1. SPiiPlus Training Class
Motion Profile Generation

2. What is Motion Profile Generation?
Motion profile generation is the process by which the controller takes a high level command and creates a finely sampled motion profile
At a minimum the controller will calculate a new position every update cycle
Advanced controllers will also calculate velocity, acceleration, and jerk (acceleration/sec)
High level command can be streamed by a host or executed directly by the motion controller
Many different algorithms can be used to generate the motion profile / trajectory
Motion profile / trajectory can be for a single or multi-axis move

3. Sampled Motion Trajectory
Position
Time

4. Motion Generation: SPiiPlus
Master
Formula
ECAT
Position
(MPOS)
Motion Generator
Axis Position (APOS)
CONNECT formula
Reference Position (RPOS)
Convert units to counts (EFAC)
Convert counts to units (EFAC)
Feedback Position (FPOS)
User Commands / External Signals
Feedback
Drive Command
MPU

5. Important ACSPL+ Motion Variables
VEL: Commanded Velocity
Motor commanded velocity in user units / second
This is the maximum velocity of the motion profile
ACC: Commanded Acceleration
Motor commanded acceleration in user units / second2
This is the maximum acceleration of the motion profile
DEC: Commanded Deceleration
Motor commanded deceleration in user units / second2
This is the maximum deceleration of the motion profile
JERK: Commanded Jerk
Motor commanded jerk in user units / second3
This is the maximum jerk of the motion profile
KDEC: Kill Deceleration
Used for the KILL command only

6. Important ACSPL+ Motion Variables
APOS: Axis Position
Logical axis position in user-defined units
Calculated directly from motion generator every MPU cycle
Comes before the CONNECT function
RPOS: Reference Position
Motor commanded position in user-defined units
Calculated via the CONNECT function every MPU cycle
Sent to servo processor servo loop every MPU cycle
Typically RPOS = APOS
FPOS: Feedback Position
Sensor feedback position in user-defined units
Read from servo processor every MPU cycle
PE: Position Error
Difference between RPOS and FPOS
Updated every MPU cycle

7. Important ACSPL+ Motion Variables
EFAC: Encoder Factor
Used to translate between encoder counts on the servo processor and user-defined units on the MPU
EOFFS: Encoder Offset
Offset between zero position on the servo processor and zero position on the MPU
Updated whenever RPOS or FPOS is SET (homed).
FPOS=𝐹𝑃∙EFAC+EOFFS
𝑅𝑃= RPOS−EOFFS EFAC
Note: FP is feedback position stored in the Servo Processor
RP is the reference position stored in the Servo Processor

8. Important ACSPL+ Motion Variables
RVEL: Reference Velocity
Motor commanded velocity in user units / second
Calculated as the first difference of RPOS, with optional smoothing, every MPU cycle
FVEL: Feedback Velocity
Sensor feedback velocity in user units / second
Calculated as first difference of FPOS, with optional smoothing, every MPU cycle
Δ 𝑅 = RPOS 𝑛 − RPOS 𝑛−1 𝑇
RVEL 𝑛 = Δ 𝑅 ∙ 1− RVFIL RVEL 𝑛−1 ∙ RVFIL 100
Δ 𝐹 = FPOS 𝑛 − FPOS 𝑛−1 𝑇
FVEL 𝑛 = Δ 𝐹 ∙ 1− FVFIL FVEL 𝑛−1 ∙ FVFIL 100

9. Important ACSPL+ Motion Variables
RACC: Reference Acceleration
Motor commanded acceleration in user units / second2
Calculated as the first difference of RVEL every MPU cycle
FACC: Feedback Acceleration
Sensor feedback acceleration in user units / second2
Calculated as the first difference of FVEL every MPU cycle
RACC 𝑛 = RVEL 𝑛 − RVEL 𝑛−1 𝑇
FACC 𝑛 = FVEL 𝑛 − FVEL 𝑛−1 𝑇

