Biblio

Conventional wisdom is that the textbook view describes reality, and only bad people (not good people trying to get their jobs done) break the rules. And yet it doesn't, and good people circumvent.
 

Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. Any curve traced by this wire when in static equilibrium is a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper. We prove that the set of all local solutions to this problem over all possible boundary conditions is a smooth manifold of finite dimension that can be parameterized by a single chart. We show that this chart makes it easy to implement a sampling-based algorithm for quasi-static manipulation planning. We characterize the performance of such an algorithm with experiments in simulation.

Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. The curve traced by this wire can be described as a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper. The set of all local solutions to this problem is the configuration space of the wire under quasi-static manipulation. We will show that this configuration space is a smooth manifold of finite dimension that can be parameterized by a single chart. Working in this chart—rather than in the space of boundary conditions—makes the problem of manipulation planning very easy to solve. Examples in simulation illustrate our approach.

In this paper, we study quasi-static manipulation of a planar kinematic chain with a fixed base in which each joint is a linearly elastic torsional spring. The shape of this chain when in static equilibrium can be represented as the solution to a discretetime optimal control problem, with boundary conditions that vary with the position and orientation of the last link. We prove that the set of all solutions to this problem is a smooth three-manifold that can be parameterized by a single chart. Empirical results in simulation show that straight-line paths in this chart are uniformly more likely to be feasible (as a function of distance) than straightline paths in the space of boundary conditions. These results, which are consistent with an analysis of visibility properties, suggest that the chart we derive is a better choice of space in which to apply a sampling-based algorithm for manipulation planning. We describe such an algorithm and show that it is easy to implement.

This paper presents a control strategy based on model learning for a self-assembled robotic “swimmer”. The swimmer forms when a liquid suspension of ferro-magnetic micro-particles and a non-magnetic bead are exposed to an alternating magnetic field that is oriented perpendicular to the liquid surface. It can be steered by modulating the frequency of the alternating field. We model the swimmer as a unicycle and learn a mapping from frequency to forward speed and turning rate using locally-weighted projection regression. We apply iterative linear quadratic regulation with a receding horizon to track motion primitives that could be used for path following. Hardware experiments validate our approach.

In this paper, we introduce and experimentally validate a sampling-based planning algorithm for quasi-static manipulation of a planar elastic rod. Our algorithm is an immediate consequence of deriving a global coordinate chart of finite dimension that suffices to describe all possible configurations of the rod that can be placed in static equilibrium by fixing the position and orientation of each end. Hardware experiments confirm this derivation in the case where the “rod” is a thin, flexible strip of metal that has a fixed base and that is held at the other end by an industrial robot. We show an example in which a path of the robot that was planned by our algorithm causes the metal strip to move between given start and goal configurations while remaining in quasi-static equilibrium.

This paper presents an interface that allows a human user to specify a desired path for a mobile robot in a planar workspace with noisy binary inputs that are obtained at low bit-rates through an electroencephalograph (EEG). We represent desired paths as geodesics with respect to a cost function that is defined so that each path-homotopy class contains exactly one (local) geodesic. We apply max-margin structured learning to recover a cost function that is consistent with observations of human walking paths. We derive an optimal feedback communication protocol to select a local geodesic— equivalently, a path-homotopy class—using a sequence of noisy bits. We validate our approach with experiments that quantify both how well our learned cost function characterizes human walking data and how well human subjects perform with the resulting interface in navigating a simulated robot with EEG.

Presented at the NSA Science of Security Quarterly Meeting, July 2016.

The concept of differential privacy stems from the study of private query of datasets. In this work, we apply this concept to discrete-time, linear distributed control systems in which agents need to maintain privacy of certain preferences, while sharing information for better system-level performance. The system has N agents operating in a shared environment that couples their dynamics. We show that for stable systems the performance grows as O(T3/Nε2), where T is the time horizon and ε is the differential privacy parameter. Next, we study lower-bounds in terms of the Shannon entropy of the minimal mean square estimate of the system’s private initial state from noisy communications between an agent and the server. We show that for any of noise-adding differentially private mechanism, then the Shannon entropy is at least nN(1−ln(ε/2)), where n is the dimension of the system, and t he lower bound is achieved by a Laplace-noise-adding mechanism. Finally, we study the problem of keeping the objective functions of individual agents differentially private in the context of cloud-based distributed optimization. The result shows a trade-off between the privacy of objective functions and the performance of the distributed optimization algorithm with noise.

We present a controller synthesis algorithm for a discrete time reach-avoid problem in the presence of adversaries. Our model of the adversary captures typical malicious attacks envisioned on cyber-physical systems such as sensor spoofing, controller corruption, and actuator intrusion. After formulating the problem in a general setting, we present a sound and complete algorithm for the case with linear dynamics and an adversary with a budget on the total L2-norm of its actions. The algorithm relies on a result from linear control theory that enables us to decompose and precisely compute the reachable states of the system in terms of a symbolic simulation of the adversary-free dynamics and the total uncertainty induced by the adversary. We provide constraint-based synthesis algorithms for synthesizing open-loop and a closed-loop controllers using SMT solvers.

In this paper, we develop a new framework to analyze stability and stabilizability of Linear Switched Systems (LSS) as well as their gain computations. Our approach is based on a combination of state space operator descriptions and the Youla parametrization and provides a unified way for analysis and synthesis of LSS, and in fact of Linear Time Varying (LTV) systems, in any lp induced norm sense. By specializing to the l∞ case, we show how Linear Programming (LP) can be used to test stability, stabilizability and to synthesize stabilizing controllers that guarantee a near optimal closed-loop gain.

In this work we are interested in the stability and L2-gain of hybrid systems with linear flow dynamics, periodic time-triggered jumps and nonlinear possibly set-valued jump maps. This class of hybrid systems includes various interesting applications such as periodic event-triggered control. In this paper we also show that sampled-data systems with arbitrarily switching controllers can be captured in this framework by requiring the jump map to be set-valued. We provide novel conditions for the internal stability and L2-gain analysis of these systems adopting a lifting-based approach. In particular, we establish that the internal stability and contractivity in terms of an L2-gain smaller than 1 are equivalent to the internal stability and contractivity of a particular discretetime set-valued nonlinear system. Despite earlier works in this direction, these novel characterisations are the first necessary and sufficient conditions for the stability and the contractivity of this class of hybrid systems. The results are illustrated through multiple new examples.