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

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Abstract

Autonomous robotics has permeated several industrial, research and consumer robotic applications, of which path planning is an important component. The path planning algorithm of choice is influenced by the application at hand and the history of algorithms used for such applications. The latter is dependent on an extensive conglomeration and classification of path planning literature, which is what this work focuses on. Specifically, we accomplish the following: typical classifications of path planning algorithms are provided. Such classifications rely on differences in knowledge of the environment (known/unknown), robot (model-specific/generic), and constraints (static/dynamic). This classification however, is not comprehensive. Thus, as a resolution, we propose a detailed taxonomy based on a fundamental parameter of the space, i.e. its ability to be characterized as a set of disjoint or connected points. We show that this taxonomy encompasses important attributes of path planning problems, such as connectivity and partitioning of spaces. Consequently, path planning spaces in robotics may be viewed as simply a set of points, or as manifolds. The former can further be divided into unpartitioned and partitioned spaces, of which the former uses variants of sampling algorithms, optimization algorithms, model predictive controls, and evolutionary algorithms, while the latter uses cell decomposition and graph traversal, and sampling-based optimization techniques.This article achieves the following two goals: The first is the introduction of an all-encompassing taxonomy of robotic path planning. The second is to streamline the migration of path planning work from disciplines such as mathematics and computer vision to robotics, into one comprehensive survey. Thus, the main contribution of this work is the review of works for static constraints that fall under the proposed taxonomy, i.e., specifically under topology and manifold-based methods. Additionally, further taxonomy is introduced for manifold-based path planning, based on incremental construction or one-step explicit parametrization of the space.

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Abbreviations

2LPM:

2-Link planar manipulator

ACO:

Ant colony optimization

APF:

Artificial potential field

BFP:

Best first planner

CCM:

Closed chain manipulator

CDGT:

Cell decomposition and graph traversal

CFDM:

Constraint-free discretized manifold

CFDMPP:

Constraint-free discretized manifolds-based path planner

CFM:

Constraint-free manifold

CS:

Constraint set

CV:

Certainty value

DAPF:

Dubin’s APF

DC:

Dynamic constraint

DCS:

Disjoint constraint set

DMP:

Dynamic movement primitives

DOF:

Degrees of freedom

DTD:

Dynamic topology detector

EA:

Evolutionary algorithm

EE:

End-effector

FSF:

Free space force

FSH:

Free space histogram

GA:

Genetic algorithm

GVD:

Generalized Voronoi diagram

HA*:

Homotopic A*

HB:

Homotopic bug

HBM:

Homotopy based method

HCM:

Homotopy continuation methods

HIMM:

Histogram in motion mapping

HRRT:

Homotopic RRT

HSFM:

Headed social force model

ICE:

Inner constraint edge

IFTM:

Inverse function theorem for manifolds

LAG:

L-augmented graph

LPRM:

Lazy PRM

LM-RRT:

Machine learning-based multi-RRT

MA:

Memetic algorithm

MBM:

Model based methods

MPC:

Model predictive control

MR:

Mobile robot

NAES:

Non-linear algebraic equation system

NF:

Navigation functions

NLOC:

Non-linear optimal control

NOCP:

Non-linear optimal control problem

NOP:

Non-linear optimization problem

OA:

Optimization algorithm

OCE:

Outer constraint edge

OCM:

Open chain manipulator

P-RRT*:

Potential functions-based RRT*

PDR:

Path deformation roadmap

PGD-RRT*:

Potential guided directionalized-RRT*

PPM:

Path planning manifold

PPP:

Path planning problem

PPS:

Path planning space

PPPS:

Primary path planning space

PRM:

Probabilistic road map

PRM*:

Probabilistic road map*

PSM:

Product smooth manifold

PSO:

Particle swarm optimization

RPP:

Randomized path planner

RRG:

Rapidly exploring random graph

RRT:

Rapidly exploring random tree

RRT*:

Rapidly exploring random tree*

RRT*-AB:

RRT*-adjustable bounds

SA:

Sampling algorithm

SC:

Static constraint

SFLA:

Shuffled frog leaping algorithm

SHIO:

Single homotopy inducing obstacle

SLPRM:

Semi-lazy PRM

SM:

Smooth manifold

SO:

Special orthogonal group

SPPS:

Secondary path planning space

SR:

Stationary robot

S-RRT:

Smoothly-RRT

TG:

Tangent graph

TM:

Topological manifold

T-RRT:

Transition-based RRT

UGV:

Unmanned ground vehicle

UAV:

Unmanned aerial vehicle

UUV:

Unmanned underwater vehicle

VG:

Visibility graph

VOS:

Velocity obstacle sets

VFF:

Virtual force fields

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Funding

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

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Authors and Affiliations

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

    Sindhu Radhakrishnan & Wail Gueaieb

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  1. Sindhu Radhakrishnan
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  2. Wail Gueaieb
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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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Correspondence to Wail Gueaieb.

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Radhakrishnan, S., Gueaieb, W. A state-of-the-art review on topology and differential geometry-based robotic path planning—part I: planning under static constraints. Int J Intell Robot Appl (2024). https://doi.org/10.1007/s41315-024-00330-5

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