Ken Goldberg

Eigentaste: A Constant Time Collaborative Filtering Algorithm

Eigentaste is a collaborative filtering algorithm that uses universal queries to elicit real-valued user ratings on a common set of items and applies principal component analysis (PCA) to the resulting dense subset of the ratings matrix. PCA facilitates dimensionality reduction for offline clustering of users and rapid computation of recommendations. For a database of n users, standard nearest-neighbor techniques require O(n) processing time to compute recommendations, whereas Eigentaste requires O(1) (constant) time. We compare Eigentaste to alternative algorithms using data from Jester, an online joke recommending system.Jester has collected approximately 2,500,000 ratings from 57,000 users. We use the Normalized Mean Absolute Error (NMAE) measure to compare performance of different algorithms. In the Appendix we use Uniform and Normal distribution models to derive analytic estimates of NMAE when predictions are random. On the Jester dataset, Eigentaste computes recommendations two orders of magnitude faster with no loss of accuracy. Jester is online at: http://eigentaste.berkeley.edu

Orienting polygonal parts without sensors

In manufacturing it is often necessary to orient parts prior to packing or assembly. We say that a planar part ispolygonal if its convex hull is a polygon. We consider the following problem: given a list ofn vertices describing a polygonal part whose initial orientation is unknown, find the shortest sequence of mechanical gripper actions that is guaranteed to orient the part up to symmetry in its convex hull. We show that such a sequence exists for any polygonal part by giving anO[n2 logn) algorithm for finding the sequence. Since the gripper actions do not require feedback, this result implies that any polygonal part can be orientedwithout sensors.

LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information

In this paper we present LQG-MP (linear-quadratic Gaussian motion planning), a new approach to robot motion planning that takes into account the sensors and the controller that will be used during the execution of the robot’s path. LQG-MP is based on the linear-quadratic controller with Gaussian models of uncertainty, and explicitly characterizes in advance (i.e. before execution) the a priori probability distributions of the state of the robot along its path. These distributions can be used to assess the quality of the path, for instance by computing the probability of avoiding collisions. Many methods can be used to generate the required ensemble of candidate paths from which the best path is selected; in this paper we report results using rapidly exploring random trees (RRT). We study the performance of LQG-MP with simulation experiments in three scenarios: (A) a kinodynamic car-like robot, (B) multi-robot planning with differential-drive robots, and (C) a 6-DOF serial manipulator. We also present a method that applies Kalman smoothing to make paths Ck-continuous and apply LQG-MP to precomputed roadmaps using a variant of Dijkstra’s algorithm to efficiently find high-quality paths.

Planning for Steerable Bevel-tip Needle Insertion Through 2D Soft Tissue with Obstacles

We explore motion planning for a new class of highly flexible bevel-tip medical needles that can be steered to previously unreachable targets in soft tissue. Planning for these procedures is difficult because the needles bend during insertion and cause the surrounding soft tissues to displace and deform. In this paper, we develop a planning algorithm for insertion of highly flexible bevel-tip needles into soft tissues with obstacles in a 2D imaging plane. Given an initial needle insertion plan specifying location, orientation, bevel rotation, and insertion distance, the planner combines soft tissue modeling and numerical optimization to generate a needle insertion plan that compensates for simulated tissue de formations, locally avoids polygonal obstacles, and minimizes needle insertion distance. The simulator computes soft tissue deformations using a finite element model that incorporates the effects of needle tip and frictional forces using a 2D mesh. We formulate the planning problem as a constrained nonlinear optimization problem that is locally minimized using a penalty method that converts the formulation to a sequence of unconstrained optimization problems. We apply the planner to bevel-right and bevel-left needles and generate plans for targets that are unreachable by rigid needles.

The Stochastic Motion Roadmap: A Sampling Framework for Planning with Markov Motion Uncertainty.

