1 Introduction
1.1 The idea of auxiliary input in motion control
1.2 Synthetization of the auxiliary input, goals
2 Inverse kinematics calculation alternatives
2.1 Auxiliary input synthesis on velocity level
2.1.1 Velocity level linear feedback approach (VF)
2.1.2 Velocity level direct error elimination approach (VD)
2.2 Auxiliary input synthesis on acceleration level
2.2.1 Acceleration level linear feedback approach (AF)
2.2.2 Acceleration level direct error elimination approach (AD)
3 Convergence analysis and case study examples
3.1 Convergence analysis
3.1.1 Convergence analysis of the VF approach
3.1.2 Convergence analysis of the VD approach
3.1.3 Convergence analysis of the AF approach
3.1.4 Convergence analysis of the AD approach
3.1.5 Summary on the convergence analysis
Eigen-values in non-redundant case | Extra eigen-values in redundant case | |
---|---|---|
VF | m sets of \(\lambda _{v1}\), \(\lambda _{v2}\) | \(n-m\) sets of 0, 1 |
VD | m sets of 0 | \(n-m\) sets of 1 |
AF | m sets of \(\lambda _{a1}\), \(\lambda _{a2}\), \(\lambda _{a3}\) | \(n-m\) sets of 0, 1, 1 |
AD | m sets of 0, \(-1\) | \(n-m\) sets of 1, 1 |