Galley Proof 9/02/2018; 15:36 File: ica–1-ica568.tex; BOKCTP/xhs p. 1 Integrated Computer-Aided Engineering -1 (2018) 1–12 1 DOI 10.3233/ICA-180568 IOS Press Robust grasp preimages under unknown mass and friction distributions Andrew Price a,* , Stephen Balakirsky b and Henrik Christensen c a Institute for Robotics and Intelligent Machines, Georgia Institute of Technology, Atlanta, GA, USA b Robotics and Autonomous Systems Division, Georgia Tech Research Institute, Atlanta, GA, USA c Department of Computer Science and Engineering, University of California, San Diego, CA, USA Abstract. This work introduces an algorithm for the computation of robust grasp preimages: the space of initial poses from which an object will converge into the desired grasp. Building on existing motion and friction models for pushed objects under contact, we describe a game-theoretic technique for estimating worst-case scenarios for difficult to observe properties like pressure and friction distributions. The use of this antagonistic model in the grasping simulations provides for a conservative estimate of the preimage of the given grasp. The antagonistic model is then validated against data from real grasping experiments on various robot grippers. Keywords: Grasping, grasp planning, differential games, motion planning, sliding 1. Introduction 1 As robots move into less-structured environments 2 requiring greater decision-making agility, the model- 3 ing and management of uncertainty will take on in- 4 creased importance. For parameters that are uncer- 5 tain, an important consideration will be whether the 6 robot agent knows sufficient information to proceed 7 with a plan, or whether further information needs to be 8 gathered. In addition, for parameters with a bounded 9 range of possibilities, considering the worst-case sce- 10 narios for those parameters allows for robust decision- 11 making, at the expense of increased computational 12 cost. 13 In the domain of grasping, such uncertainty comes 14 in a variety of forms. Positioning errors will creep 15 in from the perception systems and joint controllers. 16 Static model parameters may also be uncertain: the ex- 17 act mass distribution, coefficients of friction, and iner- 18 tial properties necessary for accurate simulation may 19 vary considerably from run to run, or even part to part. 20 * Corresponding author: Andrew Price, Institute for Robotics and Intelligent Machines, Georgia Institute of Technology, 801 Atlantic Dr NW, Atlanta, GA 30332, USA. E-mail: arprice@gatech.edu. In this work we will address both these types of errors: 21 errors in state and parameterization. 22 To lay out the problem explicitly, we want to answer 23 the following question: given a nominal grasp (rela- 24 tive pose, finger trajectories, and object geometries) 25 between a manipulator and a target object, what is the 26 set of initial conditions (pose perturbations) that will 27 still result in a successful grasp? Analogous to the def- 28 inition of the preimage of a mathematical function, we 29 term this set of initial conditions the preimage of the 30 grasp action. We consider the case of an object on a flat 31 table, with unknown mass and friction distributions. 32 To address these issues we may draw inspiration 33 from the toolboxes provided by the control theory com- 34 munity: robust control, differential game theory, and 35 capture sets to name a few. In this case, we will treat 36 grasping as playing a differential game against an op- 37 ponent Nature, who controls the bounded model pa- 38 rameters to our detriment. In the context of differen- 39 tial games, the preimage of the action assuming op- 40 timal opponent play is termed the capture set. In this 41 work, we will not attempt to derive an optimal grasp- 42 ing strategy given the geometries and sensor feedback, 43 but will rather evaluate the success and failure regimes 44 of a provided control strategy. 45 ISSN 1069-2509/18/$35.00 c  2018 – IOS Press and the author(s). All rights reserved uncorrected proof version