Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

In this paper, we survey the field of robotic grasping and the work that has been done in this area over the last two decades, with a slight bias toward the development of the theoretical framework and analytical results in this area.

Robotic grasping and contact: a review

Contact modeling is an important aspect of simulation of many robotic tasks. In the paper, a compliant contact model with nonlinear damping is investigated, and many previously unknown characteristics of the model are developed. Compliance is used to eliminate many of the problems associated with using rigid body models with Coulomb friction, while the use of nonlinear damping eliminates the discontinuous impact forces and most sticky tensile forces which arise in Kelvin-Voigt linear models. Two of the most important characteristics of the model are the dependence of the coefficient of restitution on velocity and damping in a physically meaningful manner, and its computational simplicity. A full mathematical development for an impact response is given, along with the effects of the system and model parameters on energy loss. A quasistatic analysis gives results which are consistent with energy loss characteristics of a more complex distributed foundation model under sustained contact conditions. A foot contact example for a walking machine is given which demonstrates the applicability of the model for impact on foot placement, sustained contact during the support phase, and the breaking of the contact upon liftoff of the foot.

A compliant contact model with nonlinear damping for simulation of robotic systems

The use of Coulomb's friction law with the principles of classical rigid-body dynamics introduces mathematical inconsistencies. Specifically, the forward dynamics problem can have no solutions or multiple solutions. In these situations, compliant contact models, while increasing the dimensionality of the state vector, can resolve these problems. The simplicity and efficiency of rigid-body models, however, provide strong motivation for their use during those portions of a simulation when the rigid-body solution is unique and stable. In this paper, we use singular perturbation analysis in conjunction with linear complementarity theory to establish conditions under which the solution predicted by the rigid-body dynamic model is stable. We employ a general model of contact compliance to derive stability criteria for planar mechanical systems. In particular, we show that for cases with one sliding contact, there is always at most one stable solution. Our approach is not directly applicable to transitions between rolling and sliding where the Coulomb friction law is discontinuous. To overcome this difficulty, we introduce a smooth nonlinear friction law, which approximates Coulomb friction. Such a friction model can also increase the efficiency of both rigid-body and compliant contact simulation. Numerical simulations for the different models and comparison with experimental results are also presented.

Analysis of Rigid-Body Dynamic Models for Simulation of Systems With Frictional Contacts

Traditional collision intensive multi-body simulations are difficult to control due to extreme sensitivity to initial conditions or model parameters Furthermore, there may be multiple ways to achieve any one goal, and it may be difficult to codify a user's preferences before they have seen the available solutions In this paper we extend simulation models to include plausible sources of uncertainty, and then use a Markov chain Monte Carlo algorithm to sample multiple animations that satisfy constraints A user can choose the animation they prefer, or applications can take direct advantage of the multiple solutions Our technique is applicable when a probability can be attached to each animation, with “good” animations having high probability, and for such cases we provide a definition of physical plausibility for animations We demonstrate our approach with examples of multi-body rigid-body simulations that satisfy constraints of various kinds, for each case presenting animations that are true to a physical model, are significantly different from each other, and yet still satisfy the constraints

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Sampling plausible solutions to multi-body constraint problems

In automated assembly lines, part feeders often impose a bottleneck that restricts throughput. To facilitate the design of parts and assembly lines, the authors estimate feedrates based on CAD models of parts. A previous paper (Golberg and Craig, 1995) described how to predict throughput for a vision-based robotic part feeder given the distribution of part poses when parts are randomly dropped on a conveyor belt. Estimating this distribution is also useful for the design of traditional feeders such as vibratory bowls. In this paper the authors describe three algorithms for estimating pose distributions. The authors review the quasi-static estimate reported in Wiegley et al. (1992) and introduce a refinement that takes into account some measure of dynamic stability. The perturbed quasi-static estimate can be computed very rapidly and is more accurate than the quasi-static. Still more accurate are estimates based on Monte Carlo simulation using Impulse, although the latter comes at the penalty of increased computation time. The authors compare estimates from all three algorithms with physical experiments.

R. Zanutta

Papers

Estimating pose statistics for robotic part feeders