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Register a new userRobotic Surveillance Based on the Meeting Time of Random Walks
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Added by
Xiaoming Duan
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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This paper analyzes the meeting time between a pair of pursuer and evader performing random walks on digraphs. The existing bounds on the meeting time usually work only for certain classes of walks and cannot be used to formulate optimization problems and design robotic strategies. First, by analyzing multiple random walks on a common graph as a single random walk on the Kronecker product graph, we provide the first closed-form expression for the expected meeting time in terms of the transition matrices of the moving agents. This novel expression leads to necessary and sufficient conditions for the meeting time to be finite and to insightful graph-theoretic interpretations. Second, based on the closed-form expression, we setup and study the minimization problem for the expected capture time for a pursuer/evader pair. We report theoretical and numerical results on basic case studies to show the effectiveness of the design.
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Force control is essential for medical robots when touching and contacting the patients body. To increase the stability and efficiency in force control, an Adaption Module could be used to adjust the parameters for different contact situations. We propose an adaptive controller with an Adaption Module which can produce control parameters based on force feedback and real-time stiffness detection. We develop methods for learning the optimal policies by value iteration and using the data generated from those policies to train the Adaptive Module. We test this controller on different zones of a persons arm. All the parameters used in practice are learned from data. The experiments show that the proposed adaptive controller can exert various target forces on different zones of the arm with fast convergence and good stability.
We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities $P^t(x,x)$ and the maximum expected hitting time $t_{rm hit}$, both in terms of the relaxation time. We also prove a discrete-time version of the first-named authors ``Meeting time lemma~ that bounds the probability of random walk hitting a deterministic trajectory in terms of hitting times of static vertices. The meeting time result is then used to bound the expected full coalescence time of multiple random walks over a graph. This last theorem is a discrete-time version of a result by the first-named author, which had been previously conjectured by Aldous and Fill. Our bounds improve on recent results by Lyons and Oveis-Gharan; Kanade et al; and (in certain regimes) Cooper et al.
Consider a system of coalescing random walks where each individual performs random walk over a finite graph G, or (more generally) evolves according to some reversible Markov chain generator Q. Let C be the first time at which all walkers have coalesced into a single cluster. C is closely related to the consensus time of the voter model for this G or Q. We prove that the expected value of C is at most a constant multiple of the largest hitting time of an element in the state space. This solves a problem posed by Aldous and Fill and gives sharp bounds in many examples, including all vertex-transitive graphs. We also obtain results on the expected time until only k>1 clusters remain. Our proof tools include a new exponential inequality for the meeting time of a reversible Markov chain and a deterministic trajectory, which we believe to be of independent interest.
Ultrasound (US) imaging is widely employed for diagnosis and staging of peripheral vascular diseases (PVD), mainly due to its high availability and the fact it does not emit radiation. However, high inter-operator variability and a lack of repeatability of US image acquisition hinder the implementation of extensive screening programs. To address this challenge, we propose an end-to-end workflow for automatic robotic US screening of tubular structures using only the real-time US imaging feedback. We first train a U-Net for real-time segmentation of the vascular structure from cross-sectional US images. Then, we represent the detected vascular structure as a 3D point cloud and use it to estimate the longitudinal axis of the target tubular structure and its mean radius by solving a constrained non-linear optimization problem. Iterating the previous processes, the US probe is automatically aligned to the orientation normal to the target tubular tissue and adjusted online to center the tracked tissue based on the spatial calibration. The real-time segmentation result is evaluated both on a phantom and in-vivo on brachial arteries of volunteers. In addition, the whole process is validated both in simulation and physical phantoms. The mean absolute radius error and orientation error ($pm$ SD) in the simulation are $1.16pm0.1~mm$ and $2.7pm3.3^{circ}$, respectively. On a gel phantom, these errors are $1.95pm2.02~mm$ and $3.3pm2.4^{circ}$. This shows that the method is able to automatically screen tubular tissues with an optimal probe orientation (i.e. normal to the vessel) and at the same to accurately estimate the mean radius, both in real-time.
This article surveys recent advancements of strategy designs for persistent robotic surveillance tasks with the focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way where the efficiency is defined with respect to relevant underlying performance metrics. We first start by reviewing the basics of Markov chains, which is the primary motion model for stochastic robotic surveillance. Then two main criteria regarding the speed and unpredictability of surveillance strategies are discussed. The central objects that appear throughout the treatment is the hitting times of Markov chains, their distributions and expectations. We formulate various optimization problems based on the concerned metrics in different scenarios and establish their respective properties.
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