-side unit 23. In the motor-side unit 23, the acceleration α m * The base side acceleration α input from the base side unit 24 is b (t+Δt) is subtracted to obtain the motor acceleration α m (t+Δt) is calculated, and then time-integrated to obtain the motor speed ω m At this time, the motor-side speed ω output to the reduction gear unit 22 in the fourth process in the motor-side unit 23 may be calculated. m The base speed ω input from the base unit 24 when (t) is calculated b Velocity ω before subtracting (t) m * (t) is the motor speed ω m Equals (t).

[0055] In this way, the form shown in Fig. 4B may be modified into the form shown in Fig. 4C, and can also be applied to the form shown in Fig. 4A. In this way, variations that are equivalent to mathematically formulating the block diagram shown in Fig. 4A and modifying it also constitute embodiments of the present invention.

[0056] [Effectiveness of this embodiment] The effectiveness of the embodiment of the present invention will be explained by explaining how the modeling method according to the embodiment of the present invention was arrived at. FIG. 6A is a block diagram showing a conventional two-inertia system model that models the articulated robot 1 shown in FIG. 1, and FIG. 6B is a block diagram showing a conventional three-inertia system model that models the articulated robot 1 shown in FIG. 1. The articulated robot 1 to be modeled is configured by connecting six axes with links, and a work tool is attached to the tip. The third axis is the axis of symmetry for control. The axes further towards the tip of this axis are assumed to be fixed (see FIG. 1).

[0057] As shown in Figures 6A and 6B, in both the conventional two-inertia system model and the three-inertia system model, the model is divided into the motor side, the reducer unit, and the load side. That is, it is divided into a load side unit 101, a reducer unit 102, and a motor side unit 103. Here, α, ω, θ, τ, i q are the acceleration, velocity, position, torque, and q-axis current, respectively. J, D, and K t , R g , K. s are the moment of inertia, viscous friction coefficient, torque constant, reduction ratio, and torsional rigidity, respectively. The subscripts m, s, L, and n indicate the motor side, torsion, load side, and nominal value, respectively. Note that L is originally a lowercase l, but we will write it as an uppercase letter to distinguish it from numbers. ref, dis, and ^ indicate the command value, disturbance, and estimated value, respectively.

[0058] The two-inertia system model shown in Fig. 6A has a motor-side moment of inertia J m and the load moment of inertia J L In the motor side unit 103, a current i q The motor torque K t i q The motor torque K t i q From τ described below m dis The value obtained by subtracting this is the motor side moment of inertia J m Divide by the motor acceleration α m is calculated, and the motor speed ω m The calculated motor speed ω m is input to the reduction gear unit 102. In the motor side unit 103, the calculated motor side speed ω m The motor viscous friction coefficient D m and the torsional torque τ input from the reduction gear unit 102. s ×Reduction ratio R g -1 Add the value of τ m dis In the reduction gear unit 102, the motor speed ωm Reduction ratio R g The load side speed ω input from the load side unit 101 is calculated from the value obtained by dividing L is subtracted and the reducer speed ω s is obtained, and the reducer speed ω s From position θ s is required, and the torsional stiffness of the reducer K s The torsional torque τ is calculated by s is calculated and input to the load side unit 101, and the reduction ratio Rg -1 The torsional torque τ input from the reduction gear unit 102 is multiplied by τ s from the disturbance torque τ L dis is drawn, and the load side moment of inertia J L Divided by the load side acceleration α L is obtained, and then the load speed ω L is obtained.

[0059] The conventional three-inertia system model shown in Fig. 6B will be described. The conventional three-inertia system model uses the motor moment of inertia J m and the first moment of inertia J L1 and the second moment of inertia J L2 The motor side unit 103 and the reducer unit 102 in the three-inertia system model are the same as those in the two-inertia system model. In the load side unit 101, the first inertial body is directly affected by the reducer unit 102, and the second inertial body is indirectly affected by the reducer unit 102 via the first inertial body. In addition, the first inertial body directly affects the reducer unit 102, and the second inertial body indirectly affects the reducer unit 102 via the first inertial body.

