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In this paper we demonstrate that a passive vibration strategy can bring a one-degree-of-freedom ball to a specified periodic trajectory from all initial conditions. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analysis to the parts feeding problem.

In previous papers we have reported successful laboratory implementations of a family of juggling algorithms. In all but the one degree of freedom case, these empirically successful algorithms have so far resisted our analytical efforts to explain why they work. This is in large measure a consequence of our inability to write down using elementary functions an expression for the closed loop dynamics they induce. We discuss in this paper a modified juggling algorithm whose resulting closed loop dynamics can be written down directly. We offer data establishing the empirical success of the new algorithm. Theoretical analysis of the closed loop dynamics is presently in progress.

A new class of control algorithms—the “mirror algorithms”— gives rise to experimentally observed juggling and catching behavior in a planar robotic mechanism. The simplest of these algorithms (on which all the others are founded) is provably correct with respect to a simplified model of the robot and its environment. This article briefly reviews the physical setup and underlying mathematical theory. It discusses two significant extensions of the fundamental algorithm to juggling two objects and catching. We provide data from successful empirical verifi cations of these control strategies and briefly speculate on the larger implications for the field of robotics.

For more information: Kod*Lab

Assembly problems require that a robot with fewer actuated degrees of freedom manipulate an environment containing a greater number of unactuated degrees of freedom. From the perspective of control theory, these problems hold considerable interest because they are characterized by the presence of non-holonomic constraints that preclude the possibility of feedback stabilization. In this sense they necessitate the introduction of a hierarchical controller. This paper explores these issues in the simple instance when all of the pieces to be assembled are constrained to lie on a line. A hierarchical controller is devised for this problem and is shown to be correct: the closed loop system achieves any desired final assembly from all initial configurations that lie in its connected component in configuration space; the generated sequence of motions never causes collisions between two pieces. Further examination of this approach interprets the controller’s mediation of conflicting subgoals as promoting an M-player game amongst the pieces to be assembled.

In the recent successful effort to achieve the spatial two-juggle – batting two freely falling balls into independent stable periodic vertical orbits by repeated impacts with a three degree of freedom robot arm, the authors have found it necessary to introduce a dynamical window manager into their real-time stereo vision. This paper describes these necessary enhancements to the original vision system and then proposes a more formal account of how such a feedback based sensor might be understood to work. Further experimentation will be required to determine the extent to which the analytical model explains (and might thus be used as a tool to improve) the performance of the system presently working in the laboratory.

We report on our recently achieved spatial two-juggle: the ability to bat two freely falling balls into stable periodic vertical trajectories with a single three degree of freedom robot arm using a real-time stereo camera system for sensory input. After a brief review of the previously reported one-juggle, we describe our initial approach to the two-juggle planning and control problem. We have developed a number of important refinements to our initial strategy in the course of getting the system to work, and these are reported in some detail. The paper concludes with a discussion of some data from typical two-juggle runs in the laboratory.

We discuss the sensory management strategy that has evolved over the course of our efforts to build a three degree of freedom robot capable of juggling two balls at once . A field rate stereo camera system passes estimates of the balls’ positions to a juggling algorithm that drives the robot’s joint actuators. In order to meet the stringent real-time constraints imposed by such a visual servoing task, we have found it necessary to pay increasingly careful attention to our strategy for controlling the dynamics of the camera window management system. The paper concludes with an initial attempt to formalize this control problem.

For more information: Kod*Lab

We present a new methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design. Complete information about the freespace and goal is encoded in the form of a special artificial potential function – a navigation function – that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robot’s actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. Since navigation functions exist for any robot and obstacle course, our methodology is completely general in principle. However, this paper is mainly concerned with certain constructive techniques for a particular class of motion planning problems. Specifically, we present a formula for navigation functions that guide a point-mass robot in a generalized sphere world. The simplest member of this family is a space obtained by puncturing a disc by an arbitrary number of smaller disjoint discs representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation that we show how to build. Our constructions exploit these coordinate transformations to adapt a navigation function on the model space to its more geometrically complicated (but topologically equivalent) instances. The formula that we present admits sphere-worlds of arbitrary dimension and is directly applicable to configuration spaces whose forbidden regions can be modeled by such generalized discs. We have implemented these navigation functions on planar scenarios, and simulation results are provided throughout the paper.