1. Robot Motion Forward and Inverse Kinematics – Next quarter PID Control
Frame-Based Motions on the AIBO
Modeling Effects of Motions

2. Automatic Control Systems, Servos, Automatic Tracking, Feedback Control

3. Automatic Control Systems
VOCABULARY:
Automatic Control Systems
Automatic: able to activate, move or regulate itself.
Control: command, direct, rule, check, limit, restrain, regulate or operate.
System: a group or combination of interrelated, independent, or interacting elements forming a collective entity.
Control engineering is concerned with modifying the behavior of dynamical systems to achieve desired goals.

4. Control System Terminology
Input - Excitation applied to a control system from an external source.
Output - The response obtained from a system
Feedback - The output of a system that is returned to modify the input.
Error - The difference between the input and the output.

5. Types of Control Systems
Open-Loop
Simple control system which performs its function without concerns for initial conditions or external inputs.
Must be closely monitored.
Closed-Loop (feedback)
Uses the output of the process to modify the process to produce the desired result.
Continually adjusts the process.

6. Control Systems

7. Transducer or Sensor Factors

8. Open Loop Controller

10. Open Loop Controller
An open-loop controller (or non-feedback controller) is a type of controller which computes its input into a system using only the current state and its model of the system
The system does not observe the output of the processes that it is controlling
Controller
Motor
Output
Input

12. Open Loop Controller (cont…)
Open-loop control is useful for well-defined systems where the relationship between input and the resultant state can be modeled by a mathematical formula
For example determining the voltage to be fed to an electric motor that drives a constant load, in order to achieve a desired speed would be a good application of open-loop control

13. Open Loop Controller (cont…)
An open-loop controller is often used in simple processes because of its simplicity and low-cost, especially in systems where feedback is not critical
Generally, to obtain a more accurate or more adaptive control, it is necessary to feed the output of the system back to the inputs of the controller

14. Open-loop control Advantages: Disadvantages: Stability not a problem
Cheaper than closed-loop
Can be used even if output cannot be measured
Disadvantages:
Changes in system or disturbances ? errors
Periodic calibration required

15. Closed Loop Controller

16. Example of a simple Control in Closed Loop

17. Closed Loop Controller
Closed-loop controllers have the following advantages over open-loop controllers:
Disturbance rejection (such as unmeasured friction in a motor)
Guaranteed performance even with model uncertainties, when the model structure does not match perfectly the real process and the model parameters are not exact
Unstable processes can be stabilized
Reduced sensitivity to parameter variations
Improved reference tracking performance

18. Closed Loop Controller
A closed-loop controller uses feedback to control states or outputs of a dynamical system
Process inputs have an effect on the process outputs, which is measured with sensors and processed by the controller; the result is used as input to the process, closing the loop
Controller
Motor
Output
Input
Output Measurement
Feedback

19. The General View of a Control Loopu

20. Feedback or Closed Loop System

21. PID Control Proportional Integral Derivative Control
The Basic Problem:
We have n joints, each with a desired position which we have specified
Each joint has an actuator which is given a command in units of torque
Most common method for determining required torques is by feedback from joint sensors

22. What is PID Control? Proportional, Integral, & Derivative Control
Proportional: Multiply current error by constant to try to resolve error
Integral: Multiply sum of previous errors by constant to resolve steady state error (error after system has come to rest)
Derivative: Multiply time derivative of error change by constant to resolve error as quickly as possible

23. Feedback Signal is subtracted

24. Feedback Signal is subtracted
Integrated circuit with differential amplifier
Motor and gears rotate the wheel
Potentiometer on the wheel
Feedback Signal is subtracted

25. Proportional Controller
Control Law
Step response of the system for proportional control only

26. Complete PID controller
Step response of the system for proportional plus integral plus derivative (PID) control.
Control Law
Kp = 20
KI = 75
KD = 0
time

27. Cruise Control

28. Example
V = velocity, speed

29. All opposing forces Force created by motor Acceleration
is derivative of speed

30. acceleration
speed
integrator
Two terminologies

32. Closed-loop (feedback) control
Advantages:
Reduced sensitivity to:
disturbance inputs
parameter changes
Can stabilize an open- loop unstable plant
Can change system dynamics:
speed of response
accuracy
reduce effect of non-linearities
Disadvantages:
Increased complexity and cost
Risk of instability

34. Advantages of a Closed-Loop Feedback System
Increased Accuracy
Increased ability to reproduce output with varied input.
Reduced Sensitivity to Disturbance
By self correcting it minimizes effects of system changes.
Smoothing and Filtering
System induced noise and distortion are reduced.
Increased Bandwidth
Produces satisfactory response to increased range of input changes.

