John F. Canny

A Computational Approach to Edge Detection

This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.

Planning optimal grasps

The authors address the problem of planning optimal grasps. Two general optimality criteria that consider the total finger force and the maximum finger force are introduced and discussed. Their formalization using various metrics on a space of generalized forces is detailed. The geometric interpretation of the two criteria leads to an efficient planning algorithm. An example of its use in a robotic environment equipped with two-jaw and three-jaw is described.<<ETX>>

Collaborative filtering with privacy via factor analysis

Collaborative filtering (CF) is valuable in e-commerce, and for direct recommendations for music, movies, news etc. But todays systems have several disadvantages, including privacy risks. As we move toward ubiquitous computing, there is a great potential for individuals to share all kinds of information about places and things to do, see and buy, but the privacy risks are severe. In this paper we describe a new method for collaborative filtering which protects the privacy of individual data. The method is based on a probabilistic factor analysis model. Privacy protection is provided by a peer-to-peer protocol which is described elsewhere, but outlined in this paper. The factor analysis approach handles missing data without requiring default values for them. We give several experiments that suggest that this is most accurate method for CF to date. The new algorithm has other advantages in speed and storage over previous algorithms. Finally, we suggest applications of the approach to other kinds of statistical analyses of survey or questionaire data.

New lower bound techniques for robot motion planning problems

We present new techniques for establishing lower bounds in robot motion planning problems. Our scheme is based on path encoding and uses homotopy equivalence classes of paths to encode state. We first apply the method to the shortest path problem in 3 dimensions. The problem is to find the shortest path under an Lp metric (e.g. a euclidean metric) between two points amid polyhedral obstacles. Although this problem has been extensively studied, there were no previously known lower bounds. We show that there may be exponentially many shortest path classes in single-source multiple-destination problems, and that the single-source single-destination problem is NP-hard. We use a similar proof technique to show that two dimensional dynamic motion planning with bounded velocity is NP-hard. Finally we extend the technique to compliant motion planning with uncertainty in control. Specifically, we consider a point in 3 dimensions which is commanded to move in a straight line, but whose actual motion may differ from the commanded motion, possibly involving sliding against obstacles. Given that the point initially lies in some start region, the problem of finding a sequence of commanded velocities which is guaranteed to move the point to the goal is shown to be non-deterministic exponential time hard, making it the first provably intractable problem in robotics.

Motion of two rigid bodies with rolling constraint

The motion of two rigid bodies under rolling constraint is considered. In particular, the following two problems are addressed: (1) given the geometry of the rigid bodies, determine the existence of an admissible path between two contact configurations; and (2) assuming that an admissible path exists, find such a path. First, the configuration space of contact is defined, and the differential equations governing the rolling constraint are derived. Then, a generalized version of Frobeniuss theorem, known as Chows theorem, for determining the existence of motion is applied. Finally, an algorithm is proposed that generates a desired path with one of the objects being flat. Potential applications of this study include adjusting grasp configurations of a multifingered robot hand without slipping, contour following without dissipation or wear by the end-effector of a manipulator, and wheeled mobile robotics. >

Collision Detection for Moving Polyhedra

We consider the collision-detection problem for a three-dimensional solid object moving among polyhedral obstacles. The configuration space for this problem is six-dimensional, and the traditional representation of the space uses three translational parameters and three angles (typically Euler angles). The constraints between the object and obstacles then involve trigonometric functions. We show that a quaternion representation of rotation yields constraints which are purely algebraic in a seven-dimensional space. By simple manipulation, the constraints may be projected down into a six-dimensional space with no increase in complexity. The algebraic form of the constraints greatly simplifies computation of collision points, and allows us to derive an efficient exact intersection test for an object which is translating and rotating among obstacles.

Kinodynamic motion planning

Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must find a minimal-time trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration. We consider the simplified case of a point mass under Newtonian mechanics, together with velocity and acceleration bounds. The point must be flown from a start to a goal, amidst polyhedral obstacles in 2D or 3D. Although exact solutions to this problem are not known, we provide the first provably good approximation algorithm, and show that it runs in polynomial time

Impulse-based simulation of rigid bodies

We introduce a promising new approach to rigid body dynamic simulation called impulse-based simulation. The method is well suited to modeling physical systems with large numbers of collisions, or with contact modes that change frequently. All types of contact (colliding, rolling, sliding, and resting) are modeled through a series of collision impulses between the objects in contact, hence the method is simpler and faster than constraint-based simulation. We have implemented an impulse-based simulator that can currently achieve interactive simulation times, and real time simulation seems within reach. In addition, the simulator has produced physically accurate results in several qualitative and quantitative experiments. After giving an overview of impulse-based dynamic simulation, we discuss collision detection and collision response in this context, and present results from several experiments.

Nonholonomic Motion Planning

Nonholonomic kinematics and the role of elliptic functions in constructive controllability, R.W. Brockett and L. Dai steering nonholonomic control systems using sinusoids, R.M. Murray and S. Shakar Sastry smooth time-periodic feedback solutions for nonholonomic motion planning, L. Gurvits and Zexiang Li lie bracket extensions and averaging - the single-bracket case, H.J. Sussmann and Wensheng Liu singularities and topological aspects in nonholonomic motion planning, J.-P. Laumond motion planning for nonholonomic dynamic systems, M. Reyhanoglu et al a differential geometric approach to motion planning, G. Lafferriere and H.J. Sussmann planning smooth paths for mobile robots, P. Jacobs and J. Canny nonholonomic control and gauge theory, R. Montgomery optimal nonholonomic motion planning for a falling cat, C. Fernandes et al nonholonomic behaviour in free-floating space manipulators and its utilization, E.G. Papadopoulos.

Planning smooth paths for mobile robots

The authors consider the problem of planning paths for a robot which has a minimum turning radius. This is a first step towards accurately modeling a robot with the kinematics of a car. The technique used is to define a set of canonical trajectories which satisfy the nonholonomic constraints imposed. A configuration space can be constructed for these trajectories in which there is a simple characterization of the boundaries of the obstacles generated by the workspace obstacles. The authors describe a graph search algorithm which divides the configuration space into sample trajectories. The characterization of the boundaries makes it possible to calculate an approximate path in time O(n/sup 3// delta log n+Alog (n/ delta )), where n is the number of obstacle vertices in the environment, A is the number of free trajectories, and delta describes the robustness of the generated path and the closeness of the approximation. The authors also describe a plane sweep for computing the configuration space obstacle for a trajectory segment. They use this to generate robust paths using a quadtree based algorithm in time O(n/sup 4/log n+(n/ delta /sup 2/)).<<ETX>>