KR20030055719A - Asymmetric acceleration and deceleration profile producing method and a acceleration and deceleration controlling method using the same for multi-joint robot - Google Patents

Abstract

PURPOSE: A method for generating the asymmetric accelerated/decelerated velocity profile of an articulated robot and a method for controlling accelerated/decelerated velocity are provided to simplify the processes of generating the velocity profile and to shorten calculating hours by using an asymmetric smooth-curve and tabulating the variation of the velocity of a motor. CONSTITUTION: A method for generating the asymmetric accelerated/decelerated velocity profile of an articulated robot comprises the steps of: asymmetrically setting the pattern of accelerated velocity in an accelerating section; and using a variation value of the velocity on each sampling section, and calculating the position of each articulation shaft on each sampling section of the accelerating section. The variation value of the velocity is calculated in advance, and is stored in a table.

Description

Asymmetric acceleration and deceleration profile producing method and a acceleration and deceleration controlling method using the same for multi-joint robot}

The present invention relates to a method for generating an acceleration / deceleration speed profile for acceleration / deceleration control of an articulated robot. More specifically, the speed profile generation process is performed by tabulating changes in motor speed for each sampling using an asymmetric curve. The present invention relates to a method for generating an acceleration / deceleration speed profile that can simplify the calculation time.

In general, an industrial articulated robot moves an end-effector to a target position by rotating each joint. Thus, a servo motor is provided for each joint as a driving source for rotating each joint. The reliability and durability of high-speed and high-precision robots depends on how much the noise and vibration generated by each joint axis of the robot can be reduced. Therefore, in controlling the servomotor of the articulated robot, it is important to minimize vibration and noise by smoothing the movement of each joint.

1 shows a control device of a general industrial robot. As shown in FIG. 1, the robot control apparatus includes a main controller 10, a command inputter 20, a motion controller 30, a joint position controller 40, and a servo driver 50. ) And an I / O input / output unit 60.

The main controller 10 processes the commands such as the current position, the target position, and the speed command of each joint input from the command inputter 20 and instructs the motion controller 30. The motion controller 30 generates the acceleration and deceleration time, the constant velocity motion time, and the velocity profile by using the command input from the main controller 1 to transmit the position data to the joint position controller 40 at every sampling period. The joint position controller 40 controls the servo driver 50 of each joint axis based on the transmitted position data so that each joint axis can be moved to the commanded position. Meanwhile, the I / O input / output unit 60 processes the I / O signals used internally and externally to the main controller 10, and the main controller 10 processes the signals according to the interrupt order.

Hereinafter, the conventional acceleration / deceleration velocity profile generation method by the control apparatus comprised as mentioned above is demonstrated.

Conventionally, the motion controller 30 calculates data such as acceleration, velocity, position, and the like every sampling period, and transfers the generated velocity profile to the joint position controller 40. How to calculate the acceleration, velocity, and position is as follows.

First, the acceleration in the acceleration section is calculated by the following equations 1a and 1b. Equation 1a is an acceleration calculation formula for each sampling section when the slope is positive, that is, when the acceleration increases with time. Equation 1b is an acceleration calculation for each sampling period when the slope is negative, that is, when the acceleration increases with time.

In Equations 1a and 1b, a [k] represents acceleration for each sampling period (k = 1, 2, ..., n), Amax represents maximum acceleration, Trf represents acceleration time, and RST represents sampling period. Represent each.

Next, the speed for each sampling section in the acceleration section is calculated by the following equation (2) using the results of the above equations (1a) and (1b).

Here, Vr (k) represents the speed in the sampling interval, and Vr (k-1) represents the speed in the immediately preceding section of the sampling interval. Similarly, a (k) means acceleration in the sampling interval and a (k-1) means acceleration in the immediately preceding section of the sampling interval.

Finally, the position data for each sampling section in the acceleration section is calculated by the following equation (3) using the result of equation (2).

Here, Dr (k) represents position data in the sampling interval, and Dr (k-1) represents position data in the immediately preceding section of the sampling interval.

On the other hand, the acceleration, speed, and position data in the deceleration section are calculated in the same manner as the calculation method in the above-mentioned acceleration section. Therefore, acceleration and velocity profiles in the acceleration section and the deceleration section are symmetrical.

