Nils Napp

Programmable parts: a demonstration of the grammatical approach to self-organization

In this paper, we introduce a robotic implementation of the theory of graph grammars (Klavins et al., 2005), which we use to model and direct self-organization in a formal, predictable and provably-correct fashion. The robots, which we call programmable parts, float passively on an air table and bind to each other upon random collisions. Once attached, they execute local rules that determine how their internal states change and whether they should remain bound. We demonstrate through experiments how they can self-organize into a global structure by executing a common graph grammar in a completely distributed fashion. The system also presents a challenge to the grammatical method (and to distributed systems approaches in general) due to the stochastic nature of its dynamics. We conclude by discussing these challenges and our initial approach to addressing them.

Optimal Rules for Programmed Stochastic Self-Assembly

We consider the control of programmable selfassembling systems whose dynamics are governed by stochastic reaction-diffusion dynamics. In our system, particles may decide the outcomes of reactions initiated by the environment, thereby steering the global system to produce a desired assembly type. We describe a method that automatically generates a program maximizing yield based on tuning the rates of experimentally determined reaction pathways. We demonstrate the method using theoretical examples and with a robotic testbed. Finally, we present, in the form of a graph grammar, a communication protocol that implements the generated programs in a distributed manner.

Setpoint regulation for stochastically interacting robots

We present an integral feedback controller that regulates the average copy number of an assembly in a system of stochastically interacting robots. The mathematical model for these robots is a tunable reaction network, which makes this approach applicable to a large class of other systems, including ones that exhibit stochastic self-assembly at various length scales. We prove that this controller works for a range of setpoints and how to compute this range both analytically and experimentally. Finally, we demonstrate these ideas on a physical testbed.

Distributed Amorphous Ramp Construction in Unstructured Environments

We present a model of construction using iterative amorphous depositions and give a distributed algorithm to reliably build ramps in unstructured environments. The relatively simple local strategy for interacting with irregularly shaped, partially built structures gives rise robust adaptive global properties. We illustrate the algorithm in both the single robot and multi-robot case via simulation and describe how to solve key technical challenges to implementing this algorithm via a robotic prototype.

A compositional framework for programming stochastically interacting robots

Large collections of simple, interacting robots can be difficult to program due to issues of concurrency and intermittent, probabilistic failures. Here, we present Guarded Command Programming with Rates, a formal framework for programming such multi-robot systems. Within this framework, we model robot behavior as a stochastic process and express concurrency and program composition using simple operations. In particular, we show how composition and other operations on programs can be used to specify increasingly complex behaviors of multi-robot systems and how stochasticity can be used to create programs that can tolerate failure of individual robots. Finally, we demonstrate our approach by encoding algorithms for routing parts in an abstract model of the Stochastic Factory Floor testbed (Galloway et al. 2010).

Materials and mechanisms for amorphous robotic construction

We present and compare three different amorphous materials for robotic construction. By conforming to surfaces they are deposited on, such materials allow robots to reliably construct in unstructured terrain. However, using amorphous materials presents a challenge to robotic manipulation. We demonstrate how deposition of each material can be automated and compare their material properties, cost, and cost in time in order to evaluate their suitability for developing amorphous robotic construction system.

Robust by composition: Programs for multi-robot systems

This paper describes how to specify the local reactive behavior of robots via guarded command programs with rates. These programs express concurrency and can be composed easily. Rates allow programs to be interpreted as Markov processes, which we use to define an appropriate notion of robustness and performance. We use composition to “robustify” programs with good performance, i.e. create a robust program with good performance from a program that has good performance but is not robust. We demonstrate this approach on a sub process of a reconfiguration program in a multi-robot system.

Robotic construction of arbitrary shapes with amorphous materials

We present a locally reactive algorithm to construct arbitrary shapes with amorphous materials. The goal is to provide methods for robust robotic construction in unstructured, cluttered terrain, where deliberative approaches with pre-fabricated construction elements are difficult to apply. Amorphous materials provide a simple way to interface with existing obstacles, as well as irregularly shaped previous depositions. The local reactive nature of these algorithms allows robots to recover from disturbances, operate in dynamic environments, and provides a way to work with scalable robot teams.

Simple passive valves for addressable pneumatic actuation

We present a method for setting the pressure of multiple chambers using a single pressure source when they are interconnected via band-pass valves. These valves can be constructed from simple passive devices that behave like leaky check valves. We present the theory of operation and design parameters for individual valves, give a control strategy for serial connections of pressure chambers, and demonstrate the approach by building prototype valves and using them to control serially connected soft-robotic actuators from a single pressure source.

Hidden Markov Models for non-well-mixed reaction networks

The behavior of systems of stochastically interacting particles, be they molecules comprising a chemical reaction network or multi-robot systems in a stochastic environment, can be described using the Chemical Master Equation (CME). In this paper we extend the applicability of the CME to the case when the underlying system of particles is not well-mixed, by constructing an extended state space. The proposed approach fits into the general framework of approximating stochastic processes by Hidden Markov Models (HMMs). We consider HMMs where the hidden states are equivalence classes of states of some underlying process. The sets of equivalence classes we consider are refinements of macrostates used in the CME. We construct a series of HMMs that use the CME to describe their hidden states. We demonstrate the approach by building a series of increasingly accurate models for a system of robots that interact in a non-well-mixed manner.