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This paper addresses the coupled navigation and control problem for fully actuated dynamical systems operating in cluttered environments. The proposed method composes local feedback control policies to address the global problem in a formally correct manner. Our contribution extends the method of sequential composition to a new class of flow-through policies, which are defined for an idealized point robot that is subject to bounds on velocity and acceleration. These policies, which are defined over convex polytopes, express natural behaviors and guarantee safe trajectories while respecting system constraints. This paper presents a constructive technique for building hybrid control systems with guaranteed transitions and stability properties. Simulation results demonstrate policy-based decision making for various initial conditions. Index Terms--Feedback control, hybrid controls, path planning.

Byline: Ravi Balasubramanian (Computer Science and Engineering, University of Washington, Box 352350, Seattle, WA 98195-2350, USA, bravi@cs.washington.edu); Alfred A. Rizzi (Boston Dynamics, 614 Massachusetts Avenue, Cambridge, MA 02139, USA); Matthew [...]

In this paper, we generalize our prior results in motion analysis to design gaits for a more general family of underactuated mechanical systems. In particular, we analyze and generate gaits for mixed mechanical systems which are systems whose motion is simultaneously governed by both a set of non-holonomic velocity constraints and a notion of a generalized momentum being instantaneously conserved along allowable directions of motion. Through proper recourse to geometric mechanics, we are able to show that the resulting motion from a gait has two portions: a geometric and a dynamic contribution. The main challenge in motion planning for a mixed system is understanding how to separate the geometric and dynamic contributions of motion due to a general gait, thus simplifying gait analysis. In this paper, we take the first step towards addressing this challenge in a generalized framework. Finally, we verify the generality of our approach by applying our techniques to novel mechanical systems which we introduce in this paper as well as by verifying that seemingly different prior motion planning results could actually be explained using the gait analysis presented in this paper. KEY WORDS--gait generation, motion control, underactuated robots, non-holonomic motion planning, mixed mechanical systems, generalized momentum, scaled momentum, variable inertia snakeboard, Stokes' theorem, 1. Introduction In a companion paper (Shammas et al., 2007), we explore gait generation and analysis techniques for two classes of mechanical systems: purely mechanical and principally kinematic systems. These [...]

In this paper we generate gaits for two types of underactuated mechanical systems: principally kinematic and purely mechanical systems. Our goal is to specify inputs in the form of gaits, that is, a sequence of controlled shape changes of a multi-bodied mechanical system that when executed would produce a desired change in the unactuated position or orientation variables of the entire mechanical system. In other words, we want to indirectly control the unactuated degrees of freedom of the mechanical system utilizing a controlled 'internal' shape change. More precisely, in this paper we develop a gait evaluation tool which easily measures the change of position, computed in a body-attached coordinate frame, due to any closed curve in the shape space. This evaluation tool is simple enough that we can use it to generate gaits or to design curves that move the mechanical system along a desired direction. Finally, we verify that this gait analysis technique applies to two seemingly different classes of mechanical systems, purely mechanical and principally kinematic systems, and unify the gait generation problem for both classes. KEY WORDS--gait generation, motion control, underactuated robots, non-holonomic motion planning, generalized momentum, purely mechanical systems, principally kinematic systems, Stokes' theorem, 1. Introduction In this paper we develop a general and intuitive formulation of the gait analysis and generation problem that applies to two classes of mechanical systems. We actually classify [...]

Abstract In spray painting applications, it is essential to generate a spray gun trajectory such that the entire surface is completely covered and receives an acceptably uniform layer of paint [...]

Abstract Effective modeling and control of multibody systems interacting with their environment through frictional contact remains a challenging problem. In this paper, we address the planar version of this problem [...]

We present a working implementation of a dynamics based architecture for visual sensing. This architecture provides field rate estimates of the positions and velocities of two independent falling balls in the face of repeated visual occlusions and departures from the field of view. The practical success of this system can be attributed to the interconnection of two strongly nonlinear dynamical systems: a novel triangulating state estimator; and an image plane window controller. We detail the architecture of this active sensor, provide data documenting its performance, and offer an analysis of its soundness in the form of a convergence proof for the estimator and a boundedness proof for the manager.

This paper presents a new model-based adaptive controller and proof of its global asymptotic stability with respect to the standard rigid-body model of robot-arm dynamics. Experimental data from a study of one new and several established globally asymptotically stable adaptive controllers on two very different robot arms 1) demonstrate the superior tracking performance afforded by the model-based algorithms over conventional PD control, 2) demonstrate and compare the superior performance of adaptive model-based algorithms over their nonadaptive counterparts, 3) reconcile several previous contrasting empirical studies, and 4) examine contexts that compromise their advantage.