10. Important ACSPL+ Motion Variables
GPHASE: Group Motion Phase
Integer value for current motion phase
0: no motion
1: acceleration buildup
2: constant acceleration
3: acceleration finishing
4: constant velocity
5: deceleration buildup
6: constant deceleration
7: deceleration finishing
GRTIME: Group Remaining Motion Time
Estimated value of time (in milliseconds) until end of current motion

11. Important ACSPL+ Motion Variables
MST: Motor State
Bitwise encoded physical motor state information
Bit 0: Enabled
Bit 1: Open Loop
Bit 5: In motion
Bit 6: Accelerating
AST: Axis State
Bitwise encoded logical axis state information
Bit 2: PEG is in progress
Bit 3: Data collection is in progress

12. Move vs. Move and Settle
Move time: time it takes for commanded motion to finish Move and settle time: time it takes for commanded motion to finish AND physical axis to settle within a specified window

13. Trajectory Algorithms

14. Step Profile: Basics Step Profile: Comments:
Instantaneous change in position
Infinite velocity
Infinite acceleration
Infinite jerk
Comments:
Not realistic
Should never be used in real motion systems

15. Step Profile: Equations
𝒙 𝒕 = 𝟎 𝑿 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕 𝒗 𝒕 = 𝟎 ∞ 𝟎 𝒕< 𝒕 𝟎 𝒕= 𝒕 𝟎 𝒕 𝟎 <𝒕 𝒂 𝒕 = 𝟎 ±∞ 𝟎 𝒕< 𝒕 𝟎 𝒕= 𝒕 𝟎 𝒕 𝟎 <𝒕 𝒋 𝒕 = 𝟎 ±∞ 𝟎 𝒕< 𝒕 𝟎 𝒕= 𝒕 𝟎 𝒕 𝟎 <𝒕

16. Step Profile: ACSPL+ Example
Should not be run on real systems!

17. 1st Order Profile: Basics
Linear position profile
Instantaneous change in velocity
Infinite acceleration
Infinite jerk
Comments:
Not realistic
Should never be used in real motion systems

18. 1st Order Profile: Equations
𝒙 𝒕 = 𝟎 𝑽 ∙(𝒕− 𝒕 𝟎 ) 𝑿 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕< 𝒕 𝟏 𝒕 𝟏 ≤𝒕
𝒗 𝒕 = 𝟎 𝑽 𝟎 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕< 𝒕 𝟏 𝒕 𝟏 ≤𝒕
𝒂 𝒕 = 𝟎 ∞ 𝟎 −∞ 𝟎 𝒕< 𝒕 𝟎 𝒕= 𝒕 𝟎 𝒕 𝟎 <𝒕< 𝒕 𝟏 𝒕= 𝒕 𝟏 𝒕 𝟏 <𝒕
𝒋 𝒕 = 𝟎 ±∞ 𝟎 ±∞ 𝟎 𝒕< 𝒕 𝟎 𝒕= 𝒕 𝟎 𝒕 𝟎 <𝒕< 𝒕 𝟏 𝒕= 𝒕 𝟏 𝒕 𝟏 <𝒕

19. 1st Order Profile: ACSPL+ Example
Should not be run on real systems!

20. 2nd Order Profile: Basics
Quadratic position profile
Linear velocity profile
Instantaneous change in acceleration
Infinite jerk
Comments:
Not realistic
Simple controllers use this type of interpolation
Results in ‘jerky’ behavior of motion systems

