JP7237447B2 - Information processing method, program, recording medium, information processing device, robot system, and article manufacturing method - Google Patents

Description

The present invention relates to a robot control data processing method, a robot control data processing apparatus, and a robot system for generating trajectory data including a path for moving a specific part of an articulated robot and speed information of the specific part at that time.

When programming a robot arm, for example, a method of designating a teaching point group corresponding to positions (or postures) at which specific parts of the robot arm are to be positioned in sequence is sometimes used. For the specific reference portion of the robot arm that takes the position and orientation of the teaching point, for example, the central position of the tool at the tip of the arm, for example TCP (Tool Center Point) is used. In this case, the teaching point is represented by coordinate values or the like indicating the position and orientation of the TCP in the work space (task space) of the arm. Alternatively, the teaching point may be specified as angle information (group) of each joint of the arm. In this case, the teaching point can be treated as a coordinate value in a virtual joint space with joint angles as coordinate axes.

When a plurality of pieces of teaching point information for positioning the TCP are prepared, the robot controller controls the path and speed for moving a specific part of the arm between one teaching point as the starting point and the next teaching point as the end point. trajectory data is generated for Although various specific description formats of the trajectory data are conceivable, for example, a list of angle command values for each joint of the robot arm at a specific time may be used. When the trajectory data is generated, it is possible to actually drive the robot arm based on this trajectory data and execute the motion programmed by the teaching point information.

In addition, the path of the teaching points between the start point and the end point can be determined by linear interpolation, by generating interpolation points between the start point and the end point, or by creating curves such as B-spline curves according to the positional relationship of a large number of teaching points. Interpolation may also be used to generate route information.

On the other hand, for industrial robot devices used in production sites for manufacturing industrial products and parts, it is desirable to be able to calculate optimum speed information for operating the robot arm in trajectory data generation from the viewpoint of work efficiency. For example, Non-Patent Document 1 describes an optimum speed calculation method for calculating the optimum operating speed of a robot that minimizes the operating time while observing various physical constraints on a route given by teaching point information. there is

When adjusting the motion speed of the robot and creating the motion trajectory on the path given by the teaching point information, for example, the speed parameters are adjusted so that the motion time of the robot is shortened while observing various physical constraints. Traditionally, this task has been done, for example, by the operator adjusting the speed parameters over and over. However, when the operator adjusts the parameters, there is a problem that the trajectory is not always optimal, or the operation time is long, and the work is complicated, requiring a large amount of man-hours for development. Therefore, it is desirable that the robot control device connected to the arm or other robot control data processing device can automatically calculate the optimum motion speed of the robot that observes various physical constraints and minimizes the motion time.

For example, Non-Patent Document 1 describes a velocity optimization method that automatically generates a trajectory with the shortest possible operation time for a given trajectory while observing joint torque constraints of a robot. Here, character expressions of various parameters in the mathematical expressions shown below are defined as follows. In each letter expression, bold letters indicate vectors. For convenience, the text of this specification uses a notation such as (·) for time differentiation, although it does not necessarily match the notation in each mathematical expression in which a dot is placed on a literal expression. For example, a notation such as s(·) is used for the velocity s, which is the first derivative of the position information.

与えられた経路に対し、ロボットの最適な軌道を生成するという問題は、与えられた経路上の速度だけを考えればよいという問題に簡略化することができる。例えば、経路上の座標値ｓを定義し、ロボットアーム（の特定部位）の運動方程式は、このｓを用いて下式（１）のように定義することができる。

The problem of generating the optimal trajectory of the robot for a given path can be reduced to the problem of only considering the velocity on the given path. For example, a coordinate value s on the path is defined, and the equation of motion of (the specific part of) the robot arm can be defined as in the following equation (1) using this s.

ここで、Ｍは質量行列、Ｃはコリオリ項、Ｇは重量項、τは関節トルクである。次に、ロボットの関節速度および関節加速度はそれぞれ下式（２）、（３）のように記述される。

Here, M is the mass matrix, C is the Coriolis term, G is the weight term, and τ is the joint torque. Next, the joint velocity and joint acceleration of the robot are described by the following equations (2) and (3), respectively.

上式（２）は、関節角速度および関節角加速度を、経路の位置を示すベクトル、即ちｑ（ｓ）と、経路上の速度、即ちｓ（・）に分解したものと考えられる。つまり、この最適速度問題は、経路が決まっていれば、その経路上を動く速度だけを考えればよく、どの方向に動くかを考えない単純な問題として扱うことが可能となる。式（３）の加速度ｓ（・・）についても同様のことが言える。

The above equation (2) can be thought of as decomposing the joint angular velocity and the joint angular acceleration into a vector indicating the position of the path, i.e. q(s), and the velocity on the path, i.e. s(.). In other words, this optimum speed problem can be treated as a simple problem, if the path is determined, only the speed of movement on that path is considered, and the direction of movement is not considered. The same can be said for the acceleration s(..) in equation (3).

Here, substituting equations (2) and (3) into equation (1) yields

その場合、ｍ（ｓ）、ｃ（ｓ）、ｇ（ｓ）は

Then m(s), c(s) and g(s) are

である。

is.