35. In general, the control system is more complex….

36. Designing control systems is complex
… simplified stages of control system design….
Humanoid robot can have more than 43 variables to control

37. Major Types of Feedback Used
Position Feedback
Used when the output is a linear distance or angular measurement.
Rate & Acceleration Feedback
Feeds back rate of motion or rate of change of motion (acceleration)
Motion smoothing
Uses a electrical/mechanical device called an accelerometer

38. Target Tracking

40. In unstable system the periodic component would not disappear

41. Target Tracking Parameters
Azimuth
Elevation
Range
Relative Target Velocity
Target’s motion with respect to the platform’s motion

43. Five Basic Functions of Angle-Tracking Servo Systems
Sense position error (magnitude and direction)
Provide position feedback
Provide velocity feedback
Provide data smoothing / stabilization
Provide a power-driving device

44. Uses of Angle-Tracking Servo Systems
Monotrack fire control radars
Homing missiles
Acoustic homing torpedoes
Aviation fire control tracking systems

46. Motion Control System

47. 3. Mechanical Transmission 4. Applications
1. Scope of Study
2. Servo System
3. Mechanical Transmission
4. Applications
Motion Control System
The primary purpose of the servo system is to control the motion of the load
Motion
Requirements
Servo
System
Mechanical
transmission

48. Motion Control System - Principles
The digital ac servo system is typically available with three modes of operation:
Torque Control Mode
Velocity Control Mode
Position Control Mode
In other words, in order to control the position the torque and velocity should be controlled.
Mechanical Transmission
Servo System
Motion Requirements

49. Motion Control System Example
2. Speed Regulator
3. AC Motor
1. Position Regulator
AC supply
Electronic commutator
4. Power Converter
Desired output
Position feedback
Speed feedback
The ac servo system consists of five major components.
5. Position Sensor

50. Motion Control System
Most applications are more complicated than directly driving load.
Common mechanical transmissions include :
timing belts,
gears,
conveyors,
leadscrews, and
rack & pinion mechanism.
Especially, the timing belt and gearbox can be utilized as a speed reducer, and the other are to be used as translators.

51. Motion Control System with linear motion
Change to linear motion…...
For instance, if the application requires linear motion of the load:
a leadscrew,
rack & pinion, or
conveyor
is used to translate the motor’s rotary motion into linear motion.
Load
Tacle
Motor
Coefficient of friction
Optional Timing Belt or Gear Reducer
Ball Nut
Ball Screw

52. Linear Servo Systems
Application of linear servo system: box packing

53. Troubles in Control Systems

54. Actuator Hysteresis

55. Mechanical Hysteresis

56. Mechanical Hysteresis - backlash

57. Friction

58. Electronic Hysteresis

59. Sony AIBO Robot
Joint Angle Limits

60. Intelligent Complete Robot
Perception
Cognition
Action
Sensors
Actuators
External World

61. What is good about robots like AIBO?
These concepts make up the low level functionality of the AIBO
Implemented once and used repeatedly
For more information about PID Control and Forward & Inverse Kinematics take Matt Mason’s Robotic Manipulation course

62. AIBO Actuators
18 degrees of freedom with a continuously controllable range of motion
3 DOF in each leg (12 total)
3 DOF in the head
2 DOF in the tail
1 DOF in the jaw
Each joint is controlled by specifying to a desired joint angle to OVirtualRobotComm.
2 binary motors for the ears
A speaker for general sound production

63. Motor Control
Each message to OVirtualRobotComm contains a set of target angles for the joints
Each target is used for a PID controller (part of the OS) that controls each motor
Each target angle is used for one 8ms motor frame
Each message contains at least 4 motor frames (32ms)

64. The Motion Interface Dynamic Walking Motion Static Frame-Based Motion
Walk Parameters
Motion Frames
Walk Engine
Frame Interpolator

65. Frame-Based Motion
Each motion is described by a series of “frames” which specify the position of the robot, and a time to interpolate between frames
Movement between frames is calculated through linear interpolation of each joint

66. Kicking A series of set positions for the robot
Linear interpolation between the frames
Kinematics and interpolation provided by CMWalkEngine
Set robot in desired positions and query the values of the joints

68. Use of Kicks in Behaviors
Modeling effects of kicking motions
Ball vision analysis
Ball trajectory angle analysis
Kick strength analysis
Kick selection for behaviors
Selection algorithm
Performance comparison

69. Kick Selection
Incorporate the kick models into the selection algorithm
The robot knows its position on the field relative to the goal and the desired ball trajectory
The robot selects appropriate kick by referencing the kick model
If no kick fits desired criteria, robot selects closest matching kick and turns/dribbles ball to appropriate position

