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This section mainly explains linear interpolation through several parts, including an introduction to EtherCAT bus motion controllers, the principles, functions, and implementation methods of linear interpolation in motion controllers, as well as simulation demonstrations of examples.

01Introduction to XPLC864E2

The XPLC864E2 is a multi-axis economical EtherCAT bus motion controller launched by Zheng Motion Technology. The XPLC series motion controllers can be applied in various scenarios requiring offline or online operation.

It is compact, fully equipped with communication functions, supports RS232 serial port, RS485 serial port, Ethernet, CAN bus, and EtherCAT bus connections to peripherals, with multiple network ports expanded through switches.

The XPLC864E2 supports mixed use of pulse axes and bus axes, with a total of 8 axes. In addition to the EtherCAT interface, the output ports can be configured for 8 pulse signal outputs, and there are two encoder inputs configurable from the input ports.

It supports up to 12 axes for linear interpolation, electronic cam, electronic gear, synchronous following, virtual axis settings, and other functions through expansion.

02Principle of Linear Interpolation

The linear interpolation algorithm uses a data sampling method, approximating the given trajectory with small segments of straight lines. The interpolation output is the distance each axis needs to move in the next interpolation cycle, allowing for high feed rates without needing to interpolate for every pulse equivalent.

The data sampling method principle employs a time division concept, dividing the contour curve into segments of contour step length l, where l=ft, based on the feed speed f and interpolation period t, and then calculating the coordinate increments for each axis participating in the interpolation motion for each interpolation cycle.

03Linear Interpolation Functionality

1. Characteristics of Linear Interpolation

Linear interpolation motion is controlled by selecting axis numbers/axis groups through the BASE command, enabling multi-axis linkage to complete linear motion.

The main axis is the first axis selected by BASE, and the interpolation motion axis parameters such as UNITS, SPEED, etc., all adopt the parameters of the main axis. The MOVE command sends the linear interpolation motion instruction, and the interpolation motion is executed sequentially in the motion buffer of the main axis. The CANCEL command can cancel the interpolation motion, achieving an emergency stop.

1. Supports linear interpolation motion for 16 axes

base(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)

2. Supports simultaneous interpolation across multiple channels

BASE(0,1)MOVE(100,200)BASE(2,3,4)MOVE(30,40,50)

2. Calculation of Interpolation Motion Parameters

Taking two-axis linear interpolation as an example: Axes 0 and 1 participate in the linear interpolation motion, as shown in the figure below.

The two-axis linear interpolation motion moves from point A on the plane to point B, with the XY axes starting simultaneously and reaching the endpoint at the same time. The motion distance for axis 0 is set to ∆X, and for axis 1, it is ∆Y, with the main axis being the first axis of BASE (in this case, the main axis is axis 0), and the interpolation motion parameters adopting those of the main axis.

If the speed of the main axis is S (the set speed of main axis 0), the actual speeds of each axis are the sub-speeds of the main axis, which are not equal to S. At this time:

• Distance of interpolation motion: X=[(∆X)²+(∆Y)²]½
• Actual speed of axis 0: S0=S×∆X/X
• Actual speed of axis 1: S1=S×∆Y/X

04Implementation of Linear InterpolationThe XPLC864E2 has a built-in linear interpolation algorithm that supports joint linear interpolation for 8 EtherCAT bus axes and can be expanded to support 12 axes of interpolation. By using the MOVE linear interpolation command, interpolation motion can be easily and efficiently completed.

1. Commands Related to Linear Interpolation

1. MOVE sends pulses to the driver to achieve linear interpolation motion.

Syntax:

• MOVE(distance1 [,distance2[,distance3 [,distance4…]]])

• MOVEABS(distance1 [,distance2 [,distance3 [,distance4…]]])

• MOVESP(distance1 [,distance2 [,distance3 [,distance4…]]])

• MOVEABSSP(distance1 [,distance2 [,distance3 [,distance4…]]])

2. The BASE command selects the axis numbers participating in the interpolation, i.e., which axes the MOVE motion is sent to.

Syntax:BASE(axis1 [,axis 2 [,axis 3 [,axis 4…]]])

3. The speed of linear interpolation motion can be freely controlled by the speed ratio, where the current speed = SPEED*SPEED_RATIO.

