Robot Kinematics
The geometry of robot motion: frames and notation, rotation matrices, Euler angles and quaternions, homogeneous transforms in SE(3), Denavit–Hartenberg parameters, forward kinematics of real arms, the product of exponentials, analytical and numerical inverse kinematics, Jacobians, singularities and manipulability, and wheeled mobile robot kinematics with a mobile-manipulator capstone.
ROB-210 Year 2 3 credits 12 lessons · 6 h 4 min
Offered by HSM University · Robotics
What you'll learn
- Represent points, vectors and coordinate frames with consistent notation, and use dot and cross products to compute angles, directions and rotational velocities
- Construct, interpret and compose rotation matrices in two and three dimensions, using their SO(3) properties to change frames and invert rotations
- Convert between rotation matrices, Euler and roll-pitch-yaw angles, axis-angle, rotation vectors and unit quaternions, and recognize gimbal lock and quaternion pitfalls
- Use homogeneous transforms in SE(3) and SE(2) to change frames, chain poses, compute inverses and relative poses, and distinguish tool-frame from world-frame motion
- Assign standard and modified Denavit–Hartenberg frames to a serial arm, read off DH parameters and build link transforms
- Compute the forward kinematics of planar, SCARA, elbow and six-axis arms, including tool transforms, URDF descriptions and the limits of model accuracy
- Describe joints as screw axes and compute forward kinematics with the product of exponentials formula
- Solve inverse kinematics analytically for 2R, 3R and elbow arms and use wrist decoupling, choosing among multiple solutions
- Solve inverse kinematics numerically with Newton–Raphson, pseudoinverse, damped least-squares and gradient methods, handling redundancy and solver failures
- Derive and compute geometric Jacobians, relate them to analytic and screw-based Jacobians, and use them for resolved-rate control and statics
- Identify and classify singularities, evaluate manipulability and workspace, and apply design, planning and control strategies that avoid singular behaviour
- Model differential-drive, Ackermann and mecanum mobile robots, integrate wheel odometry, and combine base and arm kinematics for a mobile manipulator
Course content
12 lessons · 6 h 4 min total · final exam
- 1 Points, vectors and coordinate frames 33 min · quiz
- 2 Rotation matrices in two and three dimensions 30 min · quiz
- 3 Euler angles, roll-pitch-yaw, axis-angle and quaternions 30 min · quiz
- 4 Homogeneous transforms and rigid-body motion 30 min · quiz
- 5 Denavit–Hartenberg conventions 28 min · quiz
- 6 Forward kinematics of robot arms 30 min · quiz
- 7 Product of exponentials and screw theory 29 min · quiz
- 8 Inverse kinematics: analytical methods 29 min · quiz
- 9 Inverse kinematics: numerical methods 29 min · quiz
- 10 Velocity kinematics and the Jacobian 32 min · quiz
- 11 Singularities, manipulability and workspace 30 min · quiz
- 12 Mobile robot kinematics and capstone 34 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
The geometry of robot motion: frames and notation, rotation matrices, Euler angles and quaternions, homogeneous transforms in SE(3), Denavit–Hartenberg parameters, forward kinematics of real arms, the product of exponentials, analytical and numerical inverse kinematics, Jacobians, singularities and manipulability, and wheeled mobile robot kinematics with a mobile-manipulator capstone.
Part of the Science stream, typically taken in year 2.