Robotics 1 La Sapienza

Here's the material to solve Robotics 1 exercises: explaination, code and examples.

Index

Orientation

• Relative Orientations between two expression | RPY representation of orientation

• Orientation 4x4 of frame A wrt frame B

• Orientation of frame from DH table

• Fixed axes rotation matrix

• Orientation and position of slave robot from reference on master robot

• Relative orientation of frames, expression as axis-angle

• Vector attached to a body orientation after rotations

• Cylindrical coordinates

• Relative orientation | Point coordinates

• Orientation of a vector as axis '?' of frame

Denavit-Hartenberg

• DH table recognition

• DH table: 7R Anthropomorphic

• Direct Kinematics from DH

• DH RRPRP

• 4R Comau DH

• Panda 7R

• Planar RPR

• Staubly RX 6R

• GMF 5dof RPPRR

• Planar PRPR

• Nao view 1 | view 2

• Planar RPRP

• Comau Racer 6R

• K-1207 7R spacial

• Kuka K30 6R

Motor

• Voltage to apply given speed

• Incremental Encoder: resolution | pulses per turn | pulses counted | counter going up/down

• Motor resolution linear/angular, torque, acceleration and inertia | Incremental encoder ppt, nbits

• Velocity [RPM]

• Absolute vs. Incremental encoders

• Encoder on motor or link ?

• Norm resolution with encoders on joints, uncertainties

• Resolutions from required e-e resolution | pulses per turn

Inverse Kinematics

• Inverse kinematics from DH table, planar robot

• Inverse kinematics RPY matrix

• Inverse Differential Problem

• Inverse Kinematics L-shaped 2R planar robot (position as Ac1 + Dc12)

• 3R planar robot given fi and position

• Inverse method for spacial robot

• RPR planar robot with desired position and orientation

• Rotation for a vector as axis of new frame

Numerical methods

• Methods usage, parameters, expected results

• Convergence

• Null space, stop of Gradient Descent | NR near singularities

Differential Kinematics

• Map from angular velocity to angles time derivative

• Velocity and acceleration in cartesian and joint space - circular trajectory

• Analytical Jacobian, singularities, Null and Range spaces

• Joint velocities from desired displacement | Coordinated motion

• Geometric Jacobian

• Jacobian rank, singularities, Null space for non-zero joint velocities

• Coordinated motion velocity

• Cartesian velocity from S(w)

• Singularities check of a non squared Jacobian

• Double velocity task

• Build of jacobian for particular velocity (joint-cartesian) or balancing torques

• Representations of rotation matrices time derivative

Trajectories

• Circular trajectory | Robustness

• Cubic spline trajectory and maximum values

• Smoothness and scaling factor

• Minimum feasible time generic

• Trajectory min time in joint space

• Velocity manipulability

• Quadratic cartesian trajectory for ending direction not along segment

• Linear trajectory at constant speed

• Circle with A,B,radius | Acceleration tangent/normal

• Trajectory between orientation from rotation matrices

• Trajectory between orientation matrices, axis-angle representation

• Periodic trajectory

• Path Curvature Computation

Kinematic Control

• Wrenches which no need controls (forces and torque not perturbing equilibrium)

• Control on cartesian error

• How measure position

• Plan velocity after human detection

• Control law with error specifics on tangent/normal

• Acceleration command and control law

• Acceleration command control

• Workspace 3R planar

• Velocity control on wrist and arm of 6R

• Workspace RPR planar

• Proof error converging to zero