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arXiv:2304.06479 · IEEE Access

Quantum Search Approaches to Sampling-Based Motion Planning

Paul Lathrop, Beth Boardman, Sonia Martı́nez

Published Jan 1, 2023• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/access.2023.3307316

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Jesse’s research investigates how quantum computing can assist robotic motion planning by improving sampling within discretized configuration spaces. The current project discretizes continuous configuration space into a collision-labeled grid for 3D manipulator motion planning, enabling systematic identification of collision-free and invalid regions during planning. This approach uses grid-based configuration-space search rather than planning directly in continuous space, allowing valid and invalid configurations to be identified in advance and sampled in a more structured manner. Building on prior quantum rapid-exploring random tree concepts, this work studies how quantum amplitude amplification can bias sampling toward useful regions of the search space during motion planning. Prior work in this area suggests that quantum search can be incorporated into sampling-based planners, including variants designed to improve exploration speed and parallel formulations intended to recover multiple useful samples from a shared database. The present research focuses on evaluating whether this quantum-weighted sampling strategy can improve planning efficiency in practice. Experiments are conducted using both simulated quantum hardware and real quantum hardware to compare idealized and device-limited behavior in the sampling process. The work began with a controlled 2D benchmark and is, at the time of writing, being extended toward higher-dimensional robotic manipulators. An additional research direction examines whether database-construction strategies inspired by annealing can improve exploration by promoting broader search early in planning and denser refinement later in the process.
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