2A to 2C are graphs showing acceleration, velocity, and distance profiles generated based on the acceleration, velocity, and position data calculated according to the above equations. FIG. 2A is an acceleration profile, and FIG. 2B is a velocity profile. 3 shows the distance profiles, respectively.

However, according to the conventional acceleration / deceleration velocity profile generation method as described above, there is a problem that the calculation time is long because the acceleration, velocity, and position must be calculated for each sampling period using a complex calculation equation.

In addition, according to the conventional acceleration / deceleration velocity profile generation method, as shown in FIG. 2A, the pattern of acceleration during acceleration and deceleration has a time ratio when the acceleration gradient is positive and negative. By being symmetrical, the movement of each joint axis of the robot is not smooth and there is a problem that vibration and noise occur.

The present invention has been made to solve the above problems, by using the asymmetric smooth curve (Smooth-Curve) to table the rate of change of the motor speed, to simplify the process of generating the speed profile to reduce the calculation time The present invention provides a method for generating an acceleration / deceleration speed profile.

In addition, another object of the present invention is to provide an acceleration / deceleration control method that can significantly reduce vibration and noise by smoothly controlling the movement of each joint of the robot by using the acceleration / deceleration velocity profile generation method.

1 is a block diagram of a general articulated robot control device.

Figure 2a is an acceleration profile by a conventional acceleration and deceleration velocity profile generation method.

Figure 2b is a velocity profile by a conventional method of generating a deceleration velocity profile.

Figure 2c is a distance profile by a conventional acceleration / deceleration velocity profile generation method.

3 is a flow chart illustrating a method of generating an acceleration / deceleration speed profile according to the present invention.

4 is a background diagram for pre-calculating the speed change in every sampling period in the method of generating the acceleration / deceleration speed profile according to the present invention.

Figure 5a is an acceleration profile by the acceleration / deceleration velocity profile generation method according to the present invention.

Figure 5b is a velocity profile by the acceleration / deceleration velocity profile generation method according to the present invention.

Figure 5c is a distance profile by the acceleration / deceleration velocity profile generation method according to the present invention.

<Description of Symbols for Main Parts of Drawings>

10: main controller 20: command input

30: motion controller 40: joint position controller (JPC)

50: servo driver 60: I / O input / output

The object of the present invention as described above is to set the acceleration pattern asymmetrically in the acceleration section, calculate the position of each joint axis in every sampling section of the acceleration section using the rate of change of the velocity in each sampling section. ; The rate of change of the value is expressed by the following equation,

Where S-Index-R [j] [k] is the rate of change in each sampling interval, Vr (k) is the velocity in each sampling interval, RST is the sampling period, and S _R is the acceleration interval. It is achieved by providing a method for generating an acceleration / deceleration velocity profile of an articulated robot, which is calculated in advance and stored in a table.

Here, the acceleration pattern in the acceleration section is preferably set so that the time of the section of the acceleration is positive (+) and the time of the section of the acceleration is negative (−) is 3: 7.

On the other hand, another object of the present invention is to (a) the maximum acceleration (Amax) and the average acceleration (based on the current position (q _oi ), the target position (q _fi ), the velocity (Vm) data of each joint axis input ( Aave); (b) calculating a maximum displacement (Qmax) of each movement displacement of the joint axis based on the current position (q _oi ) and the target position (q _oi ) data; (c) calculating a ratio (α) of the constant velocity exercise time to the total exercise time based on the set average acceleration (Aave), the input speed (Vm), and the maximum displacement (Qmax); (d) The total motion time Td for the input speed Vm and the maximum displacement Qmax, the acceleration and deceleration time Trf, the time Teq from acceleration to constant velocity, and the acceleration section. Calculating a sampling number Tint; (e) the speed Vi at the constant velocity section of each of the joint axes, the average value S ₁ of the moving distances in every sampling section in the acceleration section, and the average value of the moving distances in every sampling section in the deceleration section ( Calculating S ₂ ); And (f) the acceleration section position (POS) and the constant velocity section of each joint axis in each sampling section by using the calculation result in step (e) and the rate of change of the velocity in every sampling section previously stored in the table. It is achieved by providing a method for controlling the acceleration and deceleration of the articulated robot, comprising calculating the position POS 'and the position of the deceleration section POS'.

Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the present invention.

