Crossing type 2 singularities of parallel robots without pre-planned trajectory with a virtual-constraint-based controller

Abstract

The presence of Type 2 singularities in parallel robots severely affects their performances, mainly because the platform motion control is partially lost. It also leads to a size reduction of the operational workspace. Moreover, the dynamic model of the parallel mechanism degenerates and locally, the robot becomes underactuated in the singularity. It has been proven that it is possible to cross Type 2 singularities by respecting a dynamic criterion. Nevertheless, the controllers designed up to now require a pre-planned optimized trajectory including this criterion, and as a result, this strategy can only be used by qualified users. In order to avoid this drawback and to cross these types of singularities even if the trajectory is not pre-planned, this paper proposes a controller based on virtual constraints. Furthermore, the controller is integrated in a multi-control architecture in order to switch between a classical computed torque control far from the singularity and the virtual-constraint-based control law near to the singularity locus. Experimental results on a five-bar mechanism validated the automatic Type 2 singularity crossing.

A Singularity-Robust LQR Controller for Parallel Robots

“…The convergence rate of the controller can be tunned by changing the Q and R matrices of Eq. (11). The plot of Fig.…”

“…Moreover, CT controllers fail perilously near singularities because, as mentioned before, the inverse dynamics is generally unsolvable at such configurations. A possible workaround is to use multi-control architectures [11], which in the proximity of a singularity switch from a classical CT law to a controller based on virtual constraints. The solution is elegant, but the switching from one controller to the other depends on a heuristic parameter that needs to be tuned experimentally.…”

“…Therefore, we set the terminal time t f of the cost in Eq. (11) to infinity. Moreover, by using y = U ⊤x , this cost can be rewritten in terms of the local coordinates y:…”

Randomized Planning of Dynamic Motions Avoiding Forward Singularities

“…To circumvent these issues, several strategies have been proposed. For example, one can use actuation redundancy to avoid all, or almost all forward singularities [17], or design specific control laws able to traverse the singularities with bounded actions and consistent accelerations [10,12]. Although both approaches are interesting, they also come with a few caveats.…”

A New Index for Detecting and Avoiding Type II Singularities for the Control of Non-Redundant Parallel Robots

“…Hill et al (2017) applied virtual constraints in a controller to online trajectory generation during a Type II singularity crossing. The next section presents the main controllers implemented in real-time applications for crossing or avoiding a Type II singularity Briot and Arakelian (2008).…”