We present a fast method for solving rigid body contact problems with friction, based on optimizations incorporated into Lemke’s algorithm for solving linear complementarity problems. These optimizations improve computation time in general and reduce the expected solution complexity from O(n3) to nearly O(nm + m3), where n and m are the number of contacts and rigid bodies. For a fixed number of bodies the expected complexity is therefore close to O(n) . Our method also improves numerical robustness, and removes the need to explicitly compute the large matrices associated with rigid body contact problems.

This paper discusses the robotic acquisition and characterization of surface friction and roughness for real-world objects. Our motivation is the construction of detailed "reality-based" models for existing objects that can be used in haptic displays and other applications involving simulation. A key challenge addressed in this paper is the acquisition of these surface properties on real objects with nontrivial shape, and registration of these properties with respect to geometric models of the shape. We show how Coulomb friction may be effectively estimated in the presence of variations in surface normal. We also show how to estimate a stochastic process model of surface roughness. Finally, we demonstrate the robotic mapping of surface friction over an entire object, using the UBC Active Measurement Facility (ACME).

We describe a system for constructing computer models of several aspects of physical interaction behavior, by scanning the response of real objects. The behaviors we can successfully scan and model include deformation response, contact textures for interaction with force-feedback, and contact sounds. The system we describe uses a highly automated robotic facility that can scan behavior models of whole objects. We provide a comprehensive view of the modeling process, including selection of model structure, measurement, estimation, and rendering at interactive rates. The results are demonstrated with two examples: a soft stuffed toy which has significant deformation behavior, and a hard clay pot which has significant contact textures and sounds. The results described here make it possible to quickly construct physical interaction models of objects for applications in games, animation, and e-commerce.

We present an integrated system in which an operator uses a simulated environment to program part-mating and contact tasks. Generation of models within this virtual environment is facilitated using a fast, occlusion tolerant, 3D grey-scale vision system which can recognize and accurately locate objects within the work site. A major goal of this work is to make robotic programming easy and intuitive for untrained users working with standard desktop hardware. Simulation offers the ease-of-use benefits of "programming by demonstration", coupled with the ability to create a programmer-friendly virtual environment. Within a simulated environment, it is also straightforward to track and interpret an operator's actions. The simulator models objects as polyhedra and implements full 3D contact dynamics. When a manipulation task is completed, local planning techniques are used to turn the virtual environment's motion sequence history into a set of robot motion commands capable of realizing the prescribed task.

A new method of handling the kinematic singularities of serial robotic manipulators is proposed. The idea is to transform the manipulator's workspace W into a desingularized workspace W*. Robotic motions can then be planned anywhere in W*, subject to limits on spatial velocity and acceleration, and the resulting joint velocities and accelerations will be well-behaved and bounded. W* differs from W only near a singularity surface, where a deformation is applied in the direction normal to the surface. While the technique does not handle self-motion singularities and may not be practical in some cases, it is very easy to implement for certain manipulators, such as the PUMA, which is studied in the paper. When applicable, the method offers various advantages when compared with other methods of singularity control.

An algorithm is presented which computes feasible manipulator trajectories along fixed paths in the presence of kinematic singularities. The resulting trajectories are close to minimum time, given an inverse kinematic solution for the path and bounds on joint velocities and accelerations. The algorithm has complexity O(M log M), with respect to the number of joint coordinates M, and works using "coordinate pivoting", in which the path timing is generated locally with respect to whichever joint coordinate is changing the fastest. This allows the handling of singularities, including linear self-motions (e.g., wrist singularities), where the path speed is zero but other joint velocities are non-zero. Examples involving the PUMA manipulator are shown.

It is shown that smooth spatial paths for nonredundant serial robots can always be smoothly reparametrized in the vicinity of kinematic singularities with finite root multiplicity using a Puiseux series. This reparametrization, based on the algebraic structure of the manipulator kinematics, is formed using the /spl nu/th root of the path parameter distance to the singularity, where /spl nu/ is some integer not exceeding the root multiplicity of the singularity. By contrast, self-motion singularities, which have infinite root multiplicity, do not possess such a reparametrization. However, smooth motions directly through such singularities are generally possible because approaching path solutions are unaffected by them. These results help quantify how joint derivatives blow up at singularities, and can readily be used to generate singularity-robust motions along any path, with no spatial error. This is illustrated with an example involving the PUMA manipulator.

We describe an implemented model-based telerobotic system designed to investigate assembly and other tasks involving contact and manipulation of known objects. Key features of our system include ease of maintaining a world model at the operator site and a task-centric operator interface. Our system incorporates gray-scale model-based vision to assist in building and maintaining the local model. The local model is used to provide a task-centric operator interface, emphasizing the natural and direct manipulation of objects, with the robot's presence indicated in a more abstract fashion. The operator interface is designed to work with widely available and inexpensive desktop computers with low DOF input devices (such as a mouse). We also describe experimental results to date, which include performing assembly-like tasks over the Internet.

It is shown that the joint solution for a nonredundant robot following a piecewise analytic path can be expressed at kinematic singularities using a fractional power series (or Puiseux series). This is of use because the derivatives of such joint solutions often become infinite at singularities, making it difficult to track the path without incurring very large joint velocities and accelerations. Puiseux series provide a way to smoothly reparameterize the joint solution at singularities, which can be applied to path timing and perhaps other aspects of robot control.

An algorithm is presented for computing the necessary time-scaling to allow a non-redundant manipulator to follow a fixed Cartesian path containing kinematic singularities. The resulting trajectory is close to minimum-time, subject to bounds on joint velocities and accelerations. The algorithm assigns a series of knot points along the path, increasing the knot density in the vicinity of singularities. Appropriate path velocities are then computed for each knot point. Two experiments involving the PUMA manipulator are shown.

A techniques for transitioning between path segments that is tolerant to dynamic changes arising from sensor inputs is described. The main idea is to blend the segments together in a way that does not require advance knowledge of the paths. It is also possible to decompose the transition into an action which brings to rest the motion along the final path. By adjusting the timing of these two components, one may control the shape of the transition, in both time and space, so as to satisfy different task constraints.>