Syntax:SPEED_RATIO(axis number) = value

4. Motion pause and resume, MOVE_PAUSE pauses, MOVE_RESUME resumes motion.

Syntax:MOVE_PAUSE(mode)

5. Motion cancellation, axes/axis groups decelerate and stop, CANCEL(2) is an emergency stop, RAPIDSTOP(2) is an emergency stop for all axes.

Syntax:CANCEL(mode) AXIS(main axis), RAPIDSTOP(mode)

2. Types of Linear Interpolation

1. There are three forms of linear interpolation to choose from:

(1) MOVE relative motion command The distance parameter for interpolation motion is the relative distance from the current interpolation starting point, using SPEED for speed.(2) MOVEABS absolute motion command The distance parameter for interpolation motion is the absolute distance from the origin, adding the ABS suffix after the relative motion command, using SPEED for speed.(3) MOVESP/MOVEABSSP motion command The commands with SP use the FORCE_SPEED parameter for motion speed instead of the SPEED parameter, simply adding the SP suffix after the relative or absolute motion command. The FORCE_SPEED parameter can enter the motion buffer, facilitating dynamic speed changes.2. The differences among the three types of motion forms are explained in the examples below:(1) Relative motion example

RAPIDSTOP(2)WAIT IDLE(0)WAIT IDLE(1)BASE(0,1)DPOS=0,0ATYPE=1,1UNITS=100,100SPEED=100,100        'Motion speedACCEL=1000,1000DECEL=1000,1000FORCE_SPEED=150,150  'SP command speedSRAMP=100,100        'S curveTRIGGER              'Auto trigger oscilloscopeMOVE(200,150)        'First segment endpoint(200,150)MOVE(100,120)        'Second segment endpoint(300,270)END

(2) Absolute motion example

RAPIDSTOP(2)WAIT IDLE(0)WAIT IDLE(1)BASE(0,1)DPOS=0,0ATYPE=1,1UNITS=100,100SPEED=100,100     'Motion speedACCEL=1000,1000DECEL=1000,1000SRAMP=100,100     'S curveTRIGGER           'Auto trigger oscilloscopeMOVEABS(200,150)  'First segmentMOVEABS(100,120)  'Second segment to absolute position(100,120)END

(3) SP motion command example

RAPIDSTOP(2)WAIT IDLE(0)WAIT IDLE(1)BASE(0,1)DPOS=0,0ATYPE=1,1UNITS=100,100SPEED=100,100         'Motion speedACCEL=1000,1000DECEL=1000,1000FORCE_SPEED=150,150   'SP command speedSRAMP=100,100         'S curveTRIGGER               'Auto trigger oscilloscopeMOVE(200,150)         'First segment relative motion, speed 100MOVESP(100,120)       'Second segment SP relative motion, speed 150END

3. MOVESP Dynamic Speed Change

The MOVESP linear interpolation motion uses the speed set by FORCE_SPEED for motion and supports STARTMOVE_SPEED to customize the starting speed for each segment of SP motion, and ENDMOVE_SPEED to customize the ending speed for each segment of SP motion. If these two parameters are not used, please set them to a large value.

Example:

RAPIDSTOP(2)WAIT IDLE(0)WAIT IDLE(1)BASE(0,1)        'Select XYDPOS = 0,0MPOS = 0,0ATYPE=1,1        'Pulse mode step or servoUNITS = 100,100  'Pulse equivalentSPEED = 100,100ACCEL = 200,200DECEL = 200,200SRAMP=100,100    'S curveTRIGGER'First segmentFORCE_SPEED = 50 'First segment speed 50MOVESP(40,40)'Second segmentFORCE_SPEED = 60 'Second segment speed 60MOVESP(50,50)'Third segmentFORCE_SPEED = 80 'Third segment speed 80MOVESP(60,60)END

Speed change curve: Starting from a speed of 0, completing three segments of linear interpolation motion, with the first segment speed of 50, the second segment speed of 60, and the third segment speed of 80.

4. Speed Ratio Control of Linear Interpolation

Linear interpolation motion supports setting the SPEED_RATIO to control the proportion of the current motion speed, making the current motion speed = SPEED * SPEED_RATIO. The command takes effect immediately, thus enabling dynamic speed changes.