21. 2nd Order Profile: Equations
𝑿 𝟏 = 𝟏 𝟐 ∙ 𝑨 ∙ 𝒕 𝟏 − 𝒕 𝟎 𝟐
𝑿 𝟐 = 𝑿 𝟏 + 𝑽 ∙( 𝒕 𝟐 − 𝒕 𝟏 )
𝒙 𝒕 = 𝟎 𝟎.𝟓∙ 𝑨 ∙ (𝒕− 𝒕 𝟎 ) 𝟐 𝑿 𝟏 + 𝑽 ∙(𝒕− 𝒕 𝟏 ) 𝑿 𝟐 + 𝑽 ∙ 𝒕− 𝒕 𝟐 −𝟎.𝟓∙ 𝑨 ∙ (𝒕− 𝒕 𝟐 ) 𝟐 𝑿 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕< 𝒕 𝟏 𝒕 𝟏 ≤𝒕< 𝒕 𝟐 𝒕 𝟐 ≤𝒕< 𝒕 𝟑 𝒕 𝟑 ≤𝒕
𝒗 𝒕 = 𝟎 𝑨 ∙(𝒕− 𝒕 𝟎 ) 𝑽 𝑽 − 𝑨 ∙(𝒕− 𝒕 𝟐 ) 𝟎 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕< 𝒕 𝟏 𝒕 𝟏 ≤𝒕< 𝒕 𝟐 𝒕 𝟐 ≤𝒕< 𝒕 𝟑 𝒕 𝟑 ≤𝒕
𝒂 𝒕 = 𝟎 𝑨 𝟎 − 𝑨 𝟎 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕< 𝒕 𝟏 𝒕 𝟏 ≤𝒕< 𝒕 𝟐 𝒕 𝟐 ≤𝒕< 𝒕 𝟑 𝒕 𝟑 ≤𝒕 𝒋 𝒕 = 𝟎 ∞ 𝟎 −∞ 𝟎 −∞ 𝟎 ∞ 𝟎 𝒕< 𝒕 𝟎 𝒕= 𝒕 𝟎 𝒕 𝟎 <𝒕< 𝒕 𝟏 𝒕= 𝒕 𝟏 𝒕 𝟏 <𝒕< 𝒕 𝟐 𝒕= 𝒕 𝟐 𝒕 𝟐 <𝒕< 𝒕 𝟑 𝒕= 𝒕 𝟑 𝒕 𝟑 <𝒕

22. 2nd Order Profile: ACSPL+ Example
Not ideal for real systems

23. 3rd Order Profile: Basics
Cubic position profile
Quadratic velocity profile
Linear acceleration profile
Instantaneous change in jerk
Comments:
Realistic
Results in smooth motion
Complex profile
Requires appropriate jerk setting