[0060] In the load side unit 101, the torsional torque τ input from the reduction gear unit 102 s The second torsional torque τ s2 is drawn, and the first moment of inertia J L1 Divided by the first acceleration α on the load side Lis calculated, and the load side first speed ω is calculated by time integration. L1 is calculated and output to the speed reducer unit 102. The load side first speed ω L1 is the load side second speed ω L2 Subtract ω s2 By integration, θ s2 Next, K s2 Multiplication with the second torsional torque τ on the load side s2 is calculated. The second torsional torque τ s2 from the disturbance torque τ L dis Subtract the second moment of inertia J L2 Divide by α to get the second acceleration on the load side. L2 is calculated, and the load side second speed ω L2 is calculated.

[0061] The controlled object shown in Figure 6A is a two-inertia system with a current command i q ref From the motor speed response ω m Transfer function P tim (s) is expressed by the following equation, where ω a and ω r are the anti-resonance frequency and the resonance frequency, respectively.

number

[0062] Figure 7 shows the frequency characteristics from the current command to the motor speed using a two-inertia system model. As can be seen from Figure 7, there are two pairs of anti-resonance frequency and resonance frequency, so the parameters of the two-inertia system are found for the lowest pair of anti-resonance frequency and resonance frequency, and then a state disturbance observer and a state feedback control system are designed.

[0063] Without vibration suppression control, the controlled object will induce vibrations due to anti-resonance and resonance frequencies. Therefore, to control the state quantity of a two-inertia system, it is necessary to suppress vibrations using state feedback control. The state equation of a two-inertia system is expressed as follows:

[0064]

number

[0065] Torsional torque τ s and load side speed ω L Since it is not possible to use a sensor to detect the state, the state quantity required for state feedback is estimated using a state disturbance observer. The state disturbance observer and state feedback control are configured using the above state equations.

[0066] Fig. 8 shows the results of state feedback control for a two-inertia system. Simulation results show that non-vibration suppression can be achieved by performing state feedback control on a two-inertia system, so the control shown in Fig. 8 is effective for actuators that can be modeled as a two-inertia system.

[0067] However, in the case of industrial robots, state feedback control based on the above-mentioned two-inertia system model or state feedback control based on the three-inertia system model (see FIG. 6B) shown in Non-Patent Document 1 has not been implemented for articulated robots.

[0068] Therefore, in the articulated robot 1 shown in Figure 1, acceleration sensors capable of acquiring DC components were attached to position A of the tip and to position B on the fixed side of the motor 10 to be controlled, and the frequency characteristics from the current command to the load side acceleration and the frequency characteristics from the current command to the motor fixed side position were measured. The results are shown in Figures 9 and 10, respectively.

[0069] As shown in Fig. 9, the frequency characteristics from the current command to the load-side acceleration in the articulated robot had two resonance frequencies and one anti-resonance frequency. As shown in Fig. 9, the three-inertia system model (see Fig. 6B) shown in Non-Patent Document 1 had no anti-resonance frequency, but had two resonance frequencies (dotted lines in Fig. 9). In the actually measured frequency characteristics, the first resonance mode had a resonance frequency and an anti-resonance frequency at position A, while the second resonance mode had only a resonance frequency at position A (solid line in Fig. 9). Therefore, for lightweight, low-rigidity articulated robots, it was not possible to apply a two-inertia system model or a three-inertia system model such as that shown in Non-Patent Document 1.

[0070] As shown in FIG. 10, the frequency characteristics from the current command to the motor fixed side position B in the articulated robot had two resonance frequencies.

[0071] Therefore, the present invention was completed by focusing on the first and second resonance modes in the frequency characteristics up to the motor side speed, load side acceleration, and motor fixed side position shown in Figures 8, 9, and 10, respectively.

