TY - JOUR

T1 - Coexistence of single- and multi-scroll chaotic orbits in a single-link flexible joint robot manipulator with stable spiral and index-4 spiral repellor types of equilibria

AU - Singh, Jay Prakash

AU - Lochan, K.

AU - Kuznetsov, Nikolay V.

AU - Roy, B. K.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - This paper reports various chaotic phenomena that occur in a single-link flexible joint (SLFJ) robot manipulator. Four different cases along with subcases are considered here to show different types of chaotic behaviour in a flexible manipulator dynamics. In the first three cases, a partial state feedback as joint velocity and motor rotor velocity feedback is considered, and the resultant autonomous dynamics is considered for analyses. In the fourth case, the manipulator dynamics is considered as a non-autonomous system. The system has (1) one stable spiral and one saddle-node foci, (2) two saddle-node foci and (3) one marginally stable nature of equilibrium points. We found single- and multi-scroll chaotic orbits in these cases. However, with the motor rotor velocity feedback, the system has two unstable equilibria. One of them has an index-4 spiral repellor. In the non-autonomous case, the SLFJ robot manipulator system has an inverse crisis route to chaos and exhibits (1) transient chaos with a stable limit cycle and (2) chaotic behaviour. In all the four cases, the SLFJ manipulator dynamics exhibits coexistence of chaotic orbits, i.e. multi-stability. The various dynamical behaviours of the system are analysed using available methods like phase portrait, Lyapunov spectrum, instantaneous phase plot, Poincaré map, parameter space, bifurcation diagram, 0–1 test and frequency spectrum plot. The MATLAB simulation results support various claims made about the system. These claims are further confirmed and validated by circuit implementation using NI Multisim.

AB - This paper reports various chaotic phenomena that occur in a single-link flexible joint (SLFJ) robot manipulator. Four different cases along with subcases are considered here to show different types of chaotic behaviour in a flexible manipulator dynamics. In the first three cases, a partial state feedback as joint velocity and motor rotor velocity feedback is considered, and the resultant autonomous dynamics is considered for analyses. In the fourth case, the manipulator dynamics is considered as a non-autonomous system. The system has (1) one stable spiral and one saddle-node foci, (2) two saddle-node foci and (3) one marginally stable nature of equilibrium points. We found single- and multi-scroll chaotic orbits in these cases. However, with the motor rotor velocity feedback, the system has two unstable equilibria. One of them has an index-4 spiral repellor. In the non-autonomous case, the SLFJ robot manipulator system has an inverse crisis route to chaos and exhibits (1) transient chaos with a stable limit cycle and (2) chaotic behaviour. In all the four cases, the SLFJ manipulator dynamics exhibits coexistence of chaotic orbits, i.e. multi-stability. The various dynamical behaviours of the system are analysed using available methods like phase portrait, Lyapunov spectrum, instantaneous phase plot, Poincaré map, parameter space, bifurcation diagram, 0–1 test and frequency spectrum plot. The MATLAB simulation results support various claims made about the system. These claims are further confirmed and validated by circuit implementation using NI Multisim.

KW - Bifurcation diagram

KW - Chaos in a single-link flexible joint

KW - Coexistence of chaotic orbits (i.e. multi-stability)

KW - Lyapunov spectrum

KW - Multi-scroll

KW - Non-autonomous system

KW - Stable and unstable equilibria

KW - Transient chaos

UR - http://www.scopus.com/inward/record.url?scp=85027722911&partnerID=8YFLogxK

U2 - 10.1007/s11071-017-3726-4

DO - 10.1007/s11071-017-3726-4

M3 - Article

AN - SCOPUS:85027722911

VL - 90

SP - 1277

EP - 1299

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 2

ER -