A convex polynomial model for planar sliding mechanics: theory, application, and experimental validation

Abstract

We propose a polynomial model for planar sliding mechanics. For the force-motion mapping, we treat the set of generalized friction loads as the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. The polynomial is confined to be convex even-degree homogeneous in order to obey the maximum work inequality, symmetry, shape invariance in scale, and fast invertibility. We present a simple and statistically efficient model identification procedure using a sum-of-squares convex relaxation. We then derive the kinematic contact model that resolves the contact modes and instantaneous object motion given a position controlled manipulator action. The inherently stochastic object-to-surface friction distributions are modeled by sampling polynomial parameters from distributions that preserve sum-of-squares convexity. Thanks to the model smoothness, the mechanics of patch contact is captured while being computationally efficient without mode selection at support points. Simulation and robotic experiments on pushing and grasping validate the accuracy and efficiency of our approach.

Omnipush: accurate, diverse, real-world dataset of pushing dynamics with RGB-D video

“…Since we presented our earlier dataset on planar pushing [1], it has been directly used for: 1) Stochastic modeling: [23,10,17] 2) Modeling from rendered images: [16] 3) Model identification: [24] 4) Learning models for control: [25,26] 5) Filtering: [27] 6) Meta-learning: [28] With this new dataset we hope to further facilitate research in learning models and control.…”

Quasi-static analysis of planar sliding using friction patches

“…A more realistic friction model should be able to distinguish between static and dynamic friction coefficients. Moreover, higher-order approximation of LS proposed by Zhou et al (2018) can be adapted to our approach, although there may not exist efficient algorithms to solve the resulting systems of equation.…”

A model predictive approach for online mobile manipulation of non-holonomic objects using learned dynamics

“…Some studies are based on learning a mapping between actions and the resulting motion to describe an object’s dynamic behavior and inform future goal-directed behavior (Fitzpatrick et al, 2003; Ogata et al, 2005; Zhou et al, 2018). Li et al (2018) used a deep recurrent neural network model to learn object motion properties for planar pushing for a single object.…”