The generation of the velocity profile according to the present embodiment is performed by the general robot controller shown in FIG. 1. That is, when the main controller 10 commands the motion controller 30 by processing commands such as the current position, the target position, and the speed command of each joint input from the command inputter 20, the motion controller 30 is inputted. The command generates acceleration and deceleration time, constant velocity motion time, and smooth curve velocity profile, and transmits position data to the joint position controller (JPC) 40 at every sampling period. The joint position controller 40 controls the servo driver 50 of each joint axis based on the transmitted position data so that each joint axis can be moved to the commanded position. In addition, the I / O input / output unit 60 processes the I / O signals used internally and externally to the main controller 10, and the main controller 10 processes the signals in the interrupt order.

Referring to Figures 3 and 4 will be described in detail the speed profile generation process according to this embodiment. 3 is a flowchart illustrating a process of generating a velocity profile in the motion controller 30 according to the present embodiment, and FIG. 4 is a background diagram for generating a velocity profile according to the present embodiment, and illustrates a velocity profile over time. will be. In the time axis of FIG. 4, 0 to Trf is an acceleration section, Trf to Teq is a constant velocity section, and Teq to Td is a deceleration section.

First, as shown in FIG. 3, the motion controller 30 inputs the current position q _oi , the target position q _fi , and the speed Vm data of each joint axis of the robot from the main controller 10. Receive (S01). In the case of a six-axis robot, the current position q _oi , the target position q _fi , and the speed Vm data are inputted in the following equations (4a) to (4c).

Next, the motion controller 30 sets the maximum acceleration and the average acceleration based on the input current position q _oi , target position q _fi , and velocity Vm data, and sets the angular displacement of each axis. Calculate the maximum displacement and calculate the ratio of the constant motion time to the total exercise time (S02).

The magnitude of the maximum acceleration Amax is set as in Equation 5a below, and the average acceleration Aave is calculated by Equation 5b below.

Here, the magnitude of the maximum acceleration Amax is actually determined by the limit value of the servomotor. Further, the maximum acceleration Amax is set such that the time ratio from the start of the acceleration section to the maximum acceleration Amax and the time ratio from the arrival of the maximum acceleration Amax to the end of the acceleration section have an asymmetric pattern. Preferably, in this embodiment, as will be described later (see Fig. 5a), such a time ratio is set to be 3: 7.

On the other hand, the maximum displacement (Qmax) of each displacement of each joint axis (that is, 1 to 6 axes in the case of a six-axis robot) is calculated by the following equation (6).

In other words, the largest value of the absolute value of the difference between the target position q _fi and the current position q _{oi of} each joint axis is the maximum displacement Qmax.

Further, the ratio α of the constant velocity to the total exercise time is calculated by the following equation 7a using the results of equations 5b and 6 above.

On the other hand, Equation 7a can be summarized into a speed Vm term input from the main controller 10 as in Equation 7b below.

On the other hand, if the ratio (α) of the constant velocity exercise time to the total exercise time is negative as a result of the calculation in Equation 7a, the desired speed is determined by the speed input in step S01 and the acceleration determined in Equations 5a and 5b accordingly. Since the speed profile cannot be made, the servomotor cannot be accelerated and decelerated properly.

Therefore, if α is negative, α should be set to 0 to decelerate after acceleration without constant velocity motion and to send a warning message to the user. Thus, when α is set to 0, Equation 7b is summarized as in Equation 8 below.

After the step S02, the motion controller 30, the total motion time (Td) for the input speed (Vm) and the maximum displacement (Qmax), the acceleration time (Trf), the time from acceleration to constant velocity (Teq) and The number Tint of the acceleration section is calculated by the following equations 9a to 9d (S03). On the other hand, since the acceleration and deceleration is made symmetrically, the deceleration time is the same as the acceleration time (Trf).

In Equation 9d, RST represents every sampling period, which is a preset value according to a user's selection. Since Trf and RST are functions of time only, the sampling number Tint of the acceleration section is calculated as an integer.

After step S03, the motion controller 30 includes the speed Vi in the constant velocity section (section Trf to Teq in FIG. 4) and the acceleration section (time 0 to Trf in FIG. 4) of each joint axis. ) And the moving distance in the deceleration section (section Teq to Td in FIG. 4) (S04).