24. 3rd Order Profile: Equations
𝒙 𝒕 = 𝟎 𝟎.𝟏𝟔𝟔𝟕∙ 𝑱 ∙ (𝒕− 𝒕 𝟎 ) 𝟑 𝑿 𝟏 + 𝑽 𝟏 ∙ 𝒕− 𝒕 𝟏 +𝟎.𝟓∙ 𝑨 ∙ (𝒕− 𝒕 𝟏 ) 𝟐 𝑿 𝟐 + 𝑽 𝟐 ∙ 𝒕− 𝒕 𝟐 +𝟎.𝟓∙ 𝑨 ∙ 𝒕− 𝒕 𝟐 𝟐 −𝟎.𝟏𝟔𝟔𝟕∙ 𝑱 ∙ (𝒕− 𝒕 𝟐 ) 𝟑 𝑿 𝟑 + 𝑽 ∙ 𝒕− 𝒕 𝟑 𝑿 𝟒 + 𝑽 ∙ 𝒕− 𝒕 𝟒 −𝟎.𝟏𝟔𝟔𝟕∙ 𝑱 ∙ (𝒕− 𝒕 𝟒 ) 𝟑 𝑿 𝟓 + 𝑽 𝟑 ∙ 𝒕− 𝒕 𝟓 −𝟎.𝟓∙ 𝑨 ∙ (𝒕− 𝒕 𝟓 ) 𝟐 𝑿 𝟔 + 𝑽 𝟒 ∙ 𝒕− 𝒕 𝟔 −𝟎.𝟓∙ 𝑨 ∙ 𝒕− 𝒕 𝟔 𝟐 +𝟎.𝟏𝟔𝟔𝟕∙ 𝑱 ∙ (𝒕− 𝒕 𝟔 ) 𝟑 𝑿 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕≤ 𝒕 𝟏 𝒕 𝟏 ≤𝒕≤ 𝒕 𝟐 𝒕 𝟐 ≤𝒕≤ 𝒕 𝟑 𝒕 𝟑 ≤𝒕≤ 𝒕 𝟒 𝒕 𝟒 ≤𝒕≤ 𝒕 𝟓 𝒕 𝟓 ≤𝒕≤ 𝒕 𝟔 𝒕 𝟔 ≤𝒕≤ 𝒕 𝟕 𝒕> 𝒕 𝟕
𝒗 𝒕 = 𝟎 𝟎.𝟓∙ 𝑱 ∙ (𝒕− 𝒕 𝟎 ) 𝟐 𝑽 𝟏 + 𝑨 ∙ 𝒕− 𝒕 𝟏 𝑽 𝟐 + 𝑨 ∙ 𝒕− 𝒕 𝟐 −𝟎.𝟓∙ 𝑱 ∙ (𝒕− 𝒕 𝟐 ) 𝟐 𝑽 𝑽 −𝟎.𝟓∙ 𝑱 ∙ (𝒕− 𝒕 𝟒 ) 𝟐 𝑽 𝟑 − 𝑨 ∙ 𝒕− 𝒕 𝟓 𝑽 𝟒 − 𝑨 ∙ 𝒕− 𝒕 𝟔 +𝟎.𝟓∙ 𝑱 ∙ (𝒕− 𝒕 𝟔 ) 𝟐 𝟎 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕≤ 𝒕 𝟏 𝒕 𝟏 ≤𝒕≤ 𝒕 𝟐 𝒕 𝟐 ≤𝒕≤ 𝒕 𝟑 𝒕 𝟑 ≤𝒕≤ 𝒕 𝟒 𝒕 𝟒 ≤𝒕≤ 𝒕 𝟓 𝒕 𝟓 ≤𝒕≤ 𝒕 𝟔 𝒕 𝟔 ≤𝒕≤ 𝒕 𝟕 𝒕> 𝒕 𝟕

25. 3rd Order Profile: Equations
𝒂 𝒕 = 𝟎 𝑱 ∙(𝒕− 𝒕 𝟎 ) 𝑨 𝑨 − 𝑱 ∙(𝒕− 𝒕 𝟐 ) 𝟎 − 𝑱 ∙(𝒕− 𝒕 𝟒 ) − 𝑨 − 𝑨 + 𝑱 ∙(𝒕− 𝒕 𝟔 ) 𝟎 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕≤ 𝒕 𝟏 𝒕 𝟏 ≤𝒕≤ 𝒕 𝟐 𝒕 𝟐 ≤𝒕≤ 𝒕 𝟑 𝒕 𝟑 ≤𝒕≤ 𝒕 𝟒 𝒕 𝟒 ≤𝒕≤ 𝒕 𝟓 𝒕 𝟓 ≤𝒕≤ 𝒕 𝟔 𝒕 𝟔 ≤𝒕≤ 𝒕 𝟕 𝒕> 𝒕 𝟕
𝒋 𝒕 = 𝟎 𝑱 𝟎 − 𝑱 𝟎 − 𝑱 𝟎 𝑱 𝟎 𝒕< 𝒕 𝟎 𝒕 𝟎 ≤𝒕≤ 𝒕 𝟏 𝒕 𝟏 ≤𝒕≤ 𝒕 𝟐 𝒕 𝟐 ≤𝒕≤ 𝒕 𝟑 𝒕 𝟑 ≤𝒕≤ 𝒕 𝟒 𝒕 𝟒 ≤𝒕≤ 𝒕 𝟓 𝒕 𝟓 ≤𝒕≤ 𝒕 𝟔 𝒕 𝟔 ≤𝒕≤ 𝒕 𝟕 𝒕> 𝒕 𝟕

