Optimized NURBS Curves Modelling Using Genetic Algorithm for Mobile Robot Navigation

Jalel, Sawssen; Marthon, Philippe; Hamouda, Atef

doi:10.1007/978-3-319-23192-1_45

Cited by 4 publications

(9 citation statements)

References 13 publications

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“… With the exception of N c , which has been set empirically and represents the number of NURBS individuals composing the population of each piece-wise linear solution

, the number of EOP iterations N i , the cross-over probability p cross and the mutation probability p mut are taken from Jalel et al ( 2015 ) . …”

Section: Methodsmentioning

confidence: 99%

“…where u ∈ [0, 1] is the independent variable used to define the NURBS curve in parametric form, The reader is referred to Favaro et al, (under submission) for further details. With the exception of Nc, which has been set empirically and represents the number of NURBS individuals composing the population of each piece-wise linear solution sol i s , the number of EOP iterations N i , the cross-over probability pcross and the mutation probability pmut are taken from Jalel et al (2015).…”

Section: Evolutionary Optimization Procedures (Eop)mentioning

confidence: 99%

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Automated Steerable Path Planning for Deep Brain Stimulation Safeguarding Fiber Tracts and Deep Gray Matter Nuclei

et al. 2019

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Deep Brain Stimulation (DBS) is a neurosurgical procedure consisting in the stereotactic implantation of stimulation electrodes to specific brain targets, such as deep gray matter nuclei. Current solutions to place the electrodes rely on rectilinear stereotactic trajectories (RTs) manually defined by surgeons, based on pre-operative images. An automatic path planner that accurately targets subthalamic nuclei (STN) and safeguards critical surrounding structures is still lacking. Also, robotically-driven curvilinear trajectories (CTs) computed on the basis of state-of-the-art neuroimaging would decrease DBS invasiveness, circumventing patient-specific obstacles. This work presents a new algorithm able to estimate a pool of DBS curvilinear trajectories for reaching a given deep target in the brain, in the context of the EU's Horizon EDEN2020 project. The prospect of automatically computing trajectory plans relying on sophisticated newly engineered steerable devices represents a breakthrough in the field of microsurgical robotics. By tailoring the paths according to single-patient anatomical constraints, as defined by advanced preoperative neuroimaging including diffusion MR tractography, this planner ensures a higher level of safety than the standard rectilinear approach. Ten healthy controls underwent Magnetic Resonance Imaging (MRI) on 3T scanner, including 3DT1-weighted sequences, 3Dhigh-resolution time-of-flight MR angiography (TOF-MRA) and high angular resolution diffusion MR sequences. A probabilistic q-ball residual-bootstrap MR tractography algorithm was used to reconstruct motor fibers, while the other deep gray matter nuclei surrounding STN and vessels were segmented on T1 and TOF-MRA images, respectively. These structures were labeled as obstacles. The reliability of the automated planner was evaluated; CTs were compared to RTs in terms of efficacy and safety. Targeting the anterior STN, CTs performed significantly better in maximizing the minimal distance from critical structures, by finding a tuned balance between all obstacles. Moreover, CTs resulted superior in reaching the center of mass (COM) of STN, as well as in optimizing the entry angle in STN and in the skull surface.

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“… With the exception of N c , which has been set empirically and represents the number of NURBS individuals composing the population of each piece-wise linear solution

, the number of EOP iterations N i , the cross-over probability p cross and the mutation probability p mut are taken from Jalel et al ( 2015 ) . …”

Section: Methodsmentioning

confidence: 99%

Section: Evolutionary Optimization Procedures (Eop)mentioning

confidence: 99%

Automated Steerable Path Planning for Deep Brain Stimulation Safeguarding Fiber Tracts and Deep Gray Matter Nuclei

et al. 2019

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“…Additionally, they have to comply with the maximum curvature achievable by the needle (k P BN ). The EOP, run for each sol i j and used for tuning the NURBS parameters, has demonstrated to be able to efficiently generate a smooth, obstacle avoiding and curvature-constrained path for non-holonomic robot, featuring minimal length and minimal variations of curvature [34].…”

Section: Path Approximation and Optimizationmentioning

confidence: 99%

“…An objective function F obj is defined, which is used by the EOP to rank the performance of each ind i j,t , as in [34]:…”

Section: Path Approximation and Optimizationmentioning

confidence: 99%

An Evolutionary-Optimized Surgical Path Planner for a Programmable Bevel-Tip Needle

et al. 2021

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Path planning algorithms for steerable needles in medical applications must guarantee the anatomical obstacle avoidance, reduce the insertion length and ensure the compliance with the needle kinematics. The majority of the solutions from the literature focus either on fast computation or on path optimality, the former at the expense of sub-optimal paths, the latter by making unbearable the computation in case of a high dimensional workspace. We implemented a 3D path planner for neurosurgical applications which keeps the computational cost consistent with standard pre-operative planning algorithms and fine-tunes the estimated pathways in accordance to multiple optimization objectives. From a user-defined entry point, our method confines a sample-based path search within a subsection of the original workspace considering the degree of curvature admitted by the needle. An evolutionary optimization procedure is used to maximize the obstacle avoidance and reduce the insertion length. The pool of optimized solutions is examined through a cost function to determine the best path. Simulations on one dataset showed the ability of the planner to save time and overcome the state of the art in terms of obstacle avoidance, insertion length and probability of failure, proving this algorithm as a valid planning method for complex environments.

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“…If S and T belong to the same connected component cci (i∈[1,‥,k] where k is the number of connected components of G′), then the Bellman algorithm [19] is applied to calculate the shortest path between these two positions. Otherwise, the algorithm stops and no solution can be found for the path planning problem related to the treated case [20]. The process of shortest polyline path generation is described in Algorithm 7.…”

Section: Navigation Architecturementioning

confidence: 99%

A New Path Generation Algorithm Based on Accurate NURBS Curves

Jalel

Marthon

Hamouda

2016

International Journal of Advanced Robotic Systems

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The process of finding an optimum, smooth and feasible global path for mobile robot navigation usually involves determining the shortest polyline path, which will be subsequently smoothed to satisfy the requirements. Within this context, this paper deals with a novel roadmap algorithm for generating an optimal path in terms of NonUniform Rational B-Splines (NURBS) curves. The generated path is well constrained within the curvature limit by exploiting the influence of the weight parameter of NURBS and/or the control points' locations. The novelty of this paper lies in the fact that NURBS curves are not used only as a means of smoothing, but they are also involved in meeting the system's constraints via a suitable parameterization of the weights and locations of control points. The accurate parameterization of weights allows for a greater benefit to be derived from the influence and geometrical effect of this factor, which has not been well investigated in previous works. The effectiveness of the proposed algorithm is demonstrated through extensive MATLAB computer simulations.

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Optimized NURBS Curves Modelling Using Genetic Algorithm for Mobile Robot Navigation

Cited by 4 publications

References 13 publications

Automated Steerable Path Planning for Deep Brain Stimulation Safeguarding Fiber Tracts and Deep Gray Matter Nuclei

Automated Steerable Path Planning for Deep Brain Stimulation Safeguarding Fiber Tracts and Deep Gray Matter Nuclei

An Evolutionary-Optimized Surgical Path Planner for a Programmable Bevel-Tip Needle

A New Path Generation Algorithm Based on Accurate NURBS Curves

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