With this transformation, the problem of "what speed to move on the path in order to optimize the motion time while keeping the joint torque constraint" becomes "s(t) that optimizes the motion time while keeping the joint torque constraint". How to design?" is replaced by the problem. The operating time of the trajectory is determined by how s(t), which is the relationship between times t and s, is designed. That is, if s(t) that minimizes the operation time of the robot can be calculated, optimal trajectory data can be generated. Further, since the position s(t) at a specific time can be calculated by integrating s(·), s(·) can be obtained.

Now consider the trajectory s(0)=0≤s≤1=s(T) starting at t=0 and ending at t=T. Also, to generate the time-optimal trajectory, assume that tε[0,T] and s(·)>0.

From the above, this optimal speed problem can be described as the following optimization problem.

しかし、この問題は、例えばｓ（・）を変数としたとき、非線形かつ、非凸最小化問題となるため、最適解を求めるのが困難である、という問題がある。そこで、非特許文献１では、この問題に対し、ａ（ｓ）、ｂ（ｓ）という２つの変数を導入し、凸問題化を行っている（下式（１７）、（１８））。即ち

However, this problem is a non-linear and non-convex minimization problem when s(.) is a variable, and it is difficult to find an optimal solution. Therefore, in Non-Patent Document 1, two variables, a(s) and b(s), are introduced for this problem to convert it into a convex problem (formulas (17) and (18) below). Namely

とすると

and

となり、ａ（ｓ）、ｂ（ｓ）の線形の関係式が書ける。また、目的関数は式（１８）より

Then, a linear relational expression of a(s) and b(s) can be written. Also, the objective function is obtained from equation (18) as

というｂに関する凸関数で書ける。

can be written as a convex function on b.

As for the torque, the equations (17) and (18) are substituted into the equation (9).

と表現でき、これは変数ａとｂに関して線形となる。ここで、上記の最適化問題を書き直すと

which is linear in the variables a and b. Now, if we rewrite the above optimization problem as

となる。この場合、目的関数である式（２２）が凸関数であり、制約条件である式（２３）－（２９）が全て線形であるため、凸最小化問題として解くことが可能となる。

becomes. In this case, equation (22), which is the objective function, is a convex function, and equations (23) to (29), which are the constraint conditions, are all linear, so it can be solved as a convex minimization problem.

Convex minimization is a field of optimization problems, the problem of minimizing a convex function on a convex set. Convex minimization problems can be optimized more easily than general optimization problems, and have the property that the local minimum agrees with the global minimum.

In the above description, only the joint torque constraint was considered as the constraint, but it is also conceivable to apply joint angular velocity constraint, joint angular acceleration constraint, jerk constraint, hand speed constraint, hand acceleration constraint, and the like. In the following, for the sake of simplification, b(s), which is the square of s(·), is expressed as the velocity on the route, and b(s) is b and q(s) is q. We sometimes use notation such as

Similar to the torque constraint above, it is also possible to take into account the jerk constraint to generate the optimal trajectory. Here, jerk refers to the joint angle jerk of the robot arm. The jerk corresponds to the third derivative of the joint angle q with respect to time, and if the jerk is large, the vibration of the robot will be large, so it is desirable to apply the jerk constraint.

Jerk uses b, b', b'', q', q'', q'''

と書ける。ここで、ロボットアームに複数備えられた関節軸のインデックスをｉとすれば、関節軸ｉに関する上式（３１）の一般表現は

can be written as Here, if the index of a plurality of joint axes provided in the robot arm is i, the general expression of the above equation (31) regarding the joint axis i is

のようになる。そして、上記の関節トルク制約の場合と同様に

become that way. And as in the joint torque constraint case above

というジャークの上限、下限を守るよう最適速度問題を解くことができる。

It is possible to solve the optimal speed problem so as to keep the upper and lower limits of the jerk.

However, in the case of a path generated by curve interpolation such as a B-spline curve, the values of q''', q'', and q' may become almost 0 near the start and end points. In this case, the jerk becomes almost 0 no matter what speed b is given, and the problem arises that the jerk constraint cannot be calculated properly. If the trajectory is generated as it is, the jerk constraint cannot be applied near the start and end points of the route, and a phenomenon occurs in which, for example, the jerk diverges infinitely.

On the other hand, in Non-Patent Document 2, for example, as shown in FIG. 4, a coping method is adopted in which jerk is suppressed near the start and end points of a path by linearly increasing the joint angle acceleration constraint from the start and end points. ing. FIG. 4 is a graph in which the horizontal axis is the parameter s of the interpolation path and the vertical axis is the joint angular acceleration constraint. In FIG. 4, near the starting point of the path, the acceleration constraint is set to 0, and when the parameter s of the interpolation path is s1, linear interpolation is performed so that the joint angular acceleration constraint is maximized (i is the index of the joint axis). ). Also, near the end point, linear interpolation is performed so that the acceleration constraint of the joint angle takes the maximum value at s2 and becomes 0 at the end point.

With this kind of control, the joint angular acceleration can be appropriately suppressed near the start and end points, and abrupt changes in acceleration can be suppressed. Saturation can be suppressed.

