Industrial Robotics

What are industrial robots and what are they used for?

Serial vs. Parallel kinematics

Some nomenclature: base, joints, TCP

More nomenclature: movements types, speed definitions, and workspace

Coordinate systems: global, machine, tool, workpiece

Frames translations and rotations

Composition and decomposition of a rotation matrix into Euler angles

Rotation matrix properties

Combining translations and rotations into a single homogeneous transformation

Review of frame operations

General solution of forward kinematics for serial chains

Solving the forward kinematics of a 6-axes robot in 6 steps

Test your code against this example

Add a base frame and a tool to the forward kinematics solution

Introduce mechanical coupling between joint axes

Can inverse kinematics be solved in closed-form?

Multiple solutions and singularities

Solving the first half of the inverse kinematics: Joints 1-2-3

Solving the second half of the inverse kinematics: Joints 4-5-6

Test your own code against this example

Add a base frame and a tool to the inverse kinematics solution

Compensate for mechanical coupling between joint axes

Define a geometrical path in space

Point-To-Point movements: equations and properties

Interpolating in the path space: position and orientation

Introducing quaternions, their properties and the SLERP interpolation

Parametric equations for lines and circles in space

Introducing cubic Bezier splines and DeCasteljeu's algorithm

Rounding edges with quartic Bezier splines. Defining continuity of a transition.

Calculate the length of a path and modify it at run-time

Define the workspace and reduce complexity

Intersection between lines and cuboids. Wireframe model. Safe orientation cone.

Introducing capsules for self-collision detection.

Introduce exclusive zones and monitor distance between robots. Calculate distance between two capsules.

Introduce trajectory as function of path in time

Use the standard S-curve to generate jerk-limited trajectories

Explore alternatives to the S-curve: sinusoidal profiles and Bezier profiles 

Modify path speed to avoid violations of joints dynamic limits

Introduce the Jacobian to calculate path twist given joints speed

Use Gaussian filter to smooth trajectories in the time domain

Joints, Cartesian and angular speed calculations

Use the Jacobian to transform the TCP wrench into joints torques. Introduce manipulability ellipsoid.

Dynamic model: concept and parameters identification

Overview of two common methods used to solve inverse dynamics

Typical applications of dynamic model: motor sizing; torque feed-forward control; trajectory optimization; teach by hand.

Introduce list of common commands used to program robots.