[0072] In the first resonance mode, the motor side has an anti-resonance frequency and a resonance frequency, the load side acceleration (position A) has an anti-resonance frequency and a resonance frequency, and the motor fixed side position (position B) has only an anti-resonance frequency. Therefore, the first resonance mode is a vibration mode caused by the inertia and springs on the motor side and position B, and position A has a resonance frequency and an anti-resonance frequency due to the difference between the mode in which the resonance mode on the motor side is transmitted to the load side inertia and the resonance mode at position B. This means that the motor torque K t i qtransmits torque to the load side by pushing out the inertia at position B. The inertia at position B that is pushed out vibrates due to the spring component caused by the rigidity of the robot frame, but since the robot frame is placed on the ground, the steady-state value is zero.

[0073] In the second resonance mode, the motor side has an anti-resonance frequency and a resonance frequency, and positions A and B have only a resonance frequency. The second resonance mode is a vibration mode caused by the inertia and springs on the motor side and position A, and is a vibration mode that is transmitted to the load side, and the resonance of the torque transmitted to the load side appears as a resonance at position B.

[0074] [Simulation results in a three-inertia system model according to an embodiment of the present invention] A simulation was performed on the three-inertia system model shown in Figure 4A. Figure 11 shows the simulation results for the frequency characteristics from the current command to the motor-side velocity response. Figure 12 shows the simulation results for the frequency characteristics from the current command to the load-side acceleration response. Figure 13 shows the simulation results for the frequency characteristics from the current command to the base-side acceleration response. Figure 11 reveals that the frequency characteristics from the current command to the motor-side velocity response contain two sets of anti-resonant and resonant frequencies. Figure 12 reveals that the frequency characteristics from the current command to the load-side acceleration have two resonant frequencies and one anti-resonant frequency. Figure 13 reveals that the frequency characteristics from the current command to the base-side acceleration have no anti-resonant frequencies and two resonant frequencies. This demonstrates that the frequency characteristics obtained from the experiment and the simulation match. This model is therefore appropriate for a single-axis robot model.

[0075] [Conditions for numerical simulation and actual machine verification] Table 2 shows the simulation and experimental parameters used for verification. In the simulation, to compare control performance, the poles of the state disturbance observer and state feedback control of the two-inertia system model were set to the same position. Also, since the controlled object is an industrial robot, the load-side inertia fluctuates due to posture control. Therefore, a pole placement that is robust to load-side inertia fluctuations was used. The block diagram in Figure 4A was used for the simulation, and D m1 , D m2 , D s , D b , D L was set to 0. In addition, the bandwidth of the current control system and the acquisition bandwidth of the motor encoder are sufficiently higher than those of the speed control system, so they can be ignored.

[0076] [Table 2]

[0077] FIG. 14 shows simulation results for a state feedback speed control system based on a conventional two-inertia system model (hereinafter referred to as the "conventional example") and a state feedback speed control system based on a three-inertia system model according to an embodiment of the present invention (hereinafter referred to as the "present example"), with FIG. 14(a) relating to the motor speed and FIG. 14(b) relating to the load speed. The rising edge (black solid line) at time 0.1 [s] is the reference value (Reference), the gray solid line is the response value (Response (Conv.)) of the conventional example, and the dashed-dotted line is the response value (Response (Prop.)) of this example. As shown in FIG. 14, a resonance mode not considered in the conventional example induces vibration and diverges, whereas in this example, vibration suppression control of the motor speed and the load speed is achieved by feeding back the state quantity estimated by the state disturbance observer based on the three-inertia system model.

