Follow-the-leader Research Articles

A Novel Head-following Algorithm for Multi-Joint Articulated Driven Continuum Robots

Abstract Head-following (tracking) issue is a challenge in developing multi-joint continuum robots. However various approaches have been developed in head-following algorithm for articulated-driven mechanism (ADM) continuum robots, problems still exist such as low end-accuracy, large trajectory deviation, and low computational efficiency. This paper presents a novel head-following algorithm(NHF) with high precision, small trajectory deviation, and high computational efficiency for multi-joint ADM continuum robots. The proposed algorithm first uses the follow-the-leader (FTL) method to search for planning points. Secondly, the end-effector errors are calculated, split, and adjusted. Thirdly, the error judgment set is assigned based on the error rate of the end-effector, and also the joints that need to be adjusted are determined. Finally, the joint angles are iteratively adjusted. In this paper, the NHF algorithm is simulated on ADM continuum robots with saparately 10, 20 and 31 joints. The result shows that, compareing with other FTL algorithms, NHF algorithm has the highest end accuracy, and the smallest trajectory deviation.

A step-size follow-the-leader optimization algorithm with an improved step parameters

Follow the leader (FTL) algorithm is a newly developed optimization algorithm inspired by a sheep’s movement within a flock. FTL has been successfully implemented to solve power prediction problems. However, the probability of falling in local optima is high due to randomness in the step parameter. This paper proposes a step-size follow-the-leader (SFTL) algorithm with decreasing and increasing step-size combinations. The improved step parameter tunes the search space by generating a new solution to improve the accuracy and convergence rate of the FTL algorithm. Four different FTL variants have been presented in this paper to show the impact of the dynamic step-size parameter. FTL improvement is verified by testing SFTL over thirty-two fixed unimodal, unimodal, fixed multimodal, and multimodal benchmark functions. The computational results indicate that SFTL significantly improves the basic FTL algorithm and converges early compared to other algorithms. SFTL has also been tested on five real engineering design problems and obtained results show that SFTL outperformed FTL and other popular optimization algorithms.

Follow-The-Leader Mechanisms in Medical Devices: A Review on Scientific and Patent Literature.

Conventional medical instruments are not capable of passing through tortuous anatomy as required for natural orifice transluminal endoscopic surgery due to their rigid shaft designs. Nevertheless, developments in minimally invasive surgery are pushing medical devices to become more dexterous. Amongst devices with controllable flexibility, so-called Follow-The-Leader (FTL) devices possess motion capabilities to pass through confined spaces without interacting with anatomical structures. The goal of this literature study is to provide a comprehensive overview of medical devices with FTL motion. A scientific and patent literature search was performed in five databases (Scopus, PubMed, Web of Science, IEEExplore, Espacenet). Keywords were used to isolate FTL behavior in devices with medical applications. Ultimately, 35 unique devices were reviewed and categorized. Devices were allocated according to their design strategies to obtain the three fundamental sub-functions of FTL motion: steering, (controlling the leader/end-effector orientation), propagation, (advancing the device along a specific path), and conservation (memorizing the shape of the path taken by the device). A comparative analysis of the devices was carried out, showing the commonly used design choices for each sub-function and the different combinations. The advantages and disadvantages of the design aspects and an overview of their performance were provided. Devices that were initially assessed as ineligible were considered in a possible medical context or presented with FTL potential, broadening the classification. This review could aid in the development of a new generation of FTL devices by providing a comprehensive overview of the current solutions and stimulating the search for new ones.

Chaos follow the leader algorithm: Application to data classification

Classification is the process of systematically arranging the data into multiple groups, which gives a better understanding of large datasets. Considerable research has been carried out on data classification to develop a predictive model with high accuracy. This paper introduces chaos in the Follow the leader (FTL) optimization algorithm to achieve global optima for imbalanced data classification problems. In the FTL algorithm, the random parameter ω may not give enough exploration to the particles, which may lead to local stagnation problems. One of the solutions to this problem can be the replacement of the random parameter ω by a chaotic variable. For a detailed study on the chaotic behavior of ω in FTL, the algorithm is implemented with ten different chaotic maps and tested on twenty-four standard benchmark functions. Thereafter, the best chaos FTL (cFTL) algorithm is tested on six different complex real engineering problems and compared with ten meta-heuristic algorithms. Moreover, to further validate the performance of cFT, it has been applied to ten standard classification datasets collected from UCI and Kaggle data repositories. The obtained results show that cFTL outperforms FTL and other meta-heuristic algorithms.