Further, Patent Document 1 discloses a technique for performing speed combination processing when two paths are continuous and the paths are generated by different interpolation processes such as joint interpolation and linear interpolation. are doing. In the control of Patent Document 1, it is determined whether the interpolation type changes from a joint interpolation motion to a linear interpolation motion or from a linear interpolation motion to a joint interpolation motion in two continuous paths. It is determined whether speed combining processing is possible when passing through the connecting point of the two routes or its vicinity (speed combining processing availability determination unit (2)). Then, if speed combining processing is possible, an interpolation point for superimposing the speeds of the different types of interpolation motions is determined from the joint variables (speed combining calculation section (3)). According to the technique disclosed in Patent Document 1, it is possible to prevent a decrease in speed at the time of transition of the route, and therefore it is possible to suppress saturation of the jerk.

JP 2004-252814 A

Verscheure, Diederik, et al. "Time-optimal path tracking for robots: a convex optimization approach." Automatic Control, IEEE Transactions on 54.10 (2009): 2318-2327. Reynoso-Mora, Pedro, Wenjie Chen, and Masayoshi Tomizuka. "On the time-optimal trajectory planning and control of robotic manipulators along predefined paths." 2013 American Control Conference. IEEE, 2013

The technique of Non-Patent Document 1, when specific path information is given, observes physical constraints such as joint torque constraints, joint angular velocity constraints, joint angle acceleration (jerk) constraints, hand speed constraints, and hand acceleration constraints. It uses a method that transforms the optimization problem of minimizing the time into a convex problem. However, in the method of Non-Patent Document 1, no matter what speed b is given in the route where q′″, q″, and q′ are nearly 0 near the start and end points of the route as described above, There is a problem that the jerk becomes a value of almost 0, and the jerk constraint cannot be calculated properly.

On the other hand, Non-Patent Document 2 employs a method of suppressing jerk in the vicinity of the start and end points of a path by linearly increasing the joint angle acceleration constraint from the start and end points. However, there is no guarantee that the jerk constraints specified in advance will be observed, and the obtained trajectory is not necessarily the optimum trajectory. According to the method of Non-Patent Document 2, before the trajectory is optimized, the joint angular acceleration constraint is determined based on s, which is the parameter of the trajectory. This is because it is not known until the trajectory is generated. That is, the information about which jerk it will be at a certain time can only be obtained after the actual trajectory is generated after optimizing the velocity b on the path. For example, as shown in FIG. 4, the horizontal axis is the path parameter s, not time. For this reason, even if the joint angular acceleration linearly increases and decelerates at the start and end points, how the jerk, which is the third derivative of time, is constrained will generate trajectory data including path and velocity information. I won't know until later.

Japanese Patent Laid-Open No. 2002-200001 relates to a method of combining velocities when different interpolation processes are used, such as joint interpolation and linear interpolation, but there is a problem that complicated processes are required. Further, the method of Patent Document 1 is a method of performing velocity synthesis for continuous sections. Therefore, what is the speed (acceleration or jerk) control method that can be generally used when there is a condition that the speed of a specific part of the robot arm should be controlled to 0 at the teaching point that is the start or end point of the path? I can't say

Therefore, it is an object of the present invention to appropriately constrain the jerk (jerk) at the start and end points of a route so that it does not saturate, and to enable speed control to generate optimal trajectory data.

A first aspect of the present invention is information processing in which a processing unit acquires a target trajectory including a path of a predetermined part and a speed of the joint when moving a predetermined part of a robot having joints. In the method, the processing unit is configured, at a first position and/or a second position through which the predetermined part passes on the target trajectory, to determine the upper limit of the jerk at the joint when moving the predetermined part using the robot. Based on 1 constraint value , the speed of the joint when the joint is operated with the jerk set to the first constraint value is acquired as the constraint speed , and the predetermined part moves from the first position. A route is obtained by interpolating the area up to the second position, and the speed of the joint when moving the predetermined part on the route is obtained with the constraint speed as a second constraint value . It is an information processing method for

With the above configuration, it is possible to generate optimal trajectory data that can appropriately restrict jerk (jerk) from being saturated at the start and end points of the route, and perform speed control.

1 is a block diagram showing a functional configuration of a robot control data processing device according to an embodiment of the present invention; FIG. FIG. 4 is an explanatory diagram showing a two-axis configuration in the robot arm according to the embodiment of the present invention; It is a flowchart figure for demonstrating the production|generation process of the track|orbit data which concerns on embodiment of this invention. FIG. 10 is an explanatory diagram showing control of jerk constraints in Non-Patent Document 2; 1 is a block diagram showing a configuration example of a robot control data processing device or a robot control device according to an embodiment of the present invention; FIG. FIG. 3 is an explanatory diagram showing a more specific configuration example of the robot arm of FIG. 2;

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments for carrying out the present invention will be described with reference to the accompanying drawings. The configuration shown below is merely an example, and, for example, details of the configuration can be changed as appropriate by those skilled in the art without departing from the spirit of the present invention. Further, the numerical values taken up in the present embodiment are reference numerical values and do not limit the present invention.

In general, a robot arm is composed of joints and links (link mechanism). There are various types of joints arranged between links, such as rotary joints, prismatic joints, and ball joints. In addition, joints include those that are actively operated by a drive source such as a motor, and those that are passively operated without a power source. Each joint is connected by a link, and there are a serial link type in which joints and links are alternately arranged in series and a parallel link type in which a combination of joints and links are arranged in parallel. A serial link type robot arm having rotary joints will be described below as an example, but the technology described later can be similarly applied to any robot arm having links and joints regardless of the coupling mode.

