Online deformation of optimal trajectories for constrained nonprehensile manipulation

Abstract

Abstract-This paper discusses an online dynamic motion generation scheme for nonprehensile object manipulation by using a set of predefined motions and a trajectory deformation algorithm capable of incorporating positional and velocity boundary constraints. By creating optimal trajectories offline and deforming them online, computational complexity during execution is reduced considerably. As tight convex hulls of the deformed trajectories can be found, possible obstacles or workspace boundaries can be circumnavigated precisely without collision. The approach is verified through experiments on an inclined planar air-table for volleyball scenario using two 3-DoF robots.

Dynamically Consistent Online Adaptation of Fast Motions for Robotic Manipulators

“…In [34] we presented a preliminary approach for retargeting of specially designed optimal trajectories in constrained environments using cubic splines. Still, it wasn't capable of keeping desired derivative profiles and providing boundary conditions higher than velocities.…”

“…6. We presented the ball -end effector collision model based on momentum conservation in [34]. The chosen point for the rebound is…”

Spline deformation of locally optimal trajectories: Feasibility and upper bound on control inputs

“…Given system matrices of a robot model M, C, G and F, computed torque and outer loop PD controller scheme with k p , k v gains, maximum torque disturbance τ d , original optimal trajectory x o ,ẋ o , τ o and a resulting deformed trajectory x d ,ẋ d ,ẍ d satisfying given boundary conditions, the goal is to find out whether the corresponding upper bounds of the actuator torques τ ∞ are feasible at every time step. It is done by performing feasibility check not along the entire trajectory but only at some specific segmentation points of the deformed trajectory, as in [4]. The problem is reformulated as (2) where τ ∞ has to be compared with maximum input motor torque τ bound .…”

“…It was shown in [4] that the least squares solution that requires matrix inversion can be decomposed in 2 parts. The first part is a sole translation of the original optimal trajectory.…”

“…As the method does not rely on any kernel/internal state, its resolution is solely limited by the number of trajectory sampling points. In [4] the combination of a numerical optimal control method and LTE-based deformation is presented. This approach is experimentally verified using a robotic arm for constrained dynamic manipulation tasks.…”