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A state-of-the-art review on topology and differential geometry-based robotic path planning—part II: planning under dynamic constraints

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Abstract

Path planning is an intrinsic component of autonomous robotics, be it industrial, research or consumer robotics. Such avenues experience constraints around which paths must be planned. While the choice of an appropriate algorithm is application-dependent, the starting point of an ideal path planning algorithm is the review of past work. Historically, algorithms were classified based on the three tenets of autonomous robotics which are the ability to avoid different constraints (static/dynamic), knowledge of the environment (known/unknown) and knowledge of the robot (general/model specific). This division in literature however, is not comprehensive, especially with respect to dynamics constraints. Therefore, to remedy this issue, we propose a new taxonomy, based on the fundamental tenet of characterizing space, i.e., as a set of distinct, unrelated points or as a set of points that share a relationship. We show that this taxonomy is effective in addressing important parameters of path planning such as connectivity and partitioning of spaces. Therefore, path planning spaces may now be viewed either as a set of points or, as a space with structure. The former relies heavily on robot models, since the mathematical structure of the environment is not considered. Thus, the approaches used are variants of optimization algorithms and specific variants of model-based methods that are tailored to counteract effects of dynamic constraints. The latter depicts spaces as points with inter-connecting relationships, such as surfaces or manifolds. These structures allow for unique characterizations of paths using homotopy-based methods. The goals of this work, viewed specifically in light with dynamic constraints, are therefore as follows: First, we propose an all-encompassing taxonomy for robotic path planning literature that considers an underlying structure of the space. Second, we provide a detailed accumulation of works that do focus on the characterization of paths in spaces formulated to show underlying structure. This work accomplishes the goals by doing the following: It highlights existing classifications of path planning literature, identifies gaps in common classifications, proposes a new taxonomy based on the mathematical nature of the path planning space (topological properties), and provides an extensive conglomeration of literature that is encompassed by this new proposed taxonomy.

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Abbreviations

APF :

Artificial potential field

CDGT :

Cell decomposition and graph traversal

DC :

Dynamic constraint

EA :

Evolutionary algorithm

\(HA^{*}\) :

Homotopic A*

HB :

Homotopic bug

HBM :

Homotopy based method

HCM :

Homotopy continuation methods

HRRT :

Homotopic RRT

LAG :

L-augmented graph

MBM :

Model based methods

MPC :

Model predictive control

NAES :

Non-linear algebraic equation system

NF :

Navigation functions

OA :

Optimization algorithm

PPM :

Path planning manifold

PPP :

Path planning problem

PPS :

Path planning space

PRM :

Probabilistic road map

RRT :

Rapidly exploring random tree

SA :

Sampling algorithm

SC :

Static constraint

SHIO :

Single homotopy inducing obstacle

VOS :

Velocity obstacle sets

\(H-signature\) :

Unique measure associated to a homotopic class

\({{\textbf {p}}^{\text {start}}}{\in \mathcal {P}}\) :

Starting point in \({\mathcal {P}}\)

\({{\textbf {p}}^{\text {goal}}}{\in \mathcal {P}}\) :

Destination point in \({\mathcal {P}}\)

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This work was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Grant RGPIN-2014-06512.

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  1. School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Avenue, Ottawa, K1N 6N5, ON, Canada

    Sindhu Radhakrishnan & Wail Gueaieb

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  1. Sindhu Radhakrishnan
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Sindhu Radhakrishnan. The first draft of the manuscript was written by Sindhu Radhakrishnan and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Radhakrishnan, S., Gueaieb, W. A state-of-the-art review on topology and differential geometry-based robotic path planning—part II: planning under dynamic constraints. Int J Intell Robot Appl (2024). https://doi.org/10.1007/s41315-024-00331-4

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