FIG. 1 shows the configuration of a trajectory generation device as an embodiment of the robot control data processing device of the present invention. The trajectory generation device 1 includes an operation unit 2 for receiving data input by an operator, an arithmetic processing unit 3 composed of a CPU (not shown) and the like, and a storage unit 4 for storing various data. A display 21 is provided in the operation unit 2 . The display 21 can display, for example, the robot arm A and its working space in 3D (three-dimensional) graphics. Such a user interface allows the operator to visually recognize the generated trajectory of the robot.

As shown on the right side of FIG. 1, the arithmetic processing unit 3 includes model/restriction information input means 31, interpolation method/teaching point information input means 32 (teaching point input device (means)), route generation means 33, Prepare. The arithmetic processing unit 3 also includes jerk saturation axis prediction means 34 , jerk equivalent speed constraint calculation means 35 , speed constraint integration means 36 , and speed optimization means 37 . More specifically, each means constituting these arithmetic processing units 3 can be implemented by hardware and software using a CPU 601 (FIG. 5), which will be described later.

FIG. 2 very schematically shows the configuration of the robot arm A that generates trajectory data in this embodiment. In FIG. 2, the robot arm A has two axes J1 and J2 consisting of two joints (two degrees of freedom). If the joint angles of the two axes J1 and J2 of the robot arm A are θ1 and θ2, respectively, the joint angles of the robot arm A are q=(θ1, θ2)T and can be regarded as one point on the joint space. Moreover, there is a TCP (Tool Center Point) at the tip of the axis J2. Henceforth, we will simply refer to TCP as minions.

It should be noted that the robot arm A may be generally thought of as an action body in which the robot arm itself operates, and the schematic configuration of FIG. is not intended to be For example, the robot arm A may be a 6-axis articulated robot arm or a direct-acting robot arm. For example, if the robot arm A has a vertical 6-axis articulated configuration, the robot arm A can be configured as shown in FIG. 6, which will be described later.

When the parameters representing the degrees of freedom of the robot arm A (for example, joint angles and extension/contraction lengths) are the values of the coordinate axes, the joint angles of the robot arm A can be expressed as points on the joint space.

FIG. 6 shows the overall configuration of the robot arm A more specifically than the schematic configuration of FIG. In FIG. 6, a robot arm A (robot device) includes, for example, an arm body 201 of a vertical multi-joint type with six axes (joints). Each joint of the arm body 201 can be controlled to a desired position and orientation by servo-controlling a servomotor provided for each joint.

The movement of the arm body 201 of the robot arm A is controlled by the robot controller 200 . The operation of the robot arm A can be programmed (instructed) by an operation terminal 204 (for example, a teaching pendant) connected to the robot controller 200 . For example, by sequentially designating teaching points using the operation terminal 204, it is possible to program an operation to move a specific part of the robot arm A (for example, TCP: tool mounting surface at the tip of the arm) along a desired trajectory. In that case, the teaching point information is represented by three-dimensional coordinates in the work space (task space) of the robot arm A, or the like. In some cases, the operation terminal 204 can be operated by specifying the angle of each joint of the robot arm A. In this case, the teaching point information is represented by a list of angle information of each joint.

The robot arm A, particularly its robot controller 200, can be connected to the arithmetic processor 3 (robot control data processor) via a network N (FIG. 5). In that case, the teaching point information created by the teaching operation of the operation terminal 204 can be input to the arithmetic processing section 3 in step S102 (FIG. 3) described later. In a control example to be described later, the arithmetic processing unit 3 uses the teaching point information input in step S102 to execute the steps after step S104 in FIG. Then, trajectory data including a path along which the reference part of the robot arm A (for example, a specific part such as TCP) is moved and speed information of the reference part at that time is generated. In that case, the velocity information of the trajectory data is generated so that the jerk (jerk) of each joint of the robot arm A does not saturate with respect to the upper limit value determined by the constraints of the mechanism. In the following description, the processes after step S104 in FIG. 3 are assumed to be executed by the arithmetic processing section 3 (robot control data processing device). However, a configuration may be adopted in which the robot control device 200 executes the same processing to generate trajectory data including the path along which the reference portion of the robot arm A is moved and the speed information of the reference portion at that time. .

The robot arm A in FIG. 6 is configured, for example, as a 6-DOF manipulator mounted on a base and having 6 rotary joints each. Each joint of the robot arm A can be controlled at an angle designated by the robot control device 200 by a drive source arranged inside each joint, thereby controlling the robot arm A to a desired position and orientation. . As a driving source for driving each joint of the robot arm A, a servomotor or the like is used.

The trajectory data including the path of the reference part (for example, TCP) and speed information generated by the arithmetic processing unit 3 (robot control data processing device) is transmitted to the robot arm A via the network N. By controlling each joint of the arm body 201 based on the transmitted trajectory data, the robot arm A can cause the robot arm A to perform the robot motion taught by the operation terminal 204 . In that case, the trajectory data is controlled by a control procedure (for example, FIG. 3) to be described later so that the jerk (jerk) of each joint does not saturate with respect to the upper limit determined by the constraints of the mechanism. Therefore, problems such as unwanted vibration and noise occurring in the robot arm A during operation are reduced. In addition, it is possible to avoid damage to the mechanism of the robot arm A and unreasonable movements that may cause durability problems.