A Continuum Robotic Cannula With Tip Following Capability and Distal Dexterity for Intracerebral Hemorrhage Evacuation.

This paper aims to investigate a new continuum robot design and its motion implementation methods appropriate for a minimally invasive intracerebral hemorrhage (ICH) evacuation. We propose a continuum robotic cannula, consisting of a precurved body and a 2-degree-of-freedom (DoF) flexible tip, monolithically fabricated. Kinematic model with cable elongation model, and a dedicated design optimization and motion planning algorithm were developed to enable the follow-the-leader (FTL) motion of the cannula. A task-dependent Jacobian-based closed loop control was also designed to track the cannula motion during the insertion and its independent tip motion. Comprehensive experiments were conducted to verify the kinematic model and submillimeter motion coupling between the cannula precurved body and its flexible tip. The cannula was also capable of achieving FTL motion within around 2.5 mm shape deviation and control performance within submillimeter errors. It was finally demonstrated to be capable of the nonlinear insertion and tip manipulation in the brain phantom. The new cannula design, together with the proposed algorithms, provides the unique ability to access ICH in a nonlinear trajectory and dexterous tip motion. These motion capabilities of the robot in such a slender form factor will lead to more complete ICH evacuation and reduced trauma to the healthy brain tissues.

Strong Convexity of Feasible Sets in Off-line and Online Optimization

It is known that the curvature of the feasible set in convex optimization allows for algorithms with better convergence rates, and there is renewed interest in this topic for both off-line and online problems. In this paper, leveraging results on geometry and convex analysis, we further our understanding of the role of curvature in optimization: We first show the equivalence of two notions of curvature, namely, strong convexity and gauge bodies, proving a conjecture of Abernethy et al. As a consequence, this shows that the Frank–Wolfe–type method of Wang and Abernethy has accelerated convergence rate [Formula: see text] over strongly convex feasible sets without additional assumptions on the (convex) objective function. In online linear optimization, we identify two main properties that help explaining why/when follow the leader (FTL) has only logarithmic regret over strongly convex sets. This allows one to directly recover and slightly extend a recent result of Huang et al., and to show that FTL has logarithmic regret over strongly convex sets whenever the gain vectors are nonnegative. We provide an efficient procedure for approximating convex bodies by strongly convex ones while smoothly trading off approximation error and curvature. This allows one to extend the improved algorithms over strongly convex sets to general convex sets. As a concrete application, we extend results on online linear optimization with hints to general convex sets. Funding: This work was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant Bolsa de Produtividade em Pesquisa #4310516/2017-0] Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Finance Code 001) Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (Jovem Cientista do Nosso Estado), Bolsa de Produtividade em Pesquisa #312751/2021-4 from CNPq, FAPERJ [Grant “Jovem Cientista do Nosso Estado”].

A Woodpecker’s Tongue-Inspired, Bendable and Extendable Robot Manipulator With Structural Stiffness

Woodpeckers have flexible and extendable tongues that they use to reach their prey through tiny openings in trees and insect burrows. This unique capability of their tongue represents a promising design for a tool for picking up and handling objects in unstructured environments. Although continuum robots can produce dexterous movements because of their few shape constraints, the lack of structural stiffness has restricted their deployment in real-world environments. Inspired by the characteristics of woodpeckers, we designed a robot manipulator that can substantially extend its length and bend its shape in 2D space. This behavior is enabled by a backbone consisting of a chain of rigid joints and two flexible rack gears. The joints increase the payload by structurally supporting the robot. The proposed structure is 4.7 times stronger in vertical bending and 6.2 times stronger in torsion than without rigid links. Feeding the rack gears at the same and different speeds allows the robot to elongate and bend, respectively. We developed a geometric model based on a constant curvature model for motion planning. Experiments show that the robot can follow an arbitrary trajectory at an arbitrary tip angle. Lastly, we showcase various demonstrations, including deployment and storage for the backbone, follow-the-leader (FTL) motion, and whole-arm grasping in the horizontal plane.

