Worm-like Locomotion Research Articles

Optimal sliding mode control of electromagnetic worm-like locomotion systems for in-pipe robots

Optimal sliding mode control of electromagnetic worm-like locomotion systems for in-pipe robots

Design of PEIS: A Low-Cost Pipe Inspector Robot

This paper outlines the design of a novel mechatronic system for semi-automatic inspection and white-water in-pipe obstruction removals without the need for destructive methods or specialized manpower. The device is characterized by a lightweight structure and high transportability. It is composed by a front, a rear and a central module that realize the worm-like locomotion of the robot with a specifically designed driving mechanism for the straight motion of the robot along the pipeline. The proposed mechatronic system is easily adaptable to pipes of various sizes. Each module is equipped with a motor that actuates three slider-crank-based mechanisms. The central module incorporates a length-varying mechanism that allows forward and backward locomotion. The device is equipped with specific low-cost sensors that allow an operator to monitor the device and locate an obstruction in real time. The movement of the device can be automatic or controlled manually by using a specific user-friendly control board and a laptop. Preliminary laboratory tests are reported to demonstrate the engineering feasibility and effectiveness of the proposed design, which is currently under patenting.

Electromagnetic worm-like locomotion system for in-pipe robots: novel design of magnetic subsystem

This paper describes a magnetic subsystem of an electromagnetic worm-like locomotion system (WLLS) with coupled electromagnets. WLLS simple-design consists of two elastically connected ring-like segments that form two magnetically coupled electromagnetic actuators. The actuators generate longitudinal and transverse displacements which lead to locomotion due to synchronized changes of inertial, normal pressure, and friction forces. In present paper, analysis of the magnetic circuit of the WLLS had been performed. From symmetry and general consideration of magnetic system effectiveness, a novel design of the coupled magnetic circuits had been developed. The novel WLLS has two-force component electromagnetic actuators that produce the transverse and longitudinal forces. The novel design of the electromagnetic WLLS is able to move an in-pipe robots and should have better specific pulling force.

The Optimal Locomotion of a Self-Propelled Worm Actuated by Two Square Waves.

Worm-like locomotion at small scales induced by propagating a series of extensive or contraction waves has exhibited enormous possibilities in reproducing artificial mobile soft robotics. However, the optimal relation between locomotion performance and some important parameters, such as the distance between two adjacent waves, wave width, and body length, is still not clear. To solve this problem, this paper studies the optimal problem of a worm’s motion induced by two peristalsis waves in a viscous medium. Inspired by a worm’s motion, we consider that its body consists of two segments which can perform the respective shape change. Next, a quasi-static model describing the worm-like locomotion is used to investigate the relationship between its average velocity over the period and these parameters. Through the analysis of the relationship among these parameters, we find that there exist four different cases which should be addressed. Correspondingly, the average velocity in each case can be approximately derived. After that, optimization is carried out on each case to maximize the average velocity according to the Kuhn–Tucker Conditions. As a result, the optimal conditions of all of the cases are obtained. Finally, numerical and experimental verifications are carried out to demonstrate the correctness of the obtained results.

Exoskeletal transformations in Eriophyoidea: new pseudotagmic taxon Pseudotagmus africanus n. g. & n. sp. from South Africa and remarks on pseudotagmosis in eriophyoid mites

