Abstract
Stability and bifurcation analysis of a non-rigid robotic arm controlled with a time-delayed acceleration feedback loop is addressed in this work. The study aims at revealing the dynamical mechanisms leading to the appearance of limit cycle oscillations existing in the stable region of the trivial solution of the system, which is related to the combined dynamics of the robot control and its structural nonlinearities. An analytical study of the bifurcations occurring at the loss of stability illustrates that, in general, hardening structural nonlinearities at the joint promote a subcritical character of the bifurcations. Consequently, limit cycle oscillations are generated within the stable region of the trivial solution. A nonlinear control force is then developed to enforce the supercriticality of the bifurcations. Results illustrate that this strategy enables to partially eliminate limit cycle oscillations coexisting with the stable trivial solution. The mechanical system is analysed in a collocated and a non-collocated configuration, depending on the position of the sensor.
Highlights
Robots were originally developed for pick-and-place operations [25], for which extreme geometrical accuracy is not a particular need
The repeatability of positioning is more important for machining than for pick-and-place operations, which was enough for the mentioned clay prototype sculpture manufacturing
Geometrical accuracy has increased by a factor of 10 from mm to tenth of mm by applying better sensors and proportional-derivative feedback control
Summary
Robots were originally developed for pick-and-place operations [25], for which extreme geometrical accuracy is not a particular need. Since industrial robot users are hesitant to accept mounted passive and semi-active embedded solutions to increase the dynamic reflected stiffness of the end-effector, another relatively cheap solution could be using feedback sensor signals in the built-in position control of stock industrial robots This might sound impossible, but stable manufacturing might be achieved with careful parameter management, especially with the synchronisation of delays in the built-in and new feedback loop, most probably using acceleration signals. The joints and the drive of the robotic arm can introduce nonlinearities to the stiffness characteristic, which is another feature relevant for the system dynamics often neglected [31,40] This aspect was partially studied, for instance, in [8], where a lumped mass model with a cubic nonlinearity controlled by a delayed acceleration feedback signal was investigated; the implications of 1:1 resonances and 1/3 subharmonic resonances on stability were analysed. Limitations and advantages of the various configurations and control laws considered are carefully analysed
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