70. Frame-Based Motion

71. Frame-Based Motion
Each motion is described by a series of “frames” which specify the position of the robot, and a time to interpolate between frames
Movement between frames is calculated through linear interpolation of each joint

72. Examples: Valid Motion Frames
BodyPos(b,98,RAD(16));
HeadAng(b, 0.5, 1.5, 0.0);
LegPos(b,0, 123, 85, 0);
LegPos(b,1, 123,-85, 0);
LegAng(b,2, 0.1, 0.0, 0.2);
LegAng(b,3, 0.1, 0.0, 0.2); m[n].body = b;
m[n].time = 100;
n++;
BodyPos(b,98,RAD(16));
HeadAng(b, 0.5, 1.5, 0.0);
MouthAng(b,-.7);
LegPos(b,0, 123, 85,0);
LegPos(b,1, 123,-85,0);
LegPos(b,2, -80 , 75,0);
LegPos(b,3, -80 ,-75,0);
m[n].body = b;
m[n].time = 100;
n++;
LegAng(b,0, 0.0, 1.5, 0.0);
LegAng(b,1, 0.0, 1.5, 0.0);
LegAng(b,2, 0.1, 0.0, 0.2);
LegAng(b,3, 0.1, 0.0, 0.2);
m[n].body = b;
m[n].time = 100;
n++;
m[n].body = b;
m[n].time = 100;
n++;

73. Defining a Frame
The position of the robot in each frame can be described using any of the following:
Position of the legs - in terms of angles of each joint or position of the foot in motion coordinates
Angle of the head (tilt, pan, roll)
Body height and angle
Angle of the mouth
struct BodyState{
BodyPosition pos;
LegState leg[4];
HeadState head;
MouthState mouth; };

74. Questions and Problems to Solve

75. What did we learn? Problem 1
Feedback control is a fundament of robot control
Various kits (Lego Dacta Control Lab) have several demonstrations and project to explain the principles of feedback:
Line following
Speed control
Temperature control (fan, lamp, sensor)
Find on internet some of these kits and explanations of projects for high school.

76. What did we learn? Problem 2 Control of Many DOF robots is tough
In addition to classical and modern control theory we use:
fuzzy control
genetic algorithms
neural control
bio-mimetic systems
Review your control knowledge (for next quarter), but remember that in this class all knowledge is through programming.
Describe a simple robot arm which uses fuzzy logic and a motor.
Describe a mobile robot that uses a genetic algorithm and a motor. How FGA is used in relation to a motor?

77. Your task
Problem 3
Learn about the particular servo that you plan to use. If the servo was not suggested by the professor, learn about servos that are available, calculate your project requirements for a servo and pick one. The more servos we order, the cheaper the price of one.
If you do not want to use one of standard servos, your choices are:
build your own servo from a DC motor. This is a big project by itself and you must have clear reasons to do so
Use stepper motor. Remember that they are slow and weak, why you want to use them? You must be sure of your reasons

78. Your task Problem 4 Problem 5 Problem 6
Use hydraulic control. Why? You need to purchase or build your own actuator. Think about redesigning our horse leg with better syringes and oil instead of water. How can you connect the syringe to a stepper motor?
Use pneumatic control. Read first the documentation of pneumatic hand or old Electric Horse. Talk to designers.
Find pistons in Mondo-Tronics or other robot store. They are good.
Use Nintinol or other similar actutors. They are good for face muscles or similar small and weak movements.
Can they be used for a hexapod? I doubt, but try to convince me
Before you do this, read the two-volume book of Conrad and Mills
Problem 5
Problem 6

79. Formulas & Units useful to solve practical problems with motors and gears
Unit conversions of interest
1lbs = 4.45 N
1 inch = meters
1 in-lbs = 0.11 N-m
1 RPM = 60 Rev / Hour = Rad / Sec
1 mile = 5280 X 12 inches = 63,000 inches
Power = Force (N) X Velocity (m/s)
Power = Torque (N-m) X Angular Velocity (Rad/Sec)
Electrical Power = Voltage X Current

80. Problems with Motor Characteristics
Stall Current
Torque v Speed Curves
Stall Torque (T0)
Stall Current (A0)
Free Speed (Wf)
Free Current (Af)
K (slope) T0
Torque, Current
Find these data for the motors that you use.
Calculate the torque of your robot arm or mobile robot to solve problems that you want.
Draw the Torque vs Speed Curve for your motor and check if this is what you expect. A0 Af
Speed Wf
Free Current

81. Slope-Intercept (Y=mX + b)
Y=Motor Torque
m=K (discuss later)
X=Motor Speed
b=Stall Torque (T0)
K (slope) T0
Torque, Current A0 Af
Speed Wf
What is K? … It is the slope of the line.
Slope = change in Y / change in X = (0 - T0)/(Wf-0) = -T0/Wf
K = Slope = -T0/Wf
How to calculate slope when the characteristic is not linear?