In addition to true tagmata, various pseudotagmata are present in chelicerates. Greatly miniaturized and morphologically simplified phytoparasitic acariform mites of the superfamily Eriophyoidea demonstrate a distinct ability to form pseudotagmata. The prodorsum and opisthosoma are the primary divisions of the eriophyoid body. In more evolutionary derived lineages, there is a trend towards the formation of additional opisthosomal subdivisions (pseudotagmata). These subdivisions are termed here “cervix”, “postprodorsum”, “pretelosoma”, “telosoma” and “thanosoma”. Among phytoptids, only the telosomal pseudotagma is present in several sierraphytoptine genera. In diptilomiopids, pseudotagmata have not been recorded. The most diverse examples of pseudotagmatization concern vagrant mites from the family Eriophyidae. Remarkably, well developed and unusually shaped pseudotagmata are peculiar to phyllocoptines from palms, especially in the new vagrant mite Pseudotagmus africanus n. g. & n. sp., found on leaves of Hyphaene coriacea (Arecaceae) in South Africa. Pseudotagmosis is one form of body consolidation in Eriophyoidea, reducing flexibility and therefore decreasing the ability for worm-like locomotion. Consequently, the legs become more important for locomotion. The other form of body consolidation is strengthening of the exoskeleton via armoring with microtubercles, and topographical changes (e.g. formation of opisthosomal ridges and furrows). The data at hand suggest that ancestrally, eriophyoids had an elongate body comprising many annuli, which can be regarded as pseudosegments. Later, they convergently evolved various pseudotagmata via the apparent fusion of these pseudosegments. Two morphotypes of vagrant mites (“armadillo” and “pangolin”) are proposed based on the difference in the modification of dorsal opisthosomal annuli. The minimal number of dorsal annuli (six) is equal to the number of dorso-longitudinal peripheral body muscles; however, this number is unlikely to reflect the true number of segments situated behind the prodorsum in Eriophyoidea. Although legs III and IV are absent in Eriophyoidea, the cervical pseudotagmata might be reminiscent of metapodosomal segments. Future comparative myo- and neuroanatomy studies of groups of genes involved in segmentation development are necessary to reach the final conclusion on the pattern of body segmentation in Eriophyoidea.

Analysis of worm-like locomotion driven by the sine-squared strain wave in a linear viscous medium

In this paper, a worm-like locomotion in a linear resistive medium is studied to achieve controlled shape changes of the worm-like body by choosing a kind of driving with low energy expended and high-velocity locomotion in certain condition. To this end, we first develop the full dynamic model of the system under consideration to obtain the mean velocity related to friction coefficient, wave speed, linear density, body length and wave width. Correspondingly, a quasi-static model is also given from which the velocity can be expressed analytically. In the case of the shape change driven by the sine-squared strain wave (SSSW), it is seen that these two velocities will tend to uniformity with the friction coefficient or length of the body increasing or the wave speed decreasing when keeping the other parameters unchanged. Thus, the inertia term is ignorable for a large friction, a long body-length but a small wave-speed of the SSSW, which implies that the dynamical model can be reduced to the quasi-static one. The relative criterion is approximately given. As a result, the corresponding quasi-static model is employed to consider two typical drives, namely, the SSSW and the square strain wave (SSW). The result shows the shape change driven by the SSSW has an advantage in both the mean velocity and the average energy expended over that by the SSW when the necessary condition is satisfied. The analytical results are verified by numerical simulation.

Dynamics and motion control of a chain of particles on a rough surface

In this paper the mechanics and control of the motion of a straight chain of three particles interconnected with kinematical constraints are investigated. The ground contact is described by dry (discontinuous) or viscous (continuous) friction. Here, we understand this model as a methodological basis for the design of worm-like locomotion systems, i.e., non-pedal mobile robots. This kind of robots will prove an efficient form of locomotion in application to inspection of pipes or for rescue missions. In this paper, a number of issues related to the dynamics and control of artificial limbless locomotion systems are discussed. Simplest models of a limbless locomotor are two-body or three-body systems that move along a horizontal straight line. In the first part of the paper, the controls are assumed in the form of periodic functions with zero average, shifted on a phase one concerning each other. Thus, there is a traveling wave along the chain of particles. In the second part, actuator models are discussed. It is supposed that there are unknown actuator data or the worm system parameter are not known or exactly as well. The focus is on adaptive control algorithms for the worm-like locomotion systems in order to track given reference trajectories, like kinematic gaits. Finally, a prototype together with its signal processing and control software is presented. Theoretically (analytically and numerically) calculated results of the dynamical behavior of the mobile system are compared to experimental data.