[0078] Figure 15 shows the experimental results of state feedback speed control based on a three-inertia system model according to an embodiment of the present invention. The rising edges (black solid lines) at times 10 (s) and 13 (s) are the command value (Reference), the gray solid line is the experimental response value (Experiment), and the dashed-dotted line is the simulation response value (Simulation). In the experiment, speed control was performed using the command value shown in Figure 15. The simulation took into account the Coulomb friction identification value of 0.19 Nm. Figure 16 shows experimental results of state feedback speed control based on a three-inertia system model according to an embodiment of the present invention. Figure 16(a) shows the motor speed. The rising edge (black solid line) at time 13 (s) is the reference value (Reference), the solid gray line is the experimental response value (Experiment), and the dashed-dotted line is the simulation response value (Simulation). Figures 16(b) to 16(e) show the load speed (estimated value of the state disturbance observer), base speed (estimated value of the state disturbance observer), torsional torque (estimated value of the state disturbance observer), and base torque (estimated value of the state disturbance observer), respectively. The solid line shows the experimental estimate (Experiment), and the dashed-dotted line shows the simulation estimate (Simulation). Focusing on the motor speed and load speed, the simulated response and estimate values ​​match, confirming that vibration suppression performance was achieved as expected by the control design. Furthermore, since the estimated values ​​of the simulation and the estimated values ​​of the experimental results also matched for other state quantities, it was confirmed that the three-inertia system model according to the embodiment of the present invention is valid as a method for modeling industrial robots.

[0079] As described above, conventional methods for modeling industrial robots with multiple resonant modes, which model them as a two-inertia system based on the lowest resonant mode, induce vibrations because they do not consider higher resonant modes. This makes it difficult to achieve vibration suppression control with a two-inertia system model. However, as described in the embodiments of the present invention, in order to achieve vibration suppression control of industrial robots, acceleration sensors are attached to the tip and base of the robot. A new three-inertia system model according to the present invention is constructed based on the frequency characteristics of the current command, motor speed, load acceleration, and base acceleration. Vibration suppression control of industrial robots is possible by designing a state disturbance observer and a state feedback controller based on the constructed three-inertia system model. The three-inertia system model according to the embodiments of the present invention is appropriate as a model of industrial robots and can achieve vibration suppression control.

[0080] Furthermore, a modeling device may be constructed using the modeling method for an articulated robot according to an embodiment of the present invention, a control system may be constructed to calculate current components that suppress vibration and perform feedback control based on the results, or an analysis system or evaluation system may be constructed to analyze and / or evaluate vibration components to determine the safety and durability of the articulated robot.

[0081] According to an embodiment of the present invention, in a modeling method for an articulated robot having a joint comprising an arm, a reducer attached to one end of the arm, and a motor having a rotor and a stator for rotating the reducer, by taking into account vibrations caused by an inertial body including the stator between the rotor and the side to which the motor is fixed, and the spring between them, it is possible to suppress vibrations caused by anti-resonance and the first-order mode of resonance and the second-order mode of resonance in the frequency characteristics from the current command to the motor to the load-side acceleration response including the arm. [Explanation of symbols]

[0082] 1: Articulated robot 10: Motor 11: Control target side 12: Fixed side that fixes the controlled axis 13: Reducer 21: Load side unit 22: Reducer unit 23: Motor side unit 24: Base unit 30: Robot Systems 31:Robot 32: Robot control device 33: Observer (state disturbance observer) 34: State feedback control system

