Category: Uncategorized

An approach to the problem of controlling automated assembly tasks using artificial potential functions is described. The authors address the automatic generation of actuator commands for a robot manipulator that result in the motion of a collection of rigid-body parts from disassembled initial configurations to an assembled final configuration. A simple class of tasks, 2D sphere assemblies, is examined. A primitive constructive theory for the control of this class of tasks is presented. Preliminary computer simulations demonstrate that the proposed approach may provide surprisingly good performance.

We review our progress to date in eliciting dynamically dexterous behaviors from a three degree of freedom direct drive robot manipulator whose real-time stereo cameras provide 60 Hz sampled images of multiple freely falling bodies in highly structured lighting conditions. At present, the robot is capable of forcing a single ping-pong ball into a specified steady state (near) periodic vertical motion by repeated controlled impacts with a rigid paddle. The robot sustains the steady state behavior over long periods (typically thousands and thousands of impacts) and is capable of recovering from significant unexpected adversarial perturbations of the ball’s flight phase. Gain tuning experiments corroborate our contention that the stability mechanism underlying the robot’s reliability can be attributed to the same nonlinear dynamics responsible for analogous behavior in a one degree of freedom forebear. We are presently extending an algorithm for simultaneously juggling two bodies developed in that earlier work to the three dimensional case.

How is navigating a unicycle amidst obstacles like manipulating beads on a necklace? This paper addresses that question by introducing a simple control system that appears to offer a common dynamical model for both situations. System (1) consists of a trivially controlled set of “steering” state variables and an additional set of “body” state variables that can be “driven” in a direction determined by the steering variables. The task will be to bring the state of the system to some desired equilibrium using feedback. A defect in the “steered” vector field precludes the possibility of stabilization via a single continuous feedback controller – the essence of what feedback is all about – incurs the necessity of a hierarchical system.

For more information: Kod*Lab

An autonomous machine requires a description of its designated task in a language that it ‘understands’. The machine language of robots — physical mechanisms endowed with actuators and sensory devices for the purpose of performing work — is the language of dynamical systems. Since the diversity of robotic tasks is immense and our practical experience with computationally well endowed sensed and actuated mechanisms is still very slight, there seems little possibility of imposing at present a meaningful uniformity of description and command methodology on the practice of building these machines. However, a number of thematic desiderata can be articulated whose pursuit will arguably increase the ease of designing robotic algorithms that are predictably successful. This paper presents a summary of our approach to a number of robotic tasks that brings out by example the nature and utility of these desiderata.

For more information: Kod*Lab

This paper concerns a simple extension of Lord Kelvin’s observation that energy decays in a dissipative mechanical system. The global limit behavior ofsuch systems can be made essentially equivalent to that of much simpler gradient systems by the introduction of a “navigationfunction” in the role of an artificial field. This recourse to the mechanical system’s natural motion helps transform the open-ended problem of autonomous machine design into the more structured problem of finding an appropriate “cost function” in the many situations that the goal may be encoded as a setpoint problem with configuration constraints.

This paper offers a unified exposition of some recent results [13, 12, 15] heretofore scattered throughout a more mathematically oriented literature that strengthen our original suggestion [8, 9] concerning the utility of controlling natural motion as a means of simultaneously encoding, planning and effecting tasks in mechanical systems. The chief theoretical insight, Theorem 2, is a global global version of Lord Kelvin’s century old result on the dissipation of total energy. Establishing this extension yields a rather general design principlethe notion of a navigation function-that seems to have useful application in a variety of settings. Roughly speaking, it offers a checklist of criteria for achieving the strongest possible convergence properties allowed on a configuration space by a smooth and bounded force/torque control strategy. Some simple examples introduced here may aid the exposition of these ideas. A sequel [10] to this paper illustrates how the ideas may be applied in more realistic settings.

This paper presents two setpoint regulation problems that may be distinguished from the traditional preview of feedback design by the a priori impossibility of building a smooth bounded controller whose closed loop yields asymptotic stability while preserving configuration constraints. An appeal to the theoretical ideas introduced in [13] yields a solution to each of these problems in the form of a navigation function thatserves as an instance of the natural control philosophy. That is to say, the intrinsic dynamics of the mechanical system, when properly “programmed” are capable of “solving” what have often been cast as planning problems. The resulting closed loop behavior demonstrates a kind of autonomy in that the goal is achieved with probability one and with no further intervention on the part of a “higher level planner.”

An intelligent machine is autonomous. An autonomous machine can operate successfully in a diversity of situations without resort to intervention by “higher level” processes, for example, humans. Physical machines are ultimately force or torque controlled dynamical systems: the specification of input torques, whether via syntactic prescriptions or feedback controllers, results in certain classes of vector fields. Control procedures whose resulting vector fields have globally attracting goal states may properly be said to evince autonomous behavior. In this light it makes sense to “program” robots using the language of dynamical systems via feedback. This talk will review various procedures developed within the Yale Robotics Lab that result in provably autonomous behavior according to the criterion developed above. These procedures are expressed in a rudimentary “geometric programming language” appropriate to the domain of tasks being undertaken and result in closed loop dynamical systems with global convergence properties (often, the strongest that the topology of the program can allow). A variety of simulation results and physical experimental studies will attest to the practicability of these methods.

For more information: Kod*Lab

An approach to the problem of automated assembly planning and control using artificial potential functions is described. A simple class of tasks, 2D sphere assemblies, is examined. A constructive theory for the planning and control of this class of tasks is presented. Computer simulations demonstrate that the approach may provide surprisingly good performance.

In a continuing program of research in robotic control of intermittent dynamical tasks, we have constructed a three degree of freedom robot capable of juggling a ball falling freely in the earth’s gravitational field. This work is a direct extension of that previously reported in [7, 3, 5, 4]. The present paper offers a comprehensive description of the new experimental apparatus and a brief account of the more general kinematic, dynamical, and computational understanding of the previous work that underlie the operation of this new machine.

For more information: Kod*Lab