26. 3rd Order Profile: ACSPL+ Example

27. Jogging: Basics Jogging: Accelerating to constant velocity
No defined end-point
Can be done with 1st order, 2nd order or 3rd order profiles

28. Jogging: ACSPL+ Example

29. CAM Motion: Basics CAM Motion:
Multi-axis motion along a continuous path 2 or 3 dimensional space
Can involved more than 3 axes
Common in CAD/CAM applications where motion profile is a tool path created from a CAD file
Typically composed of arc and line segments

30. CAM Motion: Equations Line Segment: Arc Segment:
Constant linear velocity along an n-dimensional path
Requires knowledge of start point, end point, and velocity
𝒙 = 𝒗 ∙𝒕
Arc Segment:
Constant angular velocity along circumference of a circle
Confined to 2D plane
Requires knowledge of start point, center point or end point (or equivalent)
𝒙=𝒓∙ 𝐜𝐨𝐬 𝝎∙𝒕+𝝋 𝒚=𝒓∙ 𝐬𝐢𝐧 𝝎∙𝒕+𝝋

31. CAM Motion: ACSPL+ Example

32. Master / Slave: Basics Master / Slave Motion:
Axis is slaved to a master signal
Master signal could be an encoder, virtual axis, analog input, etc
Slave is moved to track the masters position (position lock) or velocity (velocity lock) as best as possible without exceeding its maximum velocity or acceleration
There will always be a delay between the master and slave
Common in applications where the master signal has unknown dynamics or controlled externally

33. Master / Slave: ACSPL+ Example

34. Spline: Basics Spline: Catmull-Rom: B-Spline:
Smooth piece-wise polynomial function
Used for interpolating in between data points to any degree of interpolation
Different types of splines have different properties
Catmull-Rom:
Guarantees motion through control points
Guarantees continuous position and velocity profiles (does not guarantee continuous acceleration profile)
B-Spline:
Does not guarantee motion through control points
Guarantees continuous position, velocity and acceleration profiles

35. Spline: PVT Motion PVT Motion:
User provides position, velocity, and time points
Motion generator interpolates between time points to determine position at each controller cycle
Acceleration is implicitly defined by the PVT points

36. Spline: ACSPL+ Example

37. Kinematics: Basics Kinematics: Forward Kinematics: Inverse Kinematics:
Relationship between actuators positions and end-effector positions
Common with multi-axis applications where end-effector motion is dependent on multiple actuators
Forward Kinematics:
Determining end-effector position as a function of actuator positions
Inverse Kinematics:
Determining actuator positions as a function of end-effector position

38. Kinematics: Inverse Kinematics Example
For the flexible gantry table below, determine the actuator positions as a function of the end-effector X-q position. 𝑋 1 =𝑋+ 𝐿∙ tan 𝜃 2 𝑋 2 =𝑋− 𝐿∙ tan 𝜃 2

39. Kinematics: ACSPL+ Example

40. ACSPL+ Programming Example: 1
Load program “Programming 06 – SetMotionParams.prg” to the controller
Should populate buffer 19
Open communication terminal and set it up to show DISP messages
From the communication terminal start buffer 19 at label ‘Begin’ (“START 19, BEGIN”). Follow the instructions on the screen
What happens?

41. ACSPL+ Programming Example: 2
An application requires an axis to have two modes: slow and fast. The customer wants to use a digital input (IN(0).0) to toggle between the two modes (if ‘0’, set for slow mode, if ‘1’, set for fast mode). They will use a second digital input (IN(0).1) to toggle motion.
Use buffer 20 to write the program. Once running program should not stop (hint: WHILE 1 loop).
Anytime IN(0).0 is toggled the motion parameters should switch between a slow and fast mode (determine your own slow and fast parameters)
Anytime IN(0).1 goes from low to high a new motion should be started. Use the motion command “PTP/r (axis), distance” for the motion.
Run the program and test.