A gripper 202 can be attached to the tip of the robot arm A as a tool for gripping a workpiece 203 to be worked. Fingers (claws) for handling the workpiece 203 are provided at the tip of the gripper 202 . An actuator for opening and closing the fingers is provided inside the gripper 202 . This actuator is composed of a motor, a solenoid, or any other pneumatic or hydraulic actuator. The gripper 202 is attached to the tip of the robot arm for the purpose of loading and unloading the work 203 to a specific work position or assembling the gripped work 203 to another work. The tool arranged at the tip of the robot arm A is not limited to the gripper described above, and may be an end effector having any other function.

A configuration using the CPU 601, ROM 602, RAM 603, etc. as shown in FIG.

The control device in FIG. 5 includes a CPU 601 as main control means, a ROM 602 as a storage device, and a RAM 603 . The ROM 602 can store a control program for the CPU 601, constant information, and the like for realizing a control procedure to be described later. Also, the RAM 603 is used as a work area for the CPU 601 when executing a control procedure to be described later.

5 is the arithmetic processing unit 3 in FIG. 1, the operation unit 2 is connected via the interface 607. FIG. The operation unit 2 can be composed of a terminal such as a handy terminal, or a control terminal including a keyboard, display, pointing device, and the like. 5 is the robot control device 200, the operation unit 2 can be replaced with the operation terminal 204 described above.

A network interface 605 is connected to the control device in FIG. 5 as communication means. The robot arm A can exchange, for example, the above teaching point information and trajectory data with the robot arm A via the network interface 605 . In that case, the network interface 605 may be configured with a communication standard for wired communication such as IEEE 802.3 or wireless communication such as IEEE 802.11 and 802.15. Of course, any other communication standard may be adopted. For example, if the control device in FIG.

Note that the control program of the CPU 601 for realizing the control procedure described later can also be stored in an external storage device 604 such as an HDD or SSD, or a storage unit such as the ROM 602 (for example, EEPROM area). In that case, the control program of the CPU 601 for realizing the control procedure described later can be supplied to each of the above storage units via the network interface 605 and updated to a new (different) program. Alternatively, the control program of the CPU 601 for realizing the control procedure described later is supplied to each of the above-described storage units via storage means such as various magnetic disks, optical disks, flash memories, and drive devices therefor, Also, its contents can be updated. Various storage means and storage units in which the control program of the CPU 601 for realizing the control procedure described above is stored constitute a computer-readable recording medium storing the control procedure of the present invention.

FIG. 3 shows the flow of the control procedure for realizing the trajectory generation method according to this embodiment. The illustrated procedure can be stored as a control program for the CPU 601 (FIG. 5) in, for example, the ROM 602 or the external storage device 604 as described above.

In step S100 of FIG. 3, the model/constraint information input means 31 reads the model information and constraint conditions of the robot arm A in the work space where the robot arm works. The model information of the robot arm A is, for example, design information of parts constituting the robot, and includes information such as the moment of inertia, mass, position, orientation, number of axes, etc. of each link. Constraints define physical constraints of the robot, and include conditions such as joint torque constraints, joint angular velocity constraints, joint angular acceleration constraints, jerk constraints, hand speed constraints, and hand acceleration constraints. These constraints may be described, for example, in the form of upper limit values (or lower limit values).

Next, in step S102, the interpolation method/teaching point information input means 32 receives the input of the teaching point information of the robot arm A. FIG. For example, the teaching point of the robot arm A is represented by the position and orientation of the hand (especially TCP) or the joint axis angle of each axis. The teaching point information is generally a sequence (list) of a plurality of teaching points, and is transmitted from another device such as the robot control device 200 in a robot system as shown in FIG. Further, when the robot control data processing device (arithmetic processing unit 3) of the present embodiment is configured by the robot control device 200, in step S102, for example, a teaching point input from the operation terminal 204 (teaching point input device (means)) information can be read. If the teaching point is position and orientation information of the hand (TCP), it can be converted into angle information of each joint axis by performing inverse kinematics calculation based on the position and orientation of the hand (TCP). Also, if the teaching point is an expression of each joint axis angle, the teaching point information can be converted into information on the position and orientation of the hand by forward kinematics calculation.

Further, in step S102, together with the teaching point information, the information about the interpolation method for moving to the teaching point is read. Information related to this interpolation method can be read from the operation unit 2 or the operation terminal 204 . Any method such as task space interpolation or joint space interpolation can be considered as the interpolation method, and the present invention is not particularly limited by which method is used.

Subsequently, in step S104, the route generating means 33 interpolates the section between the plurality of teaching points included in the teaching point information to generate route information. Here, the path is the trajectory of the joint angle of the robot arm in the joint space or the trajectory of the hand of the robot arm in the task space. In the present embodiment, "route" does not include "speed" information. In this embodiment, the "trajectory" or "trajectory data" is defined as a "path" in a work space (task space) or a joint space of a specific part of the robot, for example, a hand (TCP) or a joint, and its "path". and information of "speed" when moving ". That is, in the present embodiment, information in which a route has speed information is called a "trajectory (data)" to distinguish it from a "route" that does not have speed information.

