Anytime Hierarchical Clustering

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of nested partitions that satisfies a natural homogeneity requirement. Each recursive step re-edits the tree so as to improve a local measure of cluster homogeneity that is compatible with a number of commonly used (e.g., single, average, complete) linkage functions. As an alternative to the standard batch algorithms, we present numerical evidence to suggest that appropriate adaptations of this method can yield decentralized, scalable algorithms suitable for distributed/parallel computation of clustering hierarchies and online tracking of clustering trees applicable to large, dynamically changing databases and anomaly detection.Comment: 13 pages, 6 figures, 5 tables, in preparation for submission to a conferenc

The Penn Jerboa: A Platform for Exploring Parallel Composition of Templates

We have built a 12DOF, passive-compliant legged, tailed biped actuated by four brushless DC motors. We anticipate that this machine will achieve varied modes of quasistatic and dynamic balance, enabling a broad range of locomotion tasks including sitting, standing, walking, hopping, running, turning, leaping, and more. Achieving this diversity of behavior with a single under-actuated body, requires a correspondingly diverse array of controllers, motivating our interest in compositional techniques that promote mixing and reuse of a relatively few base constituents to achieve a combinatorially growing array of available choices. Here we report on the development of one important example of such a behavioral programming method, the construction of a novel monopedal sagittal plane hopping gait through parallel composition of four decoupled 1DOF base controllers. For this example behavior, the legs are locked in phase and the body is fastened to a boom to restrict motion to the sagittal plane. The platform's locomotion is powered by the hip motor that adjusts leg touchdown angle in flight and balance in stance, along with a tail motor that adjusts body shape in flight and drives energy into the passive leg shank spring during stance. The motor control signals arise from the application in parallel of four simple, completely decoupled 1DOF feedback laws that provably stabilize in isolation four corresponding 1DOF abstract reference plants. Each of these abstract 1DOF closed loop dynamics represents some simple but crucial specific component of the locomotion task at hand. We present a partial proof of correctness for this parallel composition of template reference systems along with data from the physical platform suggesting these templates are anchored as evidenced by the correspondence of their characteristic motions with a suitably transformed image of traces from the physical platform.Comment: Technical Report to Accompany: A. De and D. Koditschek, "Parallel composition of templates for tail-energized planar hopping," in 2015 IEEE International Conference on Robotics and Automation (ICRA), May 2015. v2: Used plain latex article, correct gap radius and specific force/torque number

Toward a Science of Robot Planning and Control

Programming machines to operate flexibly and autonomously in the physical world seems to require a sophisticated representation that encodes simultaneously the nature of a task, the nature of the environment within which the task is to be performed, and the nature of the robot’s capabilities with respect to both. We seek a scientific methodology of robot task encoding that encompasses the desired behavioral goals and environmental conditions as well. The methodology must balance the need for flexible expression of abstract human goals against the necessity of a eliciting a predictable response from the commanded machine. This talk focuses on the problem of motion planning as an example of how we propose to say what we mean to a robot and to know what we have said. For more information: Kod*La

Some Applications of Natural Motor Control

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

Adaptive Techniques for Mechanical Systems

Strict Lyapunov functions are constructed for a class of nonlinear feedback compensated mechanical systems, requiring no à priori information concerning the initial conditions of the closed-looped system. These Lyapunov functions may be used to design a stable adaptive version of the computed-torque algorithm for tracking a reference trajectory. A particular Lyapunov function is then generalized to permit an adaptive version of control scheme forced by reference dynamics rather than reference trajectory

Stabilizing Feedback Controllers for Robotic Assembly Problems

Assembly problems require that a robot with a few actuated degrees of freedom manipulate an environment with a greater number of unactuated degrees of freedom. Since the dynamical coupling between degrees of freedom in this setting is a function of their relative configuration, the motion of such systems is subject to constraints that preclude smooth feedback stabilization. In other words, in contrast to purely geometric motion planning problems, assembly planning cannot be carried out within the limits of traditional control theory. This paper explores the extent to which assembly planning and control may be effected by recourse to some other methodical means of generating stabilizing feedback controllers. For more information: Kod*La

Application of a new Lyapunov function to global adaptive attitude tracking

The introduction of error coordinates and a tracking potential on the rotations affords a global nonlinear version of inverse dynamics for attitude tracking. The resulting algorithm produces almost global asymptotically exact tracking: this convergence behavior is as strong as the topology of the phase space can allow. A new family of strict global Lyapunov functions for mechanical systems is applied to achieve an adaptive version of the inverse dynamics algorithm in the case that the inertial parameters of the rigid body are not known a priori. The resulting closed loop adaptive system is shown to be stable, and the rigid body phase errors are shown to converge to the limit trajectories of the non-adaptive algorithm

The Application of Total Energy as a Lyapunov Function for Mechanical Control Systems

Examination of total energy shows that the global limit behavior of a dissipative mechanical system is essentially equivalent to that of its constituent gradient vector field. The class of “navigation functions” is introduced and shown to result in “almost global” asymptotic stability for closed loop mechanical control systems upon which a navigation function has been imposed as an artifical potential energy. Two examples from the engineering literature - satellite attitude tracking and robot obstacle avoidance - are provided to demonstrate the utility of these observations. For more information: Kod*La

Strict Global Lyapunov Functions for Mechanical Systems

A novel Lyapunov function is introduced. The author treats the PD compensated mechanical system, which is defined on a configuration space which admits a trivial tangent bundle. Previous results are derived in a simpler form, namely, that such systems are exponentially stable, hence BIBO stable, and steady-state ouptut magnitudes are proportional to input magnitudes with a constant of proportionality depending in a simple fashion on the PD gain magnitudes. For more information: Kod*La

What is Robotics: Why Do We Need It and How Can We Get It?

Robotics is an emerging synthetic science concerned with programming work. Robot technologies are quickly advancing beyond the insights of the existing science. More secure intellectual foundations will be required to achieve better, more reliable and safer capabilities as their penetration into society deepens. Presently missing foundations include the identification of fundamental physical limits, the development of new dynamical systems theory and the invention of physically grounded programming languages. The new discipline needs a departmental home in the universities which it can justify both intellectually and by its capacity to attract new diverse populations inspired by the age old human fascination with robots. For more information: Kod*la