JPH03129504A - Control method for minimizing speed variation of robot - Google Patents

Abstract

PURPOSE:To smoothly drive a robot by finding out sum of squares errors between speeds and an objective speed, finding out a moving time minimizing the sum of squares from convergent calculation and controlling the robot so as to apply the locus of the tip of the robot based upon the converged moving time. CONSTITUTION:When the position and speed vectors of a start point, the position and speed vectors of an end point and a temporary moving time are applied to an expression expressing the position and speed of the tip of the robot expressed by the tertiary function of time, respective coefficients of the tertiary function. The sum of squares of errors between the speeds obtained by using these coefficients and the objective speed is found out and the moving time is found out by convergent calculation so that the sum of squares is minimized. The robot is controlled so that the locus of the tip of the robot is applied by using the calculated value. Thus, the speed variation can be minimized and the smooth locus can be obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a control method for minimizing speed fluctuations of a robot, and is particularly applied to control of a robot that performs painting and sealing operations.

[Conventional technology]

In general, robots that perform painting and sealing tasks are required to perform complex movements that are fast and smooth.

For this reason, this type of movement is achieved by specifying the speed and trajectory in detail, and in order to specify this kind of specification, the specified speed and trajectory are taught in detail at short intervals. . In other words, a smooth trajectory is obtained by specifying the speed and trajectory in detail for each short distance or for each short period of time.

However, this method has the problem that the finer specifications complicate the teaching algorithm and increase the amount of calculations, making it impossible to obtain the required high speed and making speed fluctuations unavoidable.

For this reason, it has been proposed to perform smooth trajectory control using a high-order function.

For example, in the method using the 5th order function shown in Japanese Patent Application Laid-open No. 62-72008, the condition for finding the trajectory between two points is
A trajectory that minimizes the temporal change in acceleration (jerk acceleration) is determined by giving the start and end point positions, (1) the velocity vector at the start and end points, (2) the acceleration vector at the start and end points, and (2) the travel time between the two points.

[Problem to be solved by the invention]

However, in the case of this method, the user must specify the travel time between two points, which is a scalar quantity, taking into account constraints due to the robot's capabilities, and the specified value of the travel time also affects the trajectory itself and the movement. The problem is that the speed changes.

The present invention was made to solve these problems, and an object of the present invention is to provide a control method for minimizing speed fluctuations of a robot, which can minimize speed fluctuations and obtain a smooth trajectory. .

[For production]

If we give the position vector of the starting point, the velocity vector of the starting point, the position vector of the ending point, the velocity vector of the ending point, and the temporary movement time to the equation that expresses the position and velocity of the tip of the robot expressed as a cubic function of time, the equation becomes cubic. Each coefficient of the function is determined, the sum of squares of the error between the velocity obtained using these coefficients and the target velocity is determined, and the travel time that minimizes this sum of squares is determined by convergence calculation. By controlling the robot so as to give the trajectory of the robot tip using this value, speed fluctuations can be minimized and a smooth trajectory can be obtained.

Note that although the user specifies the absolute values of the velocity vectors at the start point and the end point, the direction can be automatically determined from the previous and subsequent teaching points and does not need to be specified by the user.

〔Example〕

Examples of the present invention will be described in detail below.

The figure is a flowchart illustrating the method according to the invention.

Here, it is assumed that the position of the trajectory of the robot tip is expressed by the following cubic function of time.

Z-a t +b t2+c t+d...
...(3) z z
z z From these, the speed of the robot tip is (1) (2) (3) Differentiating the equation with time, Vx-dx/dt=3a t2+2b t+c
Song - (4) x x x...
...(5) ...(6) It is expressed as follows.

It is assumed that each of these equations is stored in advance in a storage section within the control device, and is retrieved as needed during speed control (step 510).

Here, when solving by giving the position vector of the starting point, the position vector of the ending point, the velocity vector of the starting point, the velocity vector of the ending point, and a temporary travel time, the above a Sb is obtained.

x X Cs d %a s b ,, Cs d ,,
a % bxxyyyyz , c , d can be found (step z
z z S20).

Therefore, the speed V is (Step 530).

In order to bring this speed closer to the target speed, the following target speed V, 8. An operation is performed to find the sum of squares of the errors for (step 540).

S-J' (V-V) 2dt ref' Then, the travel time that minimizes the value of S is determined by convergence calculation. In other words, it is checked whether the error has become less than a small constant value ε that allows it to be determined that the error has converged (step 550), and if so, the trajectory between the two points is determined based on this travel time. (Step 560
). At this time, speed fluctuations are at a minimum.

If it is determined that the process has not converged yet, change the travel time and repeat from step S20 (step 570).
.

In addition, if the acceleration/deceleration of each axis to realize the obtained trajectory exceeds the specified value, an operable trajectory can be obtained by lowering the speed setting values at the start point and end point and repeating from step 20. .

The above calculations are performed using a high-speed microcomputer or the like.

〔Effect of the invention〕

As described above, according to the present invention, speed fluctuations can be minimized and a trajectory having a speed close to the target speed can be provided by simply providing a start point vector, an end point vector, and a temporary travel time for position and speed. Therefore, smooth robot motion can be achieved without the user specifying an accurate movement time.

[Brief explanation of the drawing]

The figure is a flowchart illustrating the method of the invention.

Claims (1)

[Claims] For equations expressing the position and speed of the robot's tip expressed as a cubic function of time, a starting point position vector, a starting point velocity vector, an ending point position vector, an ending point velocity vector, and a temporary movement. a process of calculating each coefficient of the cubic function by giving time; a process of calculating the sum of squares of the error between the speed obtained using these coefficients and the target speed; A control method for minimizing velocity fluctuations of a robot, which is characterized by a process of determining a travel time by convergence calculation, and controlling the robot so as to give a trajectory of the robot's tip based on the converged travel time.