Reflexxes Motion Libraries: Synchronization Behavior

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Introduction

The On-Line Trajectory Generation (OTG) algorithms of the Reflexxes Motion Libraries are capable to generate

non-synchronized,

time-synchronized, and

phase-synchronized

motion trajectories.

Paths of non-, time-, and phase-synchronized trajectories for a two-degree-of-freedom system.

While the generation of non-synchronized and time-synchronized trajectories is always possible for both, the position-based and the velocity-based On-line Trajectory Generation algorithm, phase-synchronized trajectories require certain input values. The following image shows a non-, a time-, and phase-synchronized trajectory for three degrees of freedom.

Non-synchronized, time-synchronized, and phase-synchronized trajectories for a system with three degrees of freedom.

To specify the behavior of the Reflexxes Motion Library, the enumeration RMLFlags::SyncBehaviorEnum consists of four elements

and the attribute RMLFlags::SynchronizationBehavior is used to specify the synchronization behavior of the desired trajectory.

Detailed information about the flag RMLFlags::PHASE_SYNCHRONIZATION_IF_POSSIBLE can be found on page About the Flag RMLFlags::PHASE_SYNCHRONIZATION_IF_POSSIBLE.

Synchronization Behavior of the Position-based On-line Trajectory Generation Algorithm

All four values of the set RMLFlags::SyncBehaviorEnum can be used to specify the synchronization behavior of the position-based On-Line Trajectory Generation algorithm (cf. ReflexxesAPI::RMLPosition()).

An example showing, how to set-up time- and phase-synchronized motion trajectories, is shown at page Example 3 — Different Synchronization Behaviors of the Position-based algorithm. The resulting time- and phase-synchronized trajectories and paths of the two degrees of freedom of this example are depicted in the following figure.

Example of a two-degree-of-freedom time- and phase-synchronized motion trajectory (top) and corresponding paths (bottom) generated by the position-based Type IV On-Line Trajectory Generation algorithm of the Reflexxes Motion Libraries using the same input values (Type IV).

In this example, the task is to execute a motion from standstill, which is defined by ${\bf W}_0\,=\,\left(\,\!_1\vec{W}_0,\,_2\vec{W}_0\right)^T$ . After 1000 ms, a sensor event happens (unforeseen), and due to this, we have to immediately react and now have to reach a position ahead with a negative velocity. This desired state of motion, ${\bf M}_{1000}^{\,trgt}$ , is time-optimally reached after $t\,=\,3873\,ms$ (cf. figure above), and right after this, a further switching of set-points happens, such that the originally desired state of motion, ${\bf M}_0^{\,trgt}$ , shall be reached again. After $t\,=\,6756\,ms$ , this desired state is finally reached (cf. Example 3 — Different Synchronization Behaviors of the Position-based algorithm).

Synchronization Behavior of the Velocity-based On-line Trajectory Generation Algorithm

The velocity-based On-Line Trajectory Generation algorithm (cf. ReflexxesAPI::RMLVelocity()) can also generate

non-synchronized,
time-synchronized, or
phase-synchronized,

and accepts any values of RMLFlags::SyncBehaviorEnum. The default value for the corresponding flag RMLVelocityFlags::SynchronizationBehavior is RMLFlags::NO_SYNCHRONIZATION. The following image shows an example for a non-synchronized and a time-synchronized trajectory using the same input values ${\bf W}_0$ .

Example of a Three-degree-of-freedom trajectory generated by the velocity-based On-line Trajectory Generation algorithm. The left trajectory is non-synchronized;the right one is time-synchronized (Type IV).

Note:

The examples above have been generated with the Type IV Reflexxes Motion Library, which takes into account the values of

RMLPositionInputParameters::CurrentAccelerationVector (containing the the current acceleration vector $\vec{A}_i$ and
RMLPositionInputParameters::MaxJerkVector (containing the maximum jerk vector $\vec{J}_i^{\,max}$ .