We present a new motion planning framework that explicitly considers uncertainty in robot motion to maximize the probability of avoiding collisions and successfully reaching a goal. In many motion planning applications ranging from maneuvering vehicles over unfamiliar terrain to steering flexible medical needles through human tissue, the response of a robot to commanded actions cannot be precisely predicted. We propose to build a roadmap by sampling collision-free states in the configuration space and then locally sampling motions at each state to estimate state transition probabilities for each possible action. Given a query specifying initial and goal configurations, we use the roadmap to formulate a Markov Decision Process (MDP), which we solve using Infinite Horizon Dynamic Programming in polynomial time to compute stochastically optimal plans. The Stochastic Motion Roadmap (SMRM) thus combines a sampling-based roadmap representation of the configuration space, as in PRMs, with the well-established theory of MDPs. Generating both states and transition probabilities by sampling is far more flexible than previous Markov motion planning approaches based on problem-specific or grid-based discretizations. In this paper, we formulate SMRM and demonstrate it by generating non-holonomic plans for steerable needles, a new class of medical needles that follow curved paths through soft tissue and can be modeled as a variant of a Dubins car. Using randomized simulations, we show that SMRM is computationally faster than a previously reported MDP method and confirm that SMRM generates motion plans with a significantly higher probability of success compared to shortest-path plans.

A complete algorithm for designing planar fixtures using modular components

We present an implemented algorithm that accepts a polygonal description of a parts silhouette, and efficiently constructs the set of all feasible fixture designs that kinematically constrain the part in the plane. Each fixture is composed of three locators rigidly attached to the lattice and one sliding clamp, and constrains the part without relying on friction. The algorithm is based on an efficient enumeration of admissible designs that exploits part geometry and graphical force analysis. The algorithm run time is linear in the number of designs found, which is bounded by a polynomial in the number of part edges and the parts maximal diameter in lattice units. Our review of the literature suggests that this is the first fixturing algorithm that is complete in the sense that it is guaranteed to find all admissible fixture designs for an arbitrary polygonal silhouette and to identify the optimal fixture relative to an arbitrary quality metric. The algorithm does not consider out-of-plane forces or motions; however, we view this planar result as an essential component of a larger algorithm that solves the 3D fixture design problem by treating the planar and out-of-plane constraint problems separately. This approach is analogous to the widely used 3-2-1 fixture design heuristic.

Parallel microassembly with electrostatic force fields

Microscopic (submillimeter) parts are often fabricated in parallel at high density but must then be assembled into patterns with lower spatial density. We propose a new approach to microassembly using: 1) ultrasonic vibration to eliminate friction and adhesion; and 2) electrostatic forces to position and align parts in parallel. We describe experiments on the dynamic and frictional properties of collections of microscopic parts under these conditions. We first demonstrate that ultrasonic vibration can be used to overcome adhesive forces; we also compare part behavior in air and vacuum. Next, we demonstrate that parts can be positioned and aligned using a combination of vibration and electrostatic forces. Finally, we demonstrate part sorting by size. Our goal is a systematic method for designing implementable planar force fields for microassembly based on part geometry.

Collaborative teleoperation via the Internet

We describe a system that allows a distributed group of users to simultaneously teleoperate an industrial robot arm via the Internet. A Java applet at each client streams mouse motion vectors from up to 3D users; a sewer aggregates these inputs to produce a single control stream for the robot. Users receive visual feedback from a digital camera mounted above the robot arm. To our knowledge, this is the first collaboratively controlled robot on the Internet.

Interactive simulation of surgical needle insertion and steering

We present algorithms for simulating and visualizing the insertion and steering of needles through deformable tissues for surgical training and planning. Needle insertion is an essential component of many clinical procedures such as biopsies, injections, neurosurgery, and brachytherapy cancer treatment. The success of these procedures depends on accurate guidance of the needle tip to a clinical target while avoiding vital tissues. Needle insertion deforms body tissues, making accurate placement difficult. Our interactive needle insertion simulator models the coupling between a steerable needle and deformable tissue. We introduce (1) a novel algorithm for local remeshing that quickly enforces the conformity of a tetrahedral mesh to a curvilinear needle path, enabling accurate computation of contact forces, (2) an efficient method for coupling a 3D finite element simulation with a 1D inextensible rod with stick-slip friction, and (3) optimizations that reduce the computation time for physically based simulations. We can realistically and interactively simulate needle insertion into a prostate mesh of 13,375 tetrahedra and 2,763 vertices at a 25 Hz frame rate on an 8-core 3.0 GHz Intel Xeon PC. The simulation models prostate brachytherapy with needles of varying stiffness, steering needles around obstacles, and supports motion planning for robotic needle insertion. We evaluate the accuracy of the simulation by comparing against real-world experiments in which flexible, steerable needles were inserted into gel tissue phantoms.

Motion planning with sequential convex optimization and convex collision checking

We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naïve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt. We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http://rll.berkeley.edu/trajopt/ijrr.