An ensemble approach to meta-heuristic algorithms: Comparative analysis and its applications

In this paper, we intend to propose an ensemble optimization algorithm based on Follow The Leader (FTL), Multi-verse Optimizer (MVO), and Salp Swarm Algorithm (SSA) to solve constrained optimization problems. The FTL, MVO, and SSA are swarm-based algorithms that update their particle position using a selection approach. Less number of control parameters and a common selection approach make these algorithms suitable for hybridization. In this work, combinations of FTL, MVO, and SSA algorithms such as FTL_MVO, FTL_SSA, MVO_SSA, and FTL_MVO_SSA have been proposed to solve different optimization problems. The proposed ensemble optimization algorithms have been compared with base optimization algorithms on forty-eight unimodal and multimodal benchmark functions. The ensemble model has achieved significant performance improvement over base FTL, MVO, and SSA. Moreover, these algorithms have been tested on six well-known constrained optimization problems to benchmark their performance over real-world applications. Finally, the comparison with classical optimization algorithms reveals the efficacy of the proposed models.

A statistical mechanics approach to macroscopic limits of car-following traffic dynamics

We study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towards a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic processes. If FTL interactions dominate then one gets an inhomogeneous Aw–Rascle–Zhang model, whose (pseudo) pressure and stability of the uniform flow are precisely defined by some features of the microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is comparable to that of FTL interactions then one gets a Lighthill–Whitham–Richards model ruled only by the OV function. We further confirm these findings by means of numerical simulations of the particle system and the macroscopic models. Unlike other formally analogous results, our approach builds the macroscopic models as physical limits of particle dynamics rather than assessing the convergence of microscopic to macroscopic solutions under suitable numerical discretisations.

The MemoFlex II, a non-robotic approach to follow-the-leader motion of a snake-like instrument for surgery using four predetermined physical tracks

The fields of Minimally Invasive Surgery (MIS) and Natural Orifices Transluminal Endoscopic Surgery (NOTES) strive to reduce the level of invasiveness by entering the body through smaller incisions and natural orifices. Hyper-redundant snake-like instruments can help in this pursuit of reducing invasiveness. Such instruments can pass along multi-curved pathways through the body without any support or guidance from its anatomical environment. In this way, the width of the surgical pathway and thus the invasiveness of the procedure can be reduced significantly. This is referred to as Follow-the-Leader (FTL) motion.Generally, surgical instruments intended for FTL-motion are robotic systems that require medical grade actuators, sensors, and controllers, driving up costs and increasing their footprint in the operation room. Our goal was to discard the need for these elements and develop a non-robotic instrument capable of FTL-motion along pre-determined paths. A proof of concept prototype called MemoFlex II was developed, consisting of a cable-driven hyper-redundant shaft that is controlled via four physical tracks. The MemoFlex II was able to perform 3D FTL-motion along pre-determined paths. Among other things, this study reports on a Ø8 mm shaft containing seven segments and 14 degrees of freedom (DOFs) following several multi-curved paths with an average maximal footprint between 11.0 and 17.1 mm.

Design of Concentric Tube Robots Using Tube Patterning for Follow-The-Leader Deployment

Abstract Concentric tube robots (CTRs) have a great potential for use in medical applications. Coupled with a follow-the-leader (FTL) deployment, they allow navigation in constrained environments. However, they are subject to instabilities if one makes use of high curvatures for the tubes, long overlapping lengths of their curved sections, or long transmission lengths. One approach to improve their stability is to pattern the tubes of which they are composed by local removals of material along their lengths. Applying patterns on tubes was proved to be of interest for given deployed lengths of a CTR. In this article, we present a method to enlarge the application field of CTRs that deploy in a follow-the-leader manner, by integrating tube patterning in the design process, with a stability criterion. Our method allows the designer to determine a custom pattern geometry to theoretically ensure the stability of CTRs made of any number of constant curvature tubes, for a complete FTL deployment sequence, and while respecting a desired shape during deployment.