Whether the path is generated in the joint space or the task (work) space of the robot arm A depends on the interpolation method. For example, in the case of joint interpolation, the path is interpolated in the joint space, and when the hand (TCP) is moved along a straight line or an arc, the path is interpolated in the task space.

Spline interpolation, B-Spline interpolation, Bezier curve interpolation, linear interpolation, circular interpolation, etc., can be used as a method of interpolating between teaching points. For example, the position of the path is specified by a parameter. However, if the jerk (jerk) constraint is taken into account, the path should be class ^C3 with respect to the parameters. For example, for a 4th order B-Spline curve, the path is C ³ -class for the parametric variables. In this embodiment, B-Spline interpolation is used for convenience.

After path generation (S104), the joint angle (q(s)) on the path is used to differentiate s to obtain q'(s) q''(s) q''(s). These correspond to joint angle velocity, acceleration, and jerk.

Subsequently, in step S106, the jerk saturation axis prediction means 34 estimates the joint axis at which the jerk (jerk) is saturated. Here, the joint axis where the jerk (jerk) is saturated with respect to the upper (or lower) value of the jerk constraint is defined in the vicinity of the start and end points of the path, especially in the section (specific section) including the start and end points. presume.

For example, if the upper limit of jerk (obtained in step S100) is substituted for the left side of equation (32), and s near the starting point on the path is used to solve with b, the jerk is saturated near the starting point of joint axis i. It is possible to obtain the velocity b _i when . Then, among the velocities b _i for each joint axis of the robot arm A, the lowest value is set to b _min . The joint axis that takes this b _min can be specified as the joint axis where the jerk (jerk) is saturated with respect to the upper limit near the starting point. This is because b is a scalar value obtained by consolidating the speed of the articulated robot into a one-dimensional speed, and as the speed b is increased, it first reaches b _min and saturates at the jerk upper limit of that axis. Below, the index of the joint axis at which the jerk (jerk) saturates with respect to the upper limit is assumed to be i _J . A similar calculation can be performed at the end point, and the joint axis at which the jerk (jerk) is saturated with respect to the upper limit can be specified near the end point.

Also, when the route is interpolated by B-Spline interpolation as in this embodiment, |q'''| becomes larger than |q''| and |q'| , q''' only have to be taken into account. Therefore, in this embodiment, when B-Spline interpolation is performed in path generation (S104), the terms q'' and q' are ignored, and the upper limit of jerk is substituted into the left side of equation (32), and b Solve and compare the cubic equations. Here, the intention of cubing is to eliminate the 1/3 power in the equation and simplify it. Therefore, by comparing the following equations for each axis, it can be estimated that the maximum axis is the joint axis saturated with jerk.

ただし、ｉは関節軸のインデックスとし、また、ジャークの上限と下限の値は同じとする。

However, i is the index of the joint axis, and the upper and lower limits of the jerk are the same.

As described above, by predicting the joint axis that saturates the jerk near the start and end points of the path, the numerical calculation to find the velocity of the joint axis that saturates the jerk, which will be described later, only needs to be performed for that joint axis. The computational cost can be significantly reduced.

The subsequent processing of step S108 corresponds to the jerk-equivalent speed constraint calculation means 35 (jerk calculation step). In this step S108, regarding the joint axis iJ specified by the jerk saturation axis predicting means 34 (step S106), when the jerk of that axis is saturated, the speed in a specific section including the relevant start point and end point, that is, the saturation speed is obtained. By newly adopting this speed as a speed constraint, the motion of the robot arm A can be controlled so as not to deviate from the jerk constraint in the sections near the start point and the end point. Unlike jerk (jerk), velocity can be calculated accurately even near the start and end points. Therefore, the jerk that cannot be accurately calculated near the start point and the end point can be constrained as a saturation speed corresponding to the jerk. Hereinafter, the speed constraint based on the saturated speed when the joint axis is saturated with the jerk constraint may be referred to as the jerk-equivalent speed constraint.

In step S106, the jerk saturation axis predicting means 34 ignores the terms q''(s) and q'(s) and predicts the joint axis at which the jerk saturates. However, when obtaining the jerk-equivalent speed constraint in step S108, the terms q''(s) and q'(s) are taken into account in order to perform the calculation accurately.

For the joint axis iJ obtained by the jerk saturation axis predicting means, the jerk constraint is substituted for the left side of the equation (32), and the velocity _bJ on the path at that time is obtained. In this way, the jerk-equivalent speed constraint of the joint axis iJ (which saturates at the jerk upper limit first) can be obtained near the start and end points of the path.

Here, in order to substitute the jerk constraint into the left side of equation (32) and find the velocity _bJ on the path at that time by s near the start and end points, numerical calculation is required because the equation cannot be solved analytically. Become. For example, a technique such as the Runge-Kutta method may be used to sequentially determine b _J near the start and end points of the path. Here, there are various definitions of "near" the start point and the end point. You have to calculate up to s. This is because when q' increases to a certain extent, q''' and q'' also become sufficiently large, so that the jerk calculation can be performed accurately by equation (31), and jerk This is because it becomes possible to consider

In this embodiment, the joint axis where the jerk is saturated is predicted, and then the jerk-equivalent velocity constraint (to be described later) is calculated. may be a configuration in which a strong speed constraint is adopted.

