Michael S. Branicky

Stability of networked control systems

First, we review some previous work on networked control systems (NCSs) and offer some improvements. Then, we summarize the fundamental issues in NCSs and examine them with different underlying network-scheduling protocols. We present NCS models with network-induced delay and analyze their stability using stability regions and a hybrid systems technique. Following that, we discuss methods to compensate network-induced delay and present experimental results over a physical network. Then, we model NCSs with packet dropout and multiple-packet transmission as asynchronous dynamical systems and analyze their stability. Finally, we present our conclusions.

Stability of networked control systems: explicit analysis of delay

Recent technological advances have enabled distributed control systems to be implemented via networks. This allows feedback control loops to be closed over a shared communication channel. Network-induced delays are inevitable, however, when transmitting digital data between control devices. This paper analyzes the stability of such networked control systems (NCS). We first review some previous work on this topic, offering some improvements. We analyze the influence of the sampling rate and network delay on system stability. We further study the stability of NCS using a hybrid system stability analysis technique.

On the Relationship between Classical Grid Search and Probabilistic Roadmaps

We present, implement, and analyze a spectrum of closely-related planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on quasi-Monte Carlo sampling literature, we have developed deterministic variants of the PRM that use low-discrepancy and low-dispersion samples, including lattices. Classical grid search is extended using subsampling for collision detection and also the optimal-dispersion Sukharev grid, which can be considered as a kind of lattice-based roadmap to complete the spectrum. Our experimental results show that the deterministic variants of the PRM offer performance advantages in comparison to the original PRM and the recent Lazy PRM. This even includes searching using a grid with subsampled collision checking. Our theoretical analysis shows that all of our deterministic PRM variants are resolution complete and achieve the best possible asymptotic convergence rate, which is shown superior to that obtained by random sampling. Thus, in surprising contrast to recent trends, there is both experimental and theoretical evidence that some forms of grid search are superior to the original PRM.

Scheduling and feedback co-design for networked control systems

Feedback control systems wherein the control loops are closed through a real-time network are called networked control systems (NCSs). The insertion of the communication network in the feedback control loop makes the analysis and design of an NCS complex. Driving our research effort into NCSs is the point of view that the design of both the communication protocols and the interacting controlled system should not be treated as separate. In the co-design approach we propose, network issues such as bandwidth, quantization, survivability, reliability and message delay will be considered simultaneously with controlled system issues such as stability, performance, fault tolerance and adaptability. Thus, we study network scheduling when a set of NCSs are connected to the network and arbitrating for network bandwidth. We first define the basic concepts of network scheduling in NCSs. Then, we apply the rate monotonic scheduling algorithm to schedule a set of NCSs. We also formulate the optimal scheduling problem under both rate-monotonic-schedulability constraints and NCS-stability constraints, and give an example of how such optimization is carried out. Next, the assumptions of ideal transmission are relaxed: we study the above network scheduling problem with network-induced delay, packet dropouts, and multiple-packet transmissions taken into account.

Multipartite RRTs for Rapid Replanning in Dynamic Environments

The rapidly-exploring random tree (RRT) algorithm has found widespread use in the field of robot motion planning because it provides a single-shot, probabilistically complete planning method which generalizes well to a variety of problem domains. We present the multipartite RRT (MP-RRT), an RRT variant which supports planning in unknown or dynamic environments. By purposefully biasing the sampling distribution and re-using branches from previous planning iterations, MP-RRT combines the strengths of existing adaptations of RRT for dynamic motion planning. Experimental results show MP-RRT to be very effective for planning in dynamic environments with unknown moving obstacles, replanning in high-dimensional configuration spaces, and replanning for systems with space time constraints.

Universal computation and other capabilities of hybrid and continuous dynamical systems

We explore the simulation and computational capabilities of hybrid and continuous dynamical systems. The continuous dynamical systems considered are ordinary differential equations (ODEs). For hybrid systems we concentrate on models that combine ODEs and discrete dynamics (e.g., finite automata). We review and compare four such models from the literature. Notions of simulation of a discrete dynamical system by a continuous one are developed. We show that hybrid systems whose equations can describe a precise binary timing pulse (exact clock) can simulate arbitrary reversible discrete dynamical systems defined on closed subsets of R n . The simulations require continuous ODEs in IR2n with the exact clock as input. All four hybrid systems models studied here can implement exact clocks. We also prove that any discrete dynamical system in rn can be simulated by continuous ODEs in Rt2n+1. We use this to show that smooth ODEs in RI3 can simulate arbitrary Turing machines, and hence possess the power of universal computation. We use the famous asynchronous arbiter problem to distinguish between hybrid and continuous dynamical systems. We prove that one cannot build an arbiter with devices described by a system of Lipschitz ODEs. On the other hand, all four hybrid systems models considered can implement arbiters even if their ODEs are Lipschitz.

Motion Planning Under Uncertainty for Image-guided Medical Needle Steering

We develop a new motion planning algorithm for a variant of a Dubins car with binary left/right steering and apply it to steerable needles, a new class of flexible bevel-tip medical needle that physicians can steer through soft tissue to reach clinical targets inaccessible to traditional stiff needles. Our method explicitly considers uncertainty in needle motion due to patient differences and the difficulty in predicting needle/tissue interaction. The planner computes optimal steering actions to maximize the probability that the needle will reach the desired target. Given a medical image with segmented obstacles and target, our method formulates the planning problem as a Markov decision process based on an efficient discretization of the state space, models motion uncertainty using probability distributions and computes optimal steering actions using dynamic programming. This approach only requires parameters that can be directly extracted from images, allows fast computation of the optimal needle entry point and enables intra-operative optimal steering of the needle using the pre-computed dynamic programming look-up table. We apply the method to generate motion plans for steerable needles to reach targets inaccessible to stiff needles, and we illustrate the importance of considering uncertainty during motion plan optimization.

Networked control system co-simulation for co-design

We provide a general framework for networked control systems (NCSs) and review previous theoretical results for NCS co-design. We present experimental studies of control and feedback scheduling of NCSs, consisting of dynamic system simulations for the control agents and environment and packet-level network simulations for the communications. To this end, we have extended the ns-2 release in order to simulate the transmissions of plants and controllers that are modeled by ODEs (solved via a linked package). Our results show the overall control and network performances achieved while modeling the individual control and network components. Major co-design issues, such as scalability and network heterogeneity, are explored.

Introduction to Hybrid Systems

Hybrid systems arise when the continuous and the discrete meet. Combine continuous and discrete inputs, outputs, states, or dynamics, and you have a hybrid system. Particularly, hybrid systems arise from the use of finite-state logic to govern continuous physical processes (as in embedded control systems) or from topological and network constraints interacting with continuous control (as in networked control systems). This chapter provides an introduction to hybrid systems, building them up first from the completely continuous side and then from the completely discrete side. It should be accessible to control theorists and computer scientists alike.

RRTs for nonlinear, discrete, and hybrid planning and control

In this paper, we describe a planning and control approach in terms of sampling using Rapidly-exploring Random Trees (RRTs), which were introduced by LaValle. We review RRTs for motion planning and show how to use them to solve standard nonlinear control problems. We extend them to the case of hybrid systems and describe our modifications to LaValles Motion Strategy Library to allow for hybrid motion planning. Finally, we extend them to purely discrete spaces (using heuristic evaluation as a distance metric) and provide computational experiments comparing them to conventional methods, such as A.