First, the speed Vi in the constant velocity section of each joint axis is calculated by the following equation (10).

That is, the velocity Vi in the constant velocity section of each joint axis is the target position q _fi in each joint axis with respect to the maximum angular displacement Qmax calculated in Equation 6 to the velocity Vm input in step S01. It is calculated by multiplying the ratio of the absolute value of the difference between the current positions q _oi .

Next, the motion controller 30 calculates S ₁ , S ₂ , which are average values of the moving distances for every sampling in the acceleration and deceleration sections, for calculating the moving distances for every sampling in the acceleration and deceleration sections. S _{1, which} is an average moving distance for every sampling in the interval, is calculated by Equation 11a below, and S _{2, which} is an average of moving distance for every sampling in the deceleration section, is calculated by Equation 11b below.

In Equations 11a and 11b, S _R represents the moving distance in the acceleration section, that is, the area of the lower portion of the Vr graph in FIG. 4, and S _ratio is the Vr for the area of the rectangular OABC in FIG. 4 (ie, Trf × Vi). The bottom area (S _R ) ratio of the graph. Therefore, S _ratio can be represented by S _R / (Trf × Vi). On the other hand, S _R is equal to the sum of the moving distances S _r1 , S _r2 ,..., S _rn in each sampling period. In addition, S _F is a moving distance in the deceleration section, and S _F is the same as S _R in this embodiment.

After the step S04, the motion controller 30 calculates the position POS of each joint axis in every acceleration section in the acceleration section based on the value S ₁ calculated in Equation 11a by the following Equation 12a. (S05-S06).

Here, POS [t] denotes the position of each joint axis in the corresponding sampling section of the acceleration section, and POS [t-1] denotes the position of each joint axis in the section immediately preceding the corresponding sampling section of the acceleration section, S-Index- R [j] [k] represents the dimensionless rate of change of the velocity in each sampling section of the acceleration section which is tabled and stored as described later. On the other hand, 0.0001 may be omitted for convenience of calculation.

Next, the motion controller 30 calculates the position POS 'of the constant velocity section of each joint axis in each sampling section based on the following Vi value calculated in Equation 10 (S07). ~ S08).

Here, POS '[t] represents the position of each joint axis in the corresponding sampling section of the constant velocity section, and POS' [t-1] represents the position of each joint axis in the section immediately preceding the corresponding sampling section of the constant velocity section. In addition, RST represents a preset sampling period as described above.

Next, the motion controller 30 calculates the position (POS ") of the deceleration section of each joint axis for each sampling section by the following equation 12c based on the S ₂ value calculated in Equation 11a ( S09-S10).

Here, POS "[t] is the position of each joint axis in the sampling section of the deceleration section, and POS" [t-1] is the position of each joint axis in the section immediately preceding the sampling section of the deceleration section, S- Index-F [j] [k] represents the dimensionless rate of change of the velocity in each sampling section of the deceleration section stored in a table as described later. On the other hand, 0.0001 may be omitted for convenience of calculation.

On the other hand, in this embodiment, S-Index-R [j] [k] and S-Index-F [j] [k] in Equations 12a and 12c are expressed in the following Equations 13a to 13d. It is calculated in advance and stored in a table form.

Taking the case of S-Index-R [j] [k] as an example, first, the speed for each sampling section is calculated by the following equation (13a) which is the same as the above equation (2).

As described above, where Vr (k) is the speed in the corresponding sampling section k (k = k = 1, 2, ..., n) of the acceleration section, and Vr (k-1) is immediately before the sampling section. The speed in the section k-1 is shown. In addition, a (k) means the acceleration in the sampling interval, a (k-1) means the acceleration in the immediately preceding section of the sampling interval.

On the other hand, in the present embodiment, the time pattern between the portion of the acceleration in the acceleration section and the portion of the negative slope is set to approximately 3: 7 (see Fig. 5A). In this way, it is not necessary to separately calculate a (k) and a (k-1) in the equation (13a) by defining the acceleration pattern in advance.

Next, the time t is erased from Vr (k) calculated by Equation 13a to obtain the conversion rate Fr (k). That is, Fr (k) is calculated by the following equation (13b).

Here, RST represents a sampling period defined by Equation 9d. On the other hand, according to Equation 13b, it can be seen that Fr (k) can be represented in the form of a bar graph corresponding to the corresponding speed Vr (k) in each sampling section in FIG. 4.

