BSc: Robotic Systems

Robotic Systems

• Course name: Robotic Systems
• Course number:
• Knowledge area: Robotics; Robotic components; Robotic control.

Course characteristics

Key concepts of the class

• Robot hardware
• Feedback control in application to robotic systems
• Trajectory tracking and advanced control algorithms

What is the purpose of this course?

The purpose of this course is to review the concepts of linear control theory and then learn some advanced control methods while applying them to practical simple robotic systems with 1 and 2 degrees of freedom. The course also presents all the necessary background of such fundamental components of robotic manipulators as DC and BLDC motors, encoders, microcontrollers and CAN bus (communication protocol). Based on these, the course teaches the student to design and implement on practice simple and advanced control approaches and teaches the students to tune and analyze stability of selected controllers in application to robotic systems.

Prerequisites

• Calculus: ordinary and partial derivatives, definite and indefinite integrals

• CSE201 — Mathematical Analysis I
• CSE203 — Mathematical Analysis I: ordinary and partial derivatives, definite and indefinite integrals

• Analytic Geometry And Linear Algebra I and Analytic Geometry And Linear Algebra II: matrix operations, eigenvalues and eigenvectors
• CSE205 — Differential Equations: first- and second-order ODEs, state-space representation and modeling, concepts of stability (Lyapunov, asymptotic, exponential)

Course Objectives Based on Bloom’s Taxonomy

- What should a student remember at the end of the course?

By the end of the course, the students should be able to remember

• What are the fundamental principles behind DC and BLDC motors,
• How to tune PD controllers to achieve critically damped response,
• What is gravity compensation and how it is implemented in robotic systems,
• What is inverse dynamics.

- What should a student be able to understand at the end of the course?

By the end of the course, the students should be able to describe and explain

• What are the advantages of BLDC motors over DC motors,
• Why PD and PID controllers constitute the majority of industrial controllers,
• What methods exist for trajectory generation and tracking,
• How to design an inverse dynamics controller.

- What should a student be able to apply at the end of the course?

By the end of the course, the students should be able to

• Tune PD and PID controllers,
• Design stable position controllers for manipulators,
• Develop nonlinear controllers such as gravity compensation and inverse dynamics,
• Interface practical robotic hardware (BLDC motors, encoders, microcontrollers) and implement their control algorithms.

Course evaluation

Course grade breakdown

		Proposed points
Labs/seminar classes	20	30
Quizzes	30	30
Final exam	50	40

If necessary, please indicate freely your course’s features in terms of students’ performance assessment:

The course grades are given according to the following rules: In-class discussion and lab performance (6) = 30 pts (factoring in the attendance at the labs), Quizzes (3) = 30 pts, Final exam = 40 pts.

Grades range

Course grading range

		Proposed range
A. Excellent	90-100	85-100
B. Good	75-89	70-84
C. Satisfactory	60-74	55-69
D. Poor	0-59	0-54

If necessary, please indicate freely your course’s grading features.

Resources and reference material

Textbooks:

Course Sections

The main sections of the course and approximate hour distribution between them is as follows:

Section	Section Title	Teaching Hours
1	Robot Hardware	8
2	Fundamentals of Feedback Control	12
3	Trajectory Tracking and Advanced Control	12

Section 1

Section title:

Robot Hardware

Topics covered in this section:

• DC and BLDC motors
• Position sensors (encoders)
• CAN bus

What forms of evaluation were used to test students’ performance in this section?

|a|c| & Yes/No
Development of individual parts of software product code & 1
Homework and group projects & 1
Midterm evaluation & 0
Testing (written or computer based) & 1
Reports & 1
Essays & 0
Oral polls & 0
Discussions & 1

Typical questions for ongoing performance evaluation within this section

• Describe the basic operation principle of DC motors.
• What are the main advantages of BLDC motors over DC motors?
• Describe operation principles of optical and magnetic encoders.

Typical questions for seminar classes (labs) within this section

1. Rewrite the equation of DC motor in the state space form.
2. Rewrite the equation of cart pole system in the state space form with the state ${\textstyle \mathbf {x} =[\theta ,{\dot {\theta }},x,{\dot {x}}]^{T}}$.
3. Find eigen system (values and vectors) of following matrices by hand

Test questions for final assessment in this section

1. Write a differential equation that describes the mechanical part of DC motor.
2. Write a differential equation that describes the electrical part of DC motor.
3. How many CPTs must a 2-channel magnetic encoder have if you want to measure the output displacement of a DC motor with the resolution of 0.1 degree?