SLAM-Based Follow-the-Leader Deployment of Concentric Tube Robots

This paper deals with an original combination of navigation by simultaneous localization and mapping (SLAM) and follow-the-leader (FTL) deployment for the control of concentric tube robots (CTRs). The objective is to make possible the automatic navigation of such continuum robots within an anatomical structure, by simultaneously managing both collision avoidance and map updating of the environment, i.e. , of the surrounding anatomical structures. Indeed, CTRs designed to achieve a FTL deployment to date were deployed on path identified during a planning task. In this work, this limitation is overcome by embedding, in the control scheme, an online trajectory estimation, therefore allowing an autonomous deployment of CTRs with an approximate FTL behavior. The proposed hybrid control law integrates a stability criterion to ensure at the same time CTR stability during deployment, required for a FTL deployment. The interest of the approach is demonstrated through simulation using realistic anatomical data and experiments, with a 3 degrees-of-freedom CTR.

When is it best to follow the leader?

An object is hidden in one of N boxes. Initially, the probability that it is in box i is πi(0). You then search in continuous time, observing box Jt at time t, and receiving a signal as you observe: if the box you are observing does not contain the object, your signal is a Brownian motion, but if it does contain the object your signal is a Brownian motion with positive drift μ. It is straightforward to derive the evolution of the posterior distribution π(t) for the location of the object. If T denotes the first time that one of the πj(t) reaches a desired threshold 1−ε, then the goal is to find a search policy (Jt)t≥0 which minimizes the mean of T. This problem was studied by Posner and Rumsey (1966) and by Zigangirov (1966), who derive an expression for the mean time of a conjectured optimal policy, which we call follow the leader (FTL); at all times, observe the box with the highest posterior probability. Posner and Rumsey assert without proof that this is optimal, and Zigangirov offers a proof that if the prior distribution is uniform then FTL is optimal. In this paper, we show that if the prior is not uniform, then FTL is not always optimal; for uniform prior, the question remains open.

An Online Saddle Point optimization algorithm with Regularization

This paper presents an online saddle-point optimization algorithm (OSP) to solve the optimal decision-making problem in economic games. In this setting, the two mutual competing players choose a pair of optimal decisions (Nash equilibrium) at each iteration. Firstly, the Follow the Leader (FTL) algorithm is proposed to update the decisions, and the regularization term is added to stabilize the Nash equilibrium for both players. Secondly, the saddle-point regret (SP-Regret) is used to measure the gap between the cumulative payoffs and the saddle point value of the aggregate payoff functions. To this end, this paper aims to minimize it. Finally, the simulation results show that, under the proposed OSP algorithm, the SP-Regret can still be sublinear with regularization and the decision variables of both players can be constrained to fluctuate within a certain range by adding regularization, which can effectively make the Nash equilibrium stable.

Continuum Robot With Follow-the-Leader Motion for Endoscopic Third Ventriculostomy and Tumor Biopsy.

In a combined endoscopic third ventriculostomy (ETV) and endoscopic tumor biopsy (ETB) procedure, an optimal tool trajectory is mandatory to minimize trauma to surrounding cerebral tissue. This paper presents wire-driven multi-section robot with push-pull wire. The robot is tested to attain follow-the-leader (FTL) motion to place surgical instruments through narrow passages while minimizing the trauma to tissues. A wire-driven continuum robot with six sub-sections was developed and its kinematic model was proposed to achieve FTL motion. An accuracy test to assess the robot's ability to attain FTL motion along a set of elementary curved trajectory was performed. We also used hydrocephalus ventricular model created from human subject data to generate five ETV/ETB trajectories and conducted a study assessing the accuracy of the FTL motion along these clinically desirable trajectories. In the test with elementary curved paths, the maximal deviation of the robot was increased from 0.47 mm at 30 ° turn to 1.78 mm at 180 ° in a simple C-shaped curve. S-shaped FTL motion had lesser deviation ranging from 0.16 to 0.18 mm. In the phantom study, the greatest tip deviation was 1.45 mm, and the greatest path deviation was 1.23 mm. We present the application of a continuum robot with FTL motion to perform a combined ETV/ETB procedure. The validation study using human subject data indicated that the accuracy of FTL motion is relatively high. The study indicated that FTL motion may be useful tool for combined ETV and ETB.

