Tolerance Ball

Tolerance Ball 1:

[1]

 

Glue dot.

 

[2]

 

Segment, geometrical element, here: line.

 

[3]

 

Tolerance ball.

 

[4]

 

Transition, smooth path.

 

Motivation

Dynamical-
Steadiness

 
  • Segment transitions that are not two times steadily differentiable with respect to their spatial coordinate lead to dynamic-unsteadinesses, if at this transition the path velocity is not reduced to zero value.
  • Segment transitions can be smoothed out using Bézier-splines leading to the dynamics for the whole path to be steady at the segment transition, even though path velocity differs from zero.

 

Smoothening

 
  • Tolerance balls are used to smooth out dynamic unsteadiness at segment transitions.

 

Faster
Dynamics

 
  • Smoothening permitts faster dynamics.
  • The maximum segment transition velocity calculated by the system in advance has the value VeloLink.
  • The user can change the system parameter C2 for C2-velocity reduction online.
  • The segment transition velocity has the value C2 x VeloLink.

 

Definition

Segment Transition

 
  • For the smoothening a tolerance ball is placed around each segment transition.

 

Permitted
Path Deviation

 
  • Up to the extend that the path stays within the tolerance ball, this path may deviate from its predefined geometry within this tolerance ball.

 

Parameter

Radius

 
  • The user adjusts the radius of the tolerance ball.

 

Range of Validity

No
Exact Halt,
No Stop

 
  • The radius of the tolerance ball is valid modally for all segment transitions that at the segment transition do not imply an exact halt or a stop.

 

Algorithmic Behavior

Adaptive

 
  • Automatically, the radii of the tolerance balls are set adaptively.

 

Inhibit
Overlap

 
  • Setting the radii adaptively prevents from overlap of the tolerance balls. Otherwise, especially for small segments an overlap of tolerance balls could occur.

 

At the
Segment Transition

 
  • Within the tolerance ball there is no override.
  • Entering the tolerance ball the path acceleration obtains zero value.
  • Entering the tolerance ball the path velocity obtains the value of the segement transition velocity.
  • Within the tolerance ball the path acceleration stays at zero value.
  • Within the tolerance ball the path velocity remains at the value of the segment transition velocity.
  • The override induced change of velocity level is interrupted within the tolerance ball and is continued after leaving the tolerance ball.