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Stability Analysis of a Hierarchical Architecture for Discrete-Time Sensor-Based Control of Robotic Systems

Figure 1

Figure 1
Block diagram of a typical hierarchical motion control system.

Figure 2

Figure 2
Root locus of 37 with Formula$d = 2$, Formula$a = 0.329$, Formula$b = 0.975$, and Formula$T=75\,$ ms.

Figure 3

Figure 3
Limit values of Formula$k_p T$ as a function of the parameter Formula$a$ for different delays assuming that Formula$b=(1-a)$.

Figure 4

Figure 4
Input/output joint velocity data from the KUKA-KR16 industrial manipulator. It is seen that a first-order model accurately describes the joint's velocity dynamics.

Figure 5

Figure 5
Closed loop response for a small gain showing convergence to the origin for Formula${\bm e}=[e_1,\,e_2]^T$.

Figure 6

Figure 6
Closed loop response for a gain on the stability threshold showing standing oscillations.

Figure 7

Figure 7
Closed loop response for higher gains showing divergence.

Figure 8

Figure 8
Closed loop response for higher gains showing divergence from a very small initial error.

Figure 9

Figure 9
KUKA KR16 industrial robot used in the experiments.