Design and Optimization of Concentric Tube Robots Based on Surgical Tasks, Anatomical Constraints and Follow-the-Leader Deployment

Many neurological disorders are characterized by the focal and anatomically definable lesions within the brain parenchyma. Traditional treatment may introduce major trauma in neurosurgery and conventional medical devices can only trace straight trajectories. To overcome these problems, a design and optimization method for a patient-specific concentric tube robot (CTR) satisfying the constraints of anatomy, surgical tasks and follow-the-leader (FTL) deployment is proposed in this paper. CTR is a tentacle like continuum robot that can work inside confined and complex biological chambers with the ability of tracking complex 3D trajectories. It consists of pre-curved superplastic tubes with hollow cavities to accommodate the surgical tools. These merits make the CTR well suitable for minimally invasive surgeries. This paper introduces a design framework that utilizes preoperative MRI data to configure patient-specific CTR for single and multiple tasks with the minimum number of tubes. A constant curvature circular arc model is built to solve the problem of inverse kinematics. Two iterative optimization methods for single and multiple tasks are proposed to optimize the parameters of the CTR. Initial waypoints of the CTR are produced based on the FTL deployment. The waypoints are then refined using a Follow Shape Rapidly-exploring Random Tree algorithm (FSRRT) for cases that the initial configurations of the CTR cannot completely satisfy the FTL deployment. Simulations and experiments are carried out on a human brain model to validate the proposed methods. The parameters of CTR including the entire length, curvature, radius angle, number, diameter, arc length and the waypoints are obtained. The errors of the FTL deployment are found to be within 2.1mm.

A numerical framework for the stability and cardinality analysis of concentric tube robots: Introduction and application to the follow-the-leader deployment

Concentric tube robot (CTR) is a promising class of continuum robots for medical interventions given their compactness and dexterity. Their dexterity is in particular being used to achieve so called Follow-the-Leader (FTL) deployments, where the tip path draws the shape of the robot. During this kind of deployment they can however be subject to elastic instabilities, and the number of reachable configurations may vary for a given state of actuators. These cardinality and stability changes need therefore to be predicted during CTR design. Available methods and results are limited, with restrictive assumptions on number and properties of tubes. We therefore propose in this paper a numerical framework for the cardinality and stability assessment of CTR. It is based on the association of dynamic relaxation, continuation method and bifurcation analysis. The numerical framework is validated by reproducing reference results on the stability and cardinality of two-tube robots. Then, new results on three-tube CTR deploying in a FTL manner are presented. The framework genericity allows in particular to provide new insights on the behaviour of CTR with helical-shaped tubes.

Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow

We show how to view the standard Follow-the-Leader (FtL) model as a numerical method to compute numerically the solution of the Lighthill-Whitham-Richards (LWR) model for traffic flow. As a result we offer a simple proof that FtL models converge to the LWR model for traffic flow when traffic becomes dense. The proof is based on techniques used in the analysis of numerical schemes for conservation laws, and the equivalence of weak entropy solutions of conservation laws in the Lagrangian and Eulerian formulation.

Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition

We study a Follow-the-Leader (FtL) ODE model for traffic flow with rough road condition, and analyze stationary traveling wave profiles where the solutions of the FtL model trace along, near the jump in the road condition. We derive a discontinuous delay differential equation (DDDE) for these profiles. For various cases, we obtain results on existence, uniqueness and local stability of the profiles. The results here offer an alternative approximation, possibly more realistic than the classical vanishing viscosity approach, to the conservation law with discontinuous flux for traffic flow.

On minimaxity of Follow the Leader strategy in the stochastic setting

We consider the setting of prediction with expert advice with an additional assumption that each expert generates its losses i.i.d. according to some distribution. We first identify a class of “admissible” strategies, which we call permutation invariant, and show that every strategy outside this class will perform not better than some permutation invariant strategy. We then show that when the losses are binary, a simple Follow the Leader (FL) algorithm is the minimax strategy for this game, where minimaxity is simultaneously achieved for the expected regret, the pseudo-regret, and the excess risk. Furthermore, FL has also the smallest regret, pseudo-regret, and excess risk over all permutation invariant prediction strategies, simultaneously for all distributions over binary losses. We generalize these minimax results to the case in which each expert generates its losses from a distribution belonging to a one-dimensional exponential family, as well as to the case of loss vectors generated jointly from a multinomial distribution. We also show that when the losses are in the interval [0,1] and the learner competes against all distributions over [0,1], FL remains minimax only when an additional trick called “loss binarization” is applied.