82. (Y=mX + b) Continued ... Y=Motor Torque m=K = -T0/Wf X=Motor Speed
b=Stall Torque = T0
T0 (b)
K (-T0/Wf)
Torque, Current A0 Af
Speed Wf
Equation for a motor:
Torque = (-T0/Wf) * Speed + T0
How to calculate torque in any point of the characteristic curve?

83. Current (Amps) and FIRST
Speed
Torque, Current T0 Wf Af A0
Cutoff Amps
What are cutoff Amps?
Max useable amps
Limited by breakers
Need to make assumptions
Can our Motors operate above 30 amps?
- Absolutely, but not continuous.
When designing, you want to be able to perform continuously; so finding motor info at 30 amps could prove to be useful.

84. S @ 30A (W30) = (30 - A0) * Wf / (Af-A0)
Torque at Amp Limit
Speed
Torque, Current T0 Wf Af A0
Cutoff Amps
T30 = Torque at 30 Amps
W30 = Speed at 30 Amps
Current Equation:
Current = (Af-A0)/Wf * Speed + A0
Motor Equation:
Torque = (-T0/Wf) * Speed + T0
30A (W30) = (30 - A0) * Wf / (Af-A0)
30A (T30) = (-T0/Wf) * W30 + T0

85. Power - Max vs. 30 Amps Speed Torque, Current T0 Wf Af A0 Power
Power = Torque * Speed
Must give up torque for speed
Max Power occurs when:
T = T0/2 & W=Wf/2
What if max power occurs at a current higher than 30A?
Paul’s Tip #1: Design drive motor max power for 30A!
Power is Absolute - It determines the Torque - Speed tradeoff!

86. Let’s Look at Some FIRST Motors
Motor Comparisons
Let’s Look at Some FIRST Motors
Chiaphua Motor
Drill Motor
Johnson Electric Fisher-Price Motor
We will compare T0, Wf, A0, Af, T30, W30, max power (Pmax), max power (Apmax), and power at 30 amps (P30).
We will be using Dr. Joe’s motor spreadsheet updated to handle the new motors.

87. Motor Comparisons
We will be using Dr. Joe’s motor spreadsheet updated to handle the new motors.
Motor Equations:
1. Fisher-Price: T = (-0.51/20,000) * W
2. Bosch Drill: T = (-0.65/20,000) * W
3. Chiaphua: T = (-2.2/5,500) * W + 2.2

88. Combining Motors
Using multiple motors is common for drive trains. We will look at matching the big 3 motors.
I try to match at free speed, but you can match at any speed you like!!
FP and drill will match 1:1
Wf FP(drill) / Wf Chiaphua = 20000/5500 = 40/11
Gear ratio to match Chip & FP(drill) is 40/11.
We will use an efficiency of 95% for the match gear.
More to come on Gear Ratio & Efficiency in the Second Half!

89. Combined Motor Data Motor Equations:
1. F-P & Drill: T = (-1.16/20,000) * W
2. F-P & Chip: T = (-3.96/5,500) * W
3. Drill & Chip: T = (-4.45/5,500) * W
4. F-P, Drill, & Chip: T = (-6.21/5,500) * W

90. NXT® motor internals for calculations
Center of Mass of Lego Motors

91. NXT motor characteristics

92. The following charts show the characteristics of the NXT motor versus applied load.
For the dark blue curves, the NXT was powered at 9V (voltage of alkaline batteries), the magenta ones were obtained at 7.2V (voltage of NiMH batteries).
Power level is 100% for all charts.

93. This curve shows that the maximum mechanical power is obtained at a torque load of about 15 N.cm.
If you compare to the curves obtained for the RCX with motor, you see that the available mechanical power is much higher, almost 4 times!
Even powered with 7.2V NiMH batteries, the NXT can deliver more power than a RCX output with 2 paralleled motors and 9V supply.
This comes with a price of course, the current drained at that power level is much higher - you better have good batteries...

96. The current vs. torque shows a linear increase with the load.
Because of power limitations in NXT driver, and thermistor trip current in NXT motor, I suggest that you don't exceed a 15 N.cm torque for extended time periods.
Higher loads (thus current drains) are possible for short periods, but the protections will soon reduce current and available power

101. Manuela Veloso Paul E. Rybski
Sources
Manuela Veloso
Paul E. Rybski