Section 2

Section title:

Feedback Control

Topics covered in this section:

• Review of feedback control
• PD controllers
• PID controllers
• Gravity compensation
• Stability of linear systems

What forms of evaluation were used to test students’ performance in this section?

|a|c| & Yes/No
Development of individual parts of software product code & 0
Homework and group projects & 1
Midterm evaluation & 0
Testing (written or computer based) & 1
Reports & 1
Essays & 0
Oral polls & 0
Discussions & 1

Typical questions for ongoing performance evaluation within this section

1. What are overshoot and settling time?
2. How do the gains of PD controller affect transient response parameters?
3. sdf

Typical questions for seminar classes (labs) within this section

1. Find stiffness matrix of a given parallel robotic platform.
2. Perform matrix structural analysis of a cantilever beam.
3. Find stiffness matrix of a two-link manipulator with elastic joint.
4. Estimate identification accuracy for 3-link manipulator.
5. Comment on differences between compliance matrix of a manipulator obtained via CAD modeling and identification results.

Test questions for final assessment in this section

1. Describe main stiffness modeling approaches, their particularities, advantages and limitations.
2. Use variable joint model for a serial manipulator (assume all elements are flexible) to find stiffness matrix.
3. Describe particularities and difficulties of the elastostatic calibration.
4. Find the controller gains that will stabilize a system described by a second order differential equation.

Section 3

Section title:

Position tracking in robots

Topics covered in this section:

• Linear feedback control in application to manipulators
• Lyapunov stability analysis
• Stabilization and trajectory tracking

What forms of evaluation were used to test students’ performance in this section?

|a|c| & Yes/No
Development of individual parts of software product code & 0
Homework and group projects & 1
Midterm evaluation & 0
Testing (written or computer based) & 1
Reports & 0
Essays & 0
Oral polls & 0
Discussions & 1

Typical questions for ongoing performance evaluation within this section

1. Give an example of using feedback in activities of daily life.
2. Drive error dynamics equations for a given feedback control law.
3. For a given differential equation describing robot dynamics and several control laws, find which ones are stable using Lyapunov stability theory.
4. How does elasticity affect error dynamics in robot control applications?
5. What components of mechanical energy exist in robots with compliance?

Typical questions for seminar classes (labs) within this section

1. Design PD controller for a rigid two-link manipulator.
2. Numerically model behavior of compliant robot with PID controller.
3. Compare performance of linear controllers in application to rigid and 2-link manipulator control.
4. Analyze stability of a given controller.

Test questions for final assessment in this section

1. What challenges does robot compliance pose for a control system?
2. Design a position tracking controller for a given compliant system.
3. How does cable elasticity affect dynamics and control of tendon-driven robots?

Section 4

Section title:

Energy, impedance, and force control

Topics covered in this section:

• Joint-space inverse dynamics of serial manipulators
• Energy-based control of compliant robots
• Passivity-based control
• Adaptive control of flexible joint manipulators

What forms of evaluation were used to test students’ performance in this section?

|a|c| & Yes/No
Development of individual parts of software product code & 0
Homework and group projects & 1
Midterm evaluation & 0
Testing (written or computer based) & 1
Reports & 0
Essays & 0
Oral polls & 0
Discussions & 1

Typical questions for ongoing performance evaluation within this section

1. Provide examples of passive and active systems.
2. What are limit cycles?
3. What happens with the energy of passive systems with time?
4. For a given differential equation that describes pendulum dynamics, do the following:
5. Perform input-state linearization for a given system of differential equations.

Typical questions for seminar classes (labs) within this section

1. Find limit cycles of a given robot with compliance.
2. Design gravity and compliance compensator for a robot with flexible joints.
3. Implement and simulate passivity-based control over given robot.
4. For a given differential equation that describes pendulum dynamics, do the following:
   • Find control law transforming original dynamics into that of a linear mass-spring-damper system;
   • Write position error dynamics for the designed control law (inverse dynamics);
   • Repeat the previous steps if there are uncertainties in some of the system’s parameters.

Test questions for final assessment in this section

1. Provide examples of practical systems with non-collocated feedback. What unique challenges does this pose for control systems?
2. Design a position tracking controller for a given compliant system.
3. Analyze stability of a given system with passivity-based controller
4. What are the physical fundamentals behind the concept of passivity and passivity-based control?