Claims

1. When modeling an articulated robot that transmits the driving force of a motor to an arm via a reducer, a load side unit modeled as the arm; a reducer unit that models the reducer; a motor-side unit that models the motor; a base unit that models the base side that fixes the motor; Divided into In the base side unit, a process of subtracting a first torque calculated using the base side speed and the base side viscous friction coefficient; a process of subtracting a second torque calculated using the integral value of the base side speed and the base side torsional rigidity; a process of subtracting a third torque input from the motor-side unit; and A process of subtracting the torsional torque input from the reduction gear unit Then, the base side moment of inertia is calculated and the base side acceleration is calculated. In the motor side unit, A process of adding motor torques; a process of inputting the product of the base-side speed and the motor-base-side viscous friction coefficient from the base-side unit and adding them up; a process of inputting a product value of the torsional torque and the reciprocal of the reduction ratio from the reduction gear unit and subtracting the product value; and A process of subtracting the product of the speed before subtraction of the base-side speed input from the base-side unit and the motor-side viscous friction coefficient when determining the motor-side speed output to the reducer unit. the third torque obtained through the above is output to the base-side unit, an acceleration is calculated from a calculation with a motor-side moment of inertia to calculate a speed, and a base-side speed input from the base-side unit is subtracted from the calculated speed to calculate a motor-side speed, In the reduction gear unit, a process of subtracting a load side speed input from the load side unit from a product value of the motor side speed input from the motor side unit and the reciprocal of the reduction ratio; A process of adding the product of the integral value of the value obtained by the subtraction and the torsional stiffness of the reducer; and The process of adding the product of the value obtained by subtraction and the viscous friction coefficient of the reducer the torsional torque is calculated by passing through the above-mentioned process, and the torsional torque is input to the load-side unit, and the product of the torsional torque and the reciprocal of the reduction ratio is output to the motor-side unit, In the load side unit, adding the torsional torque input from the reduction gear unit; A process of subtracting the product value of the load side speed output to the reducer unit and the load side viscous friction coefficient; and Subtracting torque generated on the load side and calculating the load side moment of inertia through the base side unit, and then subtracting the base side acceleration input from the base side unit to calculate the load side acceleration. A method for modeling articulated robots.

2. When modeling an articulated robot that transmits the driving force of a motor to an arm via a reducer, a load side unit modeled as the arm; a reducer unit that models the reducer; a motor-side unit that models the motor; a base unit that models the base side that fixes the motor; Divided into In the base side unit, a process of subtracting a first torque calculated using the base side speed and the base side viscous friction coefficient; a process of subtracting a second torque calculated using the integral value of the base side speed and the base side torsional rigidity; a process of subtracting a third torque input from the motor-side unit; and A process of subtracting the torsional torque input from the reduction gear unit Then, the base side moment of inertia is calculated and the base side acceleration is calculated. In the motor side unit, A process of adding motor torques; a process of inputting the product of the base-side speed and the motor-base-side viscous friction coefficient from the base-side unit and adding them up; a process of inputting a product value of the torsional torque and the reciprocal of the reduction ratio from the reduction gear unit and subtracting the product value; and A process of subtracting the product of the speed before subtraction of the base-side speed input from the base-side unit and the motor-side viscous friction coefficient when determining the motor-side speed output to the reducer unit. the third torque obtained through the above is output to the base-side unit, an acceleration is calculated from a calculation with a motor-side moment of inertia to calculate a speed, and a base-side speed input from the base-side unit is subtracted from the calculated speed to calculate a motor-side speed, In the reduction gear unit, a process of subtracting a load side speed input from the load side unit from a product value of the motor side speed input from the motor side unit and the reciprocal of the reduction ratio; A process of adding the product of the integral value of the value obtained by the subtraction and the stiffness of the reducer; and The process of adding the product of the value obtained by subtraction and the viscous friction coefficient of the reducer the torsional torque is calculated by passing through the above-mentioned process, and the torsional torque is input to the load-side unit, and the product of the torsional torque and the reciprocal of the reduction ratio is output to the motor-side unit, In the load side unit, adding the torsional torque input from the reduction gear unit; A process of subtracting the product value of the load side speed output to the reducer unit and the load side viscous friction coefficient; and Subtracting torque generated on the load side The load side acceleration is calculated by passing through the above, and the base side speed input from the base side unit is calculated from the integral value of the load side acceleration. A method for modeling articulated robots.

3. an observer for estimating state quantities in an articulated robot that transmits a driving force of a motor to an arm via a reducer, the observer receiving a current input to the motor and an actual measured speed of the motor, and determining, as estimated values, an estimated torque generated on a base side that fixes the motor, an estimated speed generated on the base side, an estimated torsional torque of the reducer, and an estimated speed on a load side by the modeling method for an articulated robot according to claim 1 or 2; a state feedback control system that receives the reference speed of the motor, the measured speed of the motor, and the estimated values ​​obtained by the observer, and outputs the current; A robot control device comprising:

4. The robot control device according to claim 3 ; the articulated robot; A robot system having:

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