This paper presents a method for the design of time-invariant memoryless control policies for robots tasked with persistent surveillance of an area in which there are forbidden regions. We model each robot as a controlled Markov chain whose state comprises its position on a finite two-dimensional lattice and the direction of motion. The goal is to find the minimum number of robots and an associated time-invariant memoryless control policy that guarantees that the largest number of states are persistently surveilled without ever visiting a forbidden state. We propose a design method that relies on a finitely parametrized convex program inspired by entropy maximization principles. For clarity of exposition, we focus on simple dynamics and state/control spaces, however the proposed methodology can be extended to more general cases. Numerical examples are provided.

The TinyTeRP is a small, low-cost, modular robotics platform used to study robot sensing and control in large numbers of miniature robots. A fully assembled TinyTeRP costs approximately $50, is 1.7 × 1.8 × 2 cm3, and can move at speeds up to 50 cm/s. The robot is designed around a wheeled platform onto which different circuit boards can be stacked providing hardware modularity. The base module integrates a microcontroller with an 802.15.4 radio used for both sensing and communication between robots. An inertial sensing module used to improve single robot control is provided as an example of an additional sensing board. A simple `rendezvous' algorithm using received signal strength indicator (RSSI) data from the radio illustrates a distributed control algorithm with the TinyTeRP.

In this paper, we investigate the design of optimal state estimators for Markovian jump linear systems. We consider that the state has two components: the first component is finite valued and is denoted as mode, while the second (continuous) component is in a finite dimensional Euclidean space. The continuous state is driven by a zero mean, white and Gaussian process noise. The observation output has two components: the first is the mode and the second is a linear combination of the continuous state observed and zero mean, white Gaussian noise. Both output components are affected by delays, not necessarily equal. Our paradigm is to design optimal estimators for the current state, given the current output observation. We provide a solution to this paradigm by giving a recursive estimator for the continuous state, in the minimum mean square sense, and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditioned on the observed output. We show that when the mode is observed with a greater delay then the continuous output component, the optimal estimator nonlinear in the observed outputs.

We present coding strategies, which are variants of the Schalkwijk-Kailath scheme, for communicating reliably over additive white noise channels in the presence of corrupted feedback. Our framework comprises an additive white forward channel and a feedback link. We consider two types of corruption mechanisms in the feedback link. The first is quantization noise, i.e., the encoder receives the quantized values of the past outputs of the forward channel. The quantization is uniform, memoryless and time invariant. The second corruption mechanism is an arbitrarily distributed additive bounded noise. Here we allow symbol-by-symbol encoding at the input to the feedback link. We propose explicit schemes featuring positive information rate and positive error exponent. If the forward channel is additive white Gaussian (AWGN) then, as the amplitude of the noise at the feedback link decreases to zero, the rate of our schemes converges to the capacity of the channel. Moreover, the probability of error is shown to converge to zero at a doubly exponential rate. If the forward channel is AWGN and the feedback link consists of an additive bounded noise channel, with signal-to-noise ratio (SNR) constrained symbol-by-symbol encoding, then our schemes achieve rates arbitrarily close to capacity, in the limit of high SNR (at the feedback link).