BSc: Robotic Systems

Robotic Systems

• Course name: Robotic Systems
• Code discipline:
• Subject area: Robotics; Robotic components; Robotic control.

Short Description

This course covers the following concepts: Robot hardware; Feedback control in application to robotic systems; Trajectory tracking and advanced control algorithms.

Prerequisites

Prerequisite subjects

• CSE201 — Mathematical Analysis I and CSE203 — Mathematical Analysis II: ordinary and partial derivatives, definite and indefinite integrals.
• CSE202 — Analytical Geometry and Linear Algebra I and ACSE204 — 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)
• 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 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.
• 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 Topics

Course Sections and Topics

Section	Topics within the section
Robot Hardware	DC and BLDC motors Position sensors (encoders) CAN bus
Feedback Control	Review of feedback control PD controllers PID controllers Gravity compensation Stability of linear systems
Position tracking in robots	Linear feedback control in application to manipulators Lyapunov stability analysis Stabilization and trajectory tracking
Energy, impedance, and force control	Joint-space inverse dynamics of serial manipulators Energy-based control of compliant robots Passivity-based control Adaptive control of flexible joint manipulators

Intended Learning Outcomes (ILOs)

What is the main 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.

ILOs defined at three levels

Level 1: What concepts should a student know/remember/explain?

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

• 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.

Level 2: What basic practical skills should a student be able to perform?

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

• 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.

Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?

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.

Grading

Course grading range

Grade	Range	Description of performance
A. Excellent	85-100	-
B. Good	70-84	-
C. Satisfactory	55-69	-
D. Poor	0-54	-

Course activities and grading breakdown

Activity Type	Percentage of the overall course grade
Labs/seminar classes	30
Quizzes	30
Final exam	40

Teaching Methodology: Methods, techniques, & activities

Activities and Teaching Methods

Activities within each section

Learning Activities	Section 1	Section 2	Section 3	Section 4
Development of individual parts of software product code	1	0	0	0
Homework and group projects	1	1	1	1
Testing (written or computer based)	1	1	1	1
Reports	1	1	0	0
Discussions	1	1	1	1

Formative Assessment and Course Activities

Ongoing performance assessment

Section 1

Activity Type	Content	Is Graded?
Question	Describe the basic operation principle of DC motors.	1
Question	What are the main advantages of BLDC motors over DC motors?	1
Question	Describe operation principles of optical and magnetic encoders.	1
Question	Rewrite the equation of DC motor in the state space form.	0
Question	Rewrite the equation of cart pole system in the state space form with the state ${\textstyle \mathbf {x} =[\theta ,{\dot {\theta }},x,{\dot {x}}]^{T}}$ .	0
Question	Find eigen system (values and vectors) of following matrices by hand	0

Section 2

Activity Type	Content	Is Graded?
Question	What are overshoot and settling time?	1
Question	How do the gains of PD controller affect transient response parameters?	1
Question	sdf	1
Question	Find stiffness matrix of a given parallel robotic platform.	0
Question	Perform matrix structural analysis of a cantilever beam.	0
Question	Find stiffness matrix of a two-link manipulator with elastic joint.	0
Question	Estimate identification accuracy for 3-link manipulator.	0
Question	Comment on differences between compliance matrix of a manipulator obtained via CAD modeling and identification results.	0

Section 3

Activity Type	Content	Is Graded?
Question	Give an example of using feedback in activities of daily life.	1
Question	Drive error dynamics equations for a given feedback control law.	1
Question	For a given differential equation describing robot dynamics and several control laws, find which ones are stable using Lyapunov stability theory.	1
Question	How does elasticity affect error dynamics in robot control applications?	1
Question	What components of mechanical energy exist in robots with compliance?	1
Question	Design PD controller for a rigid two-link manipulator.	0
Question	Numerically model behavior of compliant robot with PID controller.	0
Question	Compare performance of linear controllers in application to rigid and 2-link manipulator control.	0
Question	Analyze stability of a given controller.	0

Section 4

Activity Type	Content	Is Graded?
Question	Provide examples of passive and active systems.	1
Question	What are limit cycles?	1
Question	What happens with the energy of passive systems with time?	1
Question	For a given differential equation that describes pendulum dynamics, do the following:	1
Question	Perform input-state linearization for a given system of differential equations.	1
Question	Find limit cycles of a given robot with compliance.	0
Question	Design gravity and compliance compensator for a robot with flexible joints.	0
Question	Implement and simulate passivity-based control over given robot.	0
Question	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.	0

Final assessment

Section 1

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

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

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

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?

The retake exam

Section 1

Section 2

Section 3

Section 4