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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Quantum Search Approaches to Sampling-Based Motion Planning

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Motion Planning Algorithms for Safety and Quantum Computing Efficiency

Motion planning remains a fundamental problem in robotics. Sampling-based algorithms use randomization to allow efficient solutions to this complex problem. As mobile robots and autonomous vehicles become more prevalent in everyday life, motion planning must be applied to increasingly challenging scenarios. Safety has become a paramount concern in motion planning for ensuring robotic applications enrich human lives. To date, many motion planning techniques to increase safety in the face of uncertain and dynamic environments have been developed. This dissertation first addresses distributional safety of Rapidly-Exploring Random Trees (RRT) through our algorithm W-Safe RRT. To acknowledge distributional uncertainty and poor modeling, W-Safe RRT uses the Wasserstein metric to provide a probabilistic bound on the distributional distance between a robot and obstacles. Human-interpretable environmental agent classification allows online safety margin adaptation. We propose and analyze an integrating region method for online classification that increases actor labeling accuracy based on behavioral feature values when compared to state of the art methods. The method performs class assignments based on local maximum likelihood in a created behavioral feature-space, allowing a notion of classification uncertainty. Model-based methods with safety guarantees can quickly become computationally in tractable, especially with multiple agents, higher dimensions, and plentiful unknowns. Sampling based algorithms have been parallelized for computation with multi-core computers and GPUs. We consider the use of quantum algorithms and computers for sampling-based motion planning for the first time. Quantum computing performs operations on superpositions of states and can solve certain problems much more efficiently than classical computers, but introduces previously unseen challenges. With Quantum-RRT, we recast the motion planning problem into a database-search structure and use Quantum Amplitude Amplification to find reachable states in the database with a quadratic performance increase over classical methods. We address two error sources with this method: quantum measurement and quantum oracle errors. We then extend this method to Parallel Quantum-RRT, which uses a manager-worker architecture with multiple parallel quantum workers to increase database search efficiency. We compare algorithm architectures and characterize probabilities of multiple workers finding solutions. Lastly, we test in simulation the quantum algorithms against classical versions in a wide variety of scenarios, concluding that a similar parallelization improvement is to be found in the quantum case as was found in the parallelization of classical RRT.

97 MATHEMATICS AND COMPUTING↗