Next, as a previous step for obtaining the rate of change of the velocity in each sampling section, Gr (k), which is a dimensionless value, is calculated by the following equation (13c).

Here, Fr (k) represents a conversion speed in each sampling section calculated in Equation 13b, S _R represents a moving distance in the deceleration section, and Tint represents a sampling number.

Finally, by multiplying the calculation result of Equation 13c by 10000, a dimensionless value corresponding to the rate of change of velocity in each sampling interval can be obtained, and the table is S-Index-R [j] [k]. . That is, it can be expressed as Equation 13d following S-Index-R [j] [k].

In this case, the numeral 10000 is introduced for convenience of calculation, and the numerical value may be appropriate or may be omitted.

When 10000 is omitted in Equation 13d, since S-Index-R [j] [k] is equal to Gr (k), S-Index-R [j] [k] is expressed as in Equation 14 below. Can be represented.

In other words, S-Index-R [j] [k] can be arranged in a table according to the sampling number (Tint). Table 1 below shows an example in which S-Index-R [j] [k] is arranged in a table according to the results of the calculations of Equations 13a to 13d.

S-Index-R [j] [k] Tint = 5 Tint = 6 Tint = 7 Tint = 8 Tint = 9 Tint = 10 1186 819 601 461 364 294 5297 3955 3005 2303 1817 1471 10975 8822 7080 5671 4624 3823 15254 13128 11193 9513 8108 6933 17288 15936 14323 12750 11279 9958 17340 16384 15118 13771 12479 17414 16697 15640 14496 17487 16887 16008 17510 17017 17521

On the other hand, S-Index-F [j] [k], which is a non-dimensionalized change rate of velocity in each sampling section in the deceleration section, is calculated and arranged in the same manner as S-Index-R [j] [k]. Can be. Table 2 below shows an example in which S-Index-F [j] [k] is tabled according to a result calculated in the same manner as in Equations 13a to 13d.

S-Index-F [j] [k] Tint = 5 Tint = 6 Tint = 7 Tint = 8 Tint = 9 Tint = 10 21304 21937 22251 22414 22571 22692 16033 17860 19118 20017 20674 21154 8750 11532 13806 15634 17013 18077 3261 5933 8445 10634 12468 14011 652 2282 4365 6421 8332 10055 456 1679 3339 5081 6758 336 1284 2642 4121 257 1016 2143 203 824 165

As described above, using S-Index-R [j] [k] and S-Index-F [j] [k] arranged in a table, each joint axis in each sampling section is expressed in Equations 12a to 12c. By calculating the position POS of the acceleration section, the position POS 'of the constant velocity section, and the position POS "of the deceleration section, it is not necessary to calculate the acceleration and the speed for every sampling period RST as conventionally.

Meanwhile, using Equations 13a to 13d, Equation 12a relating to the position of each sampling section in the acceleration section is rearranged as follows.

On the other hand, after step S05 to step S10, the motion controller 30, the position (POS) of the acceleration section of each joint axis for each sampling section calculated by the equation (12a) to (12c) and the position of the constant velocity section ( POS ') and the position of the deceleration section (POS ") are transmitted to the joint position controller (JPC) 40. The joint position controller 40 is the servo drive unit 50 of each joint axis based on the transmitted position data. To control each joint axis to the commanded position.

5A to 5C are graphs showing acceleration, velocity, and distance profiles generated by the velocity profile generation method according to the present embodiment. FIG. 5A is an acceleration profile with respect to time, and FIG. 5B is a velocity profile with respect to time. 5C shows the distance profile over time, respectively.

As described above, in the present embodiment, as shown in FIG. 5A, the time ratio between the portion of the positive slope and the portion of the negative slope of the acceleration pattern in the acceleration section is set to 3: 7. On the contrary, in the acceleration pattern in the deceleration section, the time ratio between the negative slope and the positive slope was set to 3: 7. That is, the maximum acceleration Amax in the acceleration section is located at 3/10 time between the start point of the acceleration section and the end point of the acceleration section. In this way, by configuring the acceleration pattern asymmetrically during acceleration and deceleration, it is possible to reduce noise and vibration caused by the movement of each joint of the robot.

