Robotic Approaches at the Crossroads of Chaos, Fractals and Percolation Theory

Kaygısız, Burak H.; Karahan, Murat; Erkmen, Aydan M.; Erkmen, I.

doi:10.1007/978-3-642-21922-1_6

Cited by 5 publications

(5 citation statements)

References 35 publications

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“…The reason for this choice is twofold: firstly, there are established tools, methods, and theory regarding them, and secondly, they can yield sufficiently dense and scattered environments to provide an interesting study. Related applications include cave exploring or search and rescue efforts in collapsed structures [63].…”

Section: Quantum Rrtmentioning

confidence: 99%

Quantum Search Approaches to Sampling-Based Motion Planning

Lathrop,

Boardman,

Martínez

2023

IEEE Access

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In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.

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Section: Quantum Rrtmentioning

confidence: 99%

Quantum Search Approaches to Sampling-Based Motion Planning

Lathrop,

Boardman,

Martínez

2023

IEEE Access

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Section: Quantum Rapidly Exploring Random Tree Algorithmmentioning

confidence: 99%

Motion Planning Algorithms for Safety and Quantum Computing Efficiency

Lathrop

2023

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I am grateful for the members, past and present, of the UCSD Multi-Agent Robotics Lab and other colleagues of the Contextual Robotics Institute for lunchtime discussions, coffee walks, and office company, especially those who put up with me both in lab and in sport. I would like to acknowledge the E-3 group at LANL for support over the summers, and in London, and I acknowledge Los Alamos National Laboratory for the financial support during my degree and the opportunity to take part in three lab internships.Lastly, I would like to express my deepest appreciation to my family: Dr. Lathrop, Dr. Lathrop, Dr. Lathrop, and John for their unwavering support and technical assistance during my Ph.D, to my friends: the UCSD and UMD triathlon teams, TE, and ZAPA for ensuring that I stay active in the great outdoors, and to my very good friend and colleague Dr. Alves and my chief of staff Calypso (feline) for their encouragement and strength.

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“…This scenario is quantitatively and qualitatively distinct from the situations in which perturbations develop linearly. It is a striking reality that simple devices, e.g., a double pendulum, and a very complex event such as weather follow the same dynamics, which can be predicted only for short time horizons [6]. Due to the availability of high-speed computers, new analytical techniques and sophisticated experiments, it has become evident that the chaotic phenomenon is universal in nature and has across-the-board consequences in various fields of human endeavour.…”

Section: Chaos Theory: An Overviewmentioning

confidence: 99%

“…Chaos lies within a well- Chaos and fractals (self-similar, iterated and fine puzzle. Such nonlinearities have led researchers to employ chaotic motion planning techniques for mobile robots to ensure a rapid search of the whole workspace [6]. The applications of chaos in robotics are classified into two types:…”

Section: Chaos Theory: An Overviewmentioning

confidence: 99%

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Applications of Chaotic Dynamics in Robotics

Zang

Iqbal

Zhu

et al. 2016

International Journal of Advanced Robotic Systems

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This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of deterministic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.

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Robotic Approaches at the Crossroads of Chaos, Fractals and Percolation Theory

Cited by 5 publications

References 35 publications

Quantum Search Approaches to Sampling-Based Motion Planning

Quantum Search Approaches to Sampling-Based Motion Planning

Motion Planning Algorithms for Safety and Quantum Computing Efficiency

Applications of Chaotic Dynamics in Robotics

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