Example:

RAPIDSTOP(2)WAIT IDLEBASE(0,1)              'Select axes 0, 1DPOS=0,0UNITS=1000,1000SPEED = 100,100        'Speed 100 units/sACCEL = 1000,1000DECEL = 1000,1000SRAMP = 50,50TRIGGERSPEED_RATIO = 1        'Speed ratio is 1, speed 100MOVE(100,120)          'Linear interpolationDELAY(500)             'Wait 0.5sSPEED_RATIO = 2        'Speed 200WAIT UNTIL REMAIN<50   'Wait until remaining distance is less than 50SPEED_RATIO = 0.5      'Speed reduced to 50WAIT IDLESPEED_RATIO=1END

Speed change curve:

5. Pausing and Resuming Linear Interpolation Motion

The MOVE_PAUSE command is suitable for interpolation motion and has several modes:

0 (default)	Pause the current motion.
1	Pause after the current motion is completed and before executing the next motion instruction
2	Pause after the current motion is completed and before executing the next motion instruction, and the MARK identifiers of the two instructions are different
3	Forced pause, can enter pause state even in IDLE mode This function was added in firmware version 20170513

Example:

BASE(0,1)               'Select axes 0, 1DPOS=0,0UNITS=1000,1000SPEED = 100,100         'Speed 100 units/sACCEL = 1000,1000DECEL = 1000,1000SRAMP = 50,50TRIGGERMOVE(100,100)          'Current motionMOVE(50,50)            'Buffered motionMOVE_PAUSE(1)          'Mode 1, pause after current motion is completed  DELAY(2000)MOVE_RESUME            'Resume motion, buffered motion starts executingEND

The motion curve is shown in the figure below:

05Linear Interpolation Example1. Continuous Interpolation of Two Axes to Complete a Star Trajectory

'Bus initialization enables EtherCAT bus drivers, pulse-type drivers OP open enable. BASE(0,1)UNITS=10000,10000SPEED=100,100ACCEL=1000,1000DECEL=1000,1000SRAMP=100,100DPOS=0,0MPOS=0,0TRIGGER           'Auto trigger oscilloscope'Star trajectoryMOVEABS(1.4695, 1.0676)MOVEABS(2.9389, 0.0000)MOVEABS(2.3776, 1.7275)MOVEABS(3.8471, 2.7951)MOVEABS(2.0307, 2.7951)MOVEABS(1.4695, 4.5225)MOVEABS(0.9082, 2.7951)MOVEABS(-0.9082, 2.7951)MOVEABS(0.5613, 1.7275)MOVEABS(0.0000, 0.0000)END

Oscilloscope sampling of motion waveform over time:

Oscilloscope sampling of two-axis interpolation trajectory:

2. Star Video Demonstration

This concludes the discussion on the easy-to-use linear interpolation in EtherCAT bus motion controllers by Zheng Motion Technology.

For more exciting content, please follow the “Motion Assistant” public account. For related development environments and example codes, please consult Zheng Motion Technology sales engineers: 400-089-8936.

This article is original by Zheng Motion Technology. Everyone is welcome to reprint it for mutual learning and improvement of China’s intelligent manufacturing level. The copyright of this article belongs to Zheng Motion Technology. Please indicate the source when reprinting.

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About Zheng Motion Technology

Zheng Motion Technology focuses on research in motion control technology and the development of general motion control software and hardware products, and is a national high-tech enterprise. Its main products include motion controllers, motion control cards, visual motion control integrated machines, human-machine interfaces, and expansion modules.

Zheng Motion Technology gathers outstanding talents from companies like Huawei and ZTE, actively collaborating with major universities to research the foundational technologies of motion control while adhering to independent innovation. It is one of the fastest-growing companies in the domestic industrial control field and one of the few companies that fully master core motion control technologies and real-time industrial control software platform technologies.

Backed by the thriving manufacturing industry, Zheng Motion Technology keeps pace with the times, is innovative, and is committed to continuously improving the technical applications and manufacturing levels of intelligent manufacturing equipment suppliers and end users. After years of application development with numerous partners, its products are widely used in domestic and international fields such as 3C electronics, semiconductors, printing and packaging, textiles and garments, laser processing, mechanical processing, robotics, new energy, healthcare, and stage entertainment.