Next, in step S110, the speed constraint integration means 36 newly sets the speed _bJ on the route obtained by using the jerk-equivalent speed constraint calculation means 35 in step S108 as a constraint on the speed b on the relevant route. do.

As described in Non-Patent Document 1, joint angular velocity restrictions and hand velocity restrictions can be aggregated as restrictions on the velocity b on the route. For example, the joint angular velocity is

のように記述できる。従って、関節角速度制約に相当するｂの制約ｂ_ｑを求めるには

can be written as Therefore, to obtain the constraint _bq of b, which corresponds to the joint angular velocity constraint,

をｂ_ｑで解けばよい。

is solved by b _q .

Thus, by constraining b _q as the upper limit velocity of b, the joint angular velocity can be constrained so as to comply with the target jerk constraint. In addition, the hand speed constraint value can also be calculated by the same calculation relating to b and _bp described above.

As described above, when seeking speed constraints with different calculation methods in a specific section including the start and end points of several paths, such as joint angular velocity constraints, hand speed constraints, or jerk-equivalent speed constraints, step At S110, these speed constraints are integrated. For this integration of speed constraints, for example, setting the lowest speed value among b _q , b _p , and b _J as a constraint on b can be considered. Since these are both functions of s, the smallest value within the range of possible values of s can be newly set as the speed constraint value of b. If a set speed constraint value already exists, the set speed constraint value is compared with the saturated speed, and the smaller value of the saturated speed or the speed constraint value is determined. is adopted as the speed constraint value.

Subsequently, in step S112, the speed optimization means 37 optimizes the speed b on the route. Here, the robot model input (S100) by the model/restriction information input means 31 follows a path generated by the path generation means 33 while observing various input restrictions. Optimize the velocity b above. For this purpose, for example, the optimization problem can be solved by considering constraints other than the torque constraint in the equations (22) to (30). However, the joint angular velocity constraint, the hand velocity constraint, and the jerk equivalent velocity constraint have already been integrated in step S110. As a method for solving this optimization problem, a method is conceivable in which the log-barrier method and the Newton method are used to quickly converge to the optimum solution.

The above steps S110 and S112 (speed constraint integration means 36, speed optimization means 37) set the saturation speed as the speed constraint value of the trajectory data, and then set the specific portion between the start point and the end point under specific conditions. corresponds to a speed information generating step of generating speed information for moving the .

Furthermore, in step S114, the joint angle command value generating means 38 calculates s(t) based on s(·)(s) calculated by speed optimization (S112) as in the following equation (37), and q (s) is obtained, and, for example, a joint angle command value is obtained for each fixed time Δt. However, s(0)=0. As a matter of course, this fixed time Δt is the clock cycle for the robot control device to transmit the joint angle command to the robot arm A, for example.

In this way, the trajectory data of the robot arm A is used as trajectory data for moving the specific portion (TCP or joint in the joint space) of the robot arm A along the path at a speed that satisfies the jerk constraint in a specific section including the start point and the end point. A joint angle command can be generated. By transmitting the trajectory data generated as this joint angle command value (group) to the robot arm A (or its robot controller 200), the robot arm A can be operated along the trajectory. Although the trajectory data is generated in the form of joint angle command values in step S114, the trajectory data may be of any format, and other data suitable for controlling the robot arm A (or its robot controller 200) may be used. It goes without saying that a form may be used.

As described above, according to the present embodiment, after the route information is created from the start point and the end point, based on the saturation speed corresponding to the jerk constraint in the specific section including the start point and the end point, it acts as a jerk-equivalent speed constraint. to generate speed information for the route. In this case, the saturated speed corresponding to the jerk constraint in a specific section including the start point and the end point of the route is obtained and acted as the jerk-equivalent speed constraint to be used as the speed information of the route. Thus, it is possible to generate trajectory data including a route designated by the teaching points of the start point and the end point and velocity information on the route. In that case, according to the present embodiment, it is possible to generate optimal trajectory data that can perform speed control while restricting jerk (jerk) from being saturated at the start and end points of the route.

Although the configuration of one embodiment of the present invention has been described in detail above, the configuration described above is merely an example and is not intended to limit the present invention to that configuration. It goes without saying that the technology described in the claims includes various modifications and changes of the specific examples illustrated above. The present invention supplies a program that implements one or more functions of the above-described embodiments to a system or device via a network or a storage medium, and one or more processors in the computer of the system or device read and execute the program. processing is also feasible. It can also be implemented by a circuit (for example, ASIC) that implements one or more functions.

A: Robot arm J1, J2: Joint axis 1: Trajectory generation device 2: Operation unit 3: Calculation processing unit 31: Model/restriction information input means 32: Teaching point information input means 33: Path generation Means 34 Jerk saturation axis predicting means 35 Jerk equivalent velocity constraint calculating means 36 Velocity constraint integrating means 37 Velocity optimizing means 38 Joint angle command value generating means 4 Storage unit.

