Time-varying input shaping technique applied to vibration reduction of an industrial robot

Haptics for Virtual Reality and Teleoperation

“…Individual components of vector p 1 12 have to be compared against block dimensions a, b and c. For relations in Fig. 5.13 it is clear that the particle lies within the rectangle's boundaries (we are considering only plane relations here), if the following condition is satisfied 20) where 12 . However, in this case it is not trivial to determine deformation d and reaction force direction.…”

“…First end-effector orientation is expressed in terms of RPY angles φ = ϕ ϑ ψ T from rotation matrix R(q), 20) where c ∠ represents cos(∠) and s ∠ represents sin(∠). By comparing Eqs.…”

Dissociated jerk-limited trajectory applied to time-varying vibration reduction

“…But, according to the considered workspace, the variation can generally be linearized according to the axis position. Other class of systems is the study in [12], where authors verify the proportionality of the dominating modal period of a 6 axis industrial robot with a Cartesian position of the end-effector (deduced from the joints position). At last, considering load variations, which are encountered for pick and place operations, the modal period will evolve proportionally to the square root of the load mass.…”

“…According to the complexity of the filter used (called ''shaper''), the robustness can be adapted to the behavior of the system. For instance, works presented in [12] demonstrate the effectiveness of shaping method on an industrial 6 axis robot.…”

Optimized re-entry input shapers

“…It is based on the input signal that is modified to achieve zero residual vibrations. This principle has been effectively used in many applications such as the robot manipulator (Chang et al, 2005), telescopic handler (Park et al, 2004), antisway crane (Valášek, 1995) etc.…”