As described above, according to the present invention, by configuring the acceleration pattern during acceleration and deceleration asymmetrically, it is possible to smoothly control the motion of each joint axis during the movement of the articulated robot, thereby significantly reducing vibration and noise.

In addition, in calculating the acceleration / deceleration velocity profile, S-Index-R [j] [k] and S-Index-F [j] [k], which are non-dimensionalized change rates of the speed previously stored in the table, are used. As the acceleration and velocity do not need to be calculated for each sampling period, the calculation time can be reduced.

In the above, certain preferred embodiments of the present invention have been illustrated and described. However, the present invention is not limited to the above-described embodiments, and various modifications can be made by those skilled in the art without departing from the gist of the present invention as claimed in the claims. will be.

Claims (8)

Set the acceleration pattern asymmetrically in the acceleration section, calculate the position of each joint axis in each sampling section of the acceleration section by using the rate of change of velocity in the corresponding sampling section, A method for generating an acceleration / deceleration speed profile of an articulated robot, wherein the rate of change of speed is calculated in advance by the following equation; Here, S-Index-R [j] [k] is a rate of change in every sampling section, Vr (k) is a rate in every sampling section, RST is a sampling period, and S _R is a movement in the acceleration section. Distance, and Tint is the number of samplings. The acceleration pattern of claim 1, wherein the acceleration pattern in the acceleration section is set such that the time in the section in which the acceleration is positive is positive and the time in the section in which the acceleration is negative is 3: 7. Acceleration / deceleration velocity profile generation method of a multi-joint robot. (a) setting a maximum acceleration Amax and an average acceleration Aave based on the current position q _oi , the target position q _fi , and the speed Vm data of each input joint axis; (b) calculating a maximum displacement (Qmax) of each movement displacement of the joint axis based on the current position (q _oi ) and the target position (q _oi ) data; (c) calculating a ratio (α) of the constant velocity exercise time to the total exercise time based on the set average acceleration (Aave), the input speed (Vm), and the maximum displacement (Qmax); (d) The total motion time Td for the input speed Vm and the maximum displacement Qmax, the acceleration and deceleration time Trf, the time Teq from acceleration to constant velocity, and the acceleration section. Calculating a sampling number Tint; (e) the speed Vi at the constant velocity section of each of the joint axes, the average value S ₁ of the moving distances in every sampling section in the acceleration section, and the average value of the moving distances in every sampling section in the deceleration section ( Calculating S ₂ ); And (f) The acceleration section position (POS) and the constant velocity section position of each joint axis in each sampling section by using the calculation result in step (e) and the rate of change of the velocity in every sampling section previously stored in the table. (POS ') and the step of calculating the deceleration section position (POS') comprising the acceleration and deceleration control method of the articulated robot. 4. The maximum acceleration Amax in the step (a) is an asymmetrical time ratio from the start of the acceleration section to the maximum acceleration time and from the maximum acceleration time to the end of the acceleration section. Acceleration and deceleration control method of a multi-joint robot, characterized in that it is set to be made. The method according to claim 4, wherein in step (e), the average value S ₁ of the moving distances for each sampling section in the acceleration section is calculated by the following equation. ; Here, S _R is a moving distance in the acceleration section, and Tint is a sampling number. The acceleration / deceleration control method of the articulated robot according to claim 5, wherein the acceleration section position (POS) of each joint axis in each sampling section is calculated by the following equation; Here, POS [t] is the position of each joint axis in the sampling section, POS [t-1] is the position of each joint axis in the section immediately preceding the sampling section, and S-Index-R [i] [k ] Is the rate of change of velocity in each sampling section, and S ₁ is the average of the moving distances in each sampling section. 7. The acceleration / deceleration control method of an articulated robot according to claim 6, wherein the S-Index-R [j] [k] is calculated in advance by the following equation and stored in a table; Here, Vr (k) is a speed in every sampling section, RST is a sampling period, S _R is a moving distance in an acceleration section, and Tint is a sampling number. 6. The acceleration / deceleration control method for an articulated robot according to claim 5, wherein the position of the constant velocity section (POS ') of each joint axis in each sampling section is calculated by the following equation; Here, POS '[t] is the position of each joint axis in the sampling section, POS' [t-1] is the position of each joint axis in the section immediately preceding the sampling section, and RST represents a sampling period.