Claims (25)

An information processing method in which a processing unit acquires a target trajectory including a path of a predetermined part and a speed of the joint when moving the predetermined part of a robot having joints,
The processing unit is
Based on a first constraint value relating to the upper limit of the jerk at the joint when moving the predetermined part using the robot at a first position and/or a second position through which the predetermined part passes on the target trajectory , Acquiring the speed of the joint as a constraint speed when the joint is operated with the jerk set to the first constraint value,
Obtaining a route by interpolating between the first position and the second position where the predetermined part moves,
Acquiring the speed of the joint when moving the predetermined part on the route with the constraint speed as a second constraint value;
An information processing method characterized by: In the information processing method according to claim 1,
The target trajectory includes the speed of the predetermined part when moving the predetermined part,
An information processing method characterized by: In the information processing method according to claim 1 or 2,
The interpolation process is a process of executing at least one of Splin interpolation, B-Splin interpolation, Bezier curve interpolation, linear interpolation, and circular interpolation.
An information processing method characterized by: In the information processing method according to any one of claims 1 to 3,
The first position is a starting point for movement of the predetermined portion, and the second position is an end point for movement of the predetermined portion.
An information processing method characterized by: In the information processing method according to any one of claims 1 to 4 ,
The processing unit is
At the joint when the first constraint value is set when the robot is used to move the predetermined part in the first section including the first position and/or the second section including the second position obtaining as the constraint speed the speed at which
An information processing method characterized by: In the information processing method according to claim 5 ,
The processing unit is
obtaining the constraint speed using the first constraint value and a first parameter in the first section and/or a second parameter in the second section;
An information processing method characterized by: In the information processing method according to claim 6 ,
a plurality of said joints exist,
The processing unit is
obtaining the restricted velocity using the first restricted value, the first parameter, and the second parameter at the plurality of joints;
obtaining the lowest speed among the constraint speeds obtained at the plurality of joints as the second constraint value;
An information processing method characterized by: In the information processing method according to any one of claims 1 to 7 ,
The first constraint value is obtained by at least one of a joint torque constraint, a joint angular velocity constraint, a joint angular acceleration constraint, a jerk constraint, a hand velocity constraint, and a hand acceleration constraint.
An information processing method characterized by: In the information processing method according to claim 2,
The velocity of the predetermined part is the velocity in the working space of the predetermined part, and the velocity of the joint is the velocity in the joint space of the joint,
An information processing method characterized by: In the information processing method according to claim 9 ,
The target trajectory includes a path in the joint space of the motion of the joint when moving the predetermined part,
An information processing method characterized by: A program that causes the processing unit to execute the information processing method according to any one of claims 1 to 10 . A computer-readable recording medium storing the program according to claim 11 . An information processing device that acquires a target trajectory including a path of a predetermined part and a speed of the joint when moving the predetermined part of a robot having joints ,
Based on a first constraint value relating to the upper limit of the jerk at the joint when moving the predetermined part using the robot at a first position and/or a second position through which the predetermined part passes on the target trajectory , Acquiring, as a constraint speed , the speed of the joint when the joint is operated with the jerk set to the first constraint value ;
Obtaining a route by interpolating between the first position and the second position where the predetermined part moves,
Acquiring the speed of the joint when moving the predetermined part on the route with the constraint speed as a second constraint value;
An information processing device characterized by: In the information processing device according to claim 1-3 ,
The target trajectory includes the speed of the predetermined part when moving the predetermined part,
An information processing device characterized by: In the information processing device according to claim 1-3 or 1-4 ,
The interpolation process is a process of executing at least one of Splin interpolation, B-Splin interpolation, Bezier curve interpolation, linear interpolation, and circular interpolation.
An information processing device characterized by: In the information processing apparatus according to any one of claims 1-3 to 1-5 ,
The first position is a starting point for movement of the predetermined portion, and the second position is an end point for movement of the predetermined portion.
An information processing device characterized by: In the information processing apparatus according to any one of claims 13 to 16 ,
At the joint when the first constraint value is set when the robot is used to move the predetermined part in the first section including the first position and/or the second section including the second position obtaining as the constraint speed the speed at which
An information processing device characterized by: In the information processing device according to claim 1 to 7 ,
obtaining the constraint speed using the first constraint value and a first parameter in the first section and/or a second parameter in the second section;
An information processing device characterized by: In the information processing device according to claim 18 ,
a plurality of said joints exist,
obtaining the restricted velocity using the first restricted value, the first parameter, and the second parameter at the plurality of joints;
obtaining the lowest speed among the constraint speeds obtained at the plurality of joints as the second constraint value;
An information processing device characterized by: In the information processing device according to any one of claims 13 to 19 ,
The first constraint value is obtained by at least one of a joint torque constraint, a joint angular velocity constraint, a joint angular acceleration constraint, a jerk constraint, a hand velocity constraint, and a hand acceleration constraint.
An information processing device characterized by: In the information processing device according to claim 14 ,
The velocity of the predetermined part is the velocity in the working space of the predetermined part, and the velocity of the joint is the velocity in the joint space of the joint,
An information processing device characterized by: In the information processing device according to claim 21 ,
The target trajectory includes a path in the joint space of the motion of the joint when moving the predetermined part,
An information processing device characterized by: A robot system comprising the robot for which a target trajectory is set using the information processing device according to any one of claims 1-3 to 2-2 . 24. The robot system according to claim 23 , further comprising a network for transmitting the target trajectory to said robot. A method of manufacturing an article, comprising manufacturing an article using the robot system according to claim 23 or 24 .

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