Lex-Partitioning: A New Option for BDD Search

For the exploration of large state spaces, symbolic search using binary decision diagrams (BDDs) can save huge amounts of memory and computation time. State sets are represented and modified by accessing and manipulating their characteristic functions. BDD partitioning is used to compute the image as the disjunction of smaller subimages. In this paper, we propose a novel BDD partitioning option. The partitioning is lexicographical in the binary representation of the states contained in the set that is represented by a BDD and uniform with respect to the number of states represented. The motivation of controlling the state set sizes in the partitioning is to eventually bridge the gap between explicit and symbolic search. Let n be the size of the binary state vector. We propose an O(n) ranking and unranking scheme that supports negated edges and operates on top of precomputed satcount values. For the uniform split of a BDD, we then use unranking to provide paths along which we partition the BDDs. In a shared BDD representation the efforts are O(n). The algorithms are fully integrated in the CUDD library and evaluated in strongly solving general game playing benchmarks.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611

Gain control of saccadic eye movements is probabilistic

Saccades are rapid eye movements that orient the visual axis toward objects of interest to allow their processing by the central, highacuity retina. Our ability to collect visual information efficiently relies on saccadic accuracy, which is limited by a combination of uncertainty in the location of the target and motor noise. It has been observed that saccades have a systematic tendency to fall short of their intended targets, and it has been suggested that this bias originates from a cost function that overly penalizes hypermetric errors. Here we tested this hypothesis by systematically manipulating the positional uncertainty of saccadic targets. We found that increasing uncertainty produced not only a larger spread of the saccadic endpoints but also more hypometric errors and a systematic bias toward the average of target locations in a given block, revealing that prior knowledge was integrated into saccadic planning. Moreover, by examining how variability and bias co-varied across conditions, we estimated the asymmetry of the cost function and found that it was related to individual differences in the additional time needed to program secondary saccades for correcting hypermetric errors, relative to hypometric ones. Taken together, these findings reveal that the saccadic system uses a probabilistic-Bayesian control strategy to compensate for uncertainty in a statistically principled way and to minimize the expected cost of saccadic errors

Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification

In this paper, we propose a contact-implicit trajectory optimization (CITO) method based on a variable smooth contact model (VSCM) and successive convexification (SCvx). The VSCM facilitates the convergence of gradient-based optimization without compromising physical fidelity. On the other hand, the proposed SCvx-based approach combines the advantages of direct and shooting methods for CITO. For evaluations, we consider non-prehensile manipulation tasks. The proposed method is compared to a version based on iterative linear quadratic regulator (iLQR) on a planar example. The results demonstrate that both methods can find physically-consistent motions that complete the tasks without a meaningful initial guess owing to the VSCM. The proposed SCvx-based method outperforms the iLQR-based method in terms of convergence, computation time, and the quality of motions found. Finally, the proposed SCvx-based method is tested on a standard robot platform and shown to perform efficiently for a real-world application.Comment: Accepted for publication in ICRA 201

Task planning using physics-based heuristics on manipulation actions

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In order to solve mobile manipulation problems, the efficient combination of task and motion planning is usually required. Moreover, the incorporation of physics-based information has recently been taken into account in order to plan the tasks in a more realistic way. In the present paper, a task and motion planning framework is proposed based on a modified version of the Fast-Forward task planner that is guided by physics-based knowledge. The proposal uses manipulation knowledge for reasoning on symbolic literals (both in offline and online modes) taking into account geometric information in order to evaluate the applicability as well as feasibility of actions while evaluating the heuristic cost. It results in an efficient search of the state space and in the obtention of low-cost physically-feasible plans. The proposal has been implemented and is illustrated with a manipulation problem consisting of a mobile robot and some fixed and manipulatable objects.Peer ReviewedPostprint (author's final draft

Sampling-Based Methods for Factored Task and Motion Planning

This paper presents a general-purpose formulation of a large class of discrete-time planning problems, with hybrid state and control-spaces, as factored transition systems. Factoring allows state transitions to be described as the intersection of several constraints each affecting a subset of the state and control variables. Robotic manipulation problems with many movable objects involve constraints that only affect several variables at a time and therefore exhibit large amounts of factoring. We develop a theoretical framework for solving factored transition systems with sampling-based algorithms. The framework characterizes conditions on the submanifold in which solutions lie, leading to a characterization of robust feasibility that incorporates dimensionality-reducing constraints. It then connects those conditions to corresponding conditional samplers that can be composed to produce values on this submanifold. We present two domain-independent, probabilistically complete planning algorithms that take, as input, a set of conditional samplers. We demonstrate the empirical efficiency of these algorithms on a set of challenging task and motion planning problems involving picking, placing, and pushing

Planning robot actions under position and shape uncertainty

Geometric uncertainty may cause various failures during the execution of a robot control program. Avoiding such failures makes it necessary to reason about the effects of uncertainty in order to implement robust strategies. Researchers first point out that a manipulation program has to be faced with two types of uncertainty: those that might be locally processed using appropriate sensor based motions, and those that require a more global processing leading to insert new sensing operations. Then, they briefly describe how they solved the two related problems in the SHARP system: how to automatically synthesize a fine motion strategy allowing the robot to progressively achieve a given assembly relation despite position uncertainty, and how to represent uncertainty and to determine the points where a given manipulation program might fail