Energetic analysis and experiments of earthworm-like locomotion with compliant surfaces

The energy consumption of worm robots is composed of three parts: heat losses in the motors, internal friction losses of the worm device and mechanical energy locomotion requirements which we refer to as the cost of transport (COT). The COT, which is the main focus of this paper, is composed of work against two types of external factors: (i) the resisting forces, such as weight, tether force, or fluid drag for robots navigating inside wet environments and (ii) sliding friction forces that may result from sliding either forward or backward. In a previous work, we determined the mechanical energy requirement of worm robot locomotion over compliant surfaces, independently of the efficiency of the worm device. Analytical results were obtained by summing up the external work done on the robot and alternatively, by integrating the actuator forces over the actuator motions. In this paper, we present experimental results for an earthworm robot fitted with compliant contacts and these are post-processed to estimate the energy expenditure of the device. The results show that due to compliance, the COT of our device is increased by up to four-fold compared to theoretical predictions for rigid-contact worm-like locomotion.

Efficient worm-like locomotion: slip and control of soft-bodied peristaltic robots

In this work, we present a dynamic simulation of an earthworm-like robot moving in a pipe with radially symmetric Coulomb friction contact. Under these conditions, peristaltic locomotion is efficient if slip is minimized. We characterize ways to reduce slip-related losses in a constant-radius pipe. Using these principles, we can design controllers that can navigate pipes even with a narrowing in radius. We propose a stable heteroclinic channel controller that takes advantage of contact force feedback on each segment. In an example narrowing pipe, this controller loses 40% less energy to slip compared to the best-fit sine wave controller. The peristaltic locomotion with feedback also has greater speed and more consistent forward progress.

Analysis of worm-like locomotion

Nature is a storehouse of great ideas, which are mostly so well planned, that engineers can apply them directly via examining, understanding and imitating the natural working principles. Snakes and worms can be found in almost every region of our planet. Their success is mainly based on the simple construction of their body and their robust locomotion technique. Snakes and worms move their body periodically, to generate propulsive force and get forward, using the interaction with the surrounding environment. The aim of this work is the analysis of a particular worm-like locomotion technique through numerical simulations. The worm is modeled by a multibody system containing lumped masses constrained to each other by ideal rigid rods. The periodic motion of the worm body is achieved via the use of an artificial muscle-like actuator system. The results and experiences can be exploited in future work when a worm-like robot will be built for exploration and rescue purposes.

Worm-like robotic systems: Generation, analysis and shift of gaits using adaptive control

The starting point of this work is a biologically inspired model of a worm-like locomotion system (WLLS). The mechanical model comprises discrete mass points connected by viscoelastic force actuators. Ground contact is constituted by ideal spikes which act as constraint forces, preventing backward motion for each mass point equipped with them. The distances between each two consecutive mass points are changed by an adaptive controller in order to track a reference trajectory. In combination with the ground contact via spikes, this results in a (undulatory) locomotion of the system.After presenting the aforementioned model and the adaptive controller, the construction of specific reference functions, which result in certain gaits, is described. For this purpose an existing algorithm is used; it allows for defining the number and succession of the active spikes as well as the resulting velocity. In the following gait examination, simulations for worm systems with four mass points are carried out to find a selection of those gaits most suitable in terms of actuator and spikes load. Prior to implementing the automatic gait change, simulations are carried out to determine the criteria for shifting: actuator and spike forces. With those criteria, the choice of the optimal gait depends on both locomotion speed and ground inclination. An approximation of the forces mentioned before enables a formulation of inclination-dependent speed intervals. This leads to a combination of speed adjustment and gait change that enables optimal crawling for predefined limits of actuator or spike forces.

Adaptive Control of Singularly Perturbed Worm-Like Locomotion Systems

We consider a certain type of a worm-like locomotion system: a three mass point system. We assume that this worm is towing a payload, so the masses differ extremely, and we have to deal with a singularly perturbed system. The dynamics equations are coupled via a small parameter \({{\varepsilon}}\) , which is typical for singularly perturbed systems. In order to apply simple adaptive feedback mechanisms (to approach desired properties of the worm motion) we have to guarantee the minimum-phase property (among others) of such systems. We show that such properties are preserved under singular perturbation. This is done within a general system class via construction of a normal form to gain deeper insight and to analyze such systems. We present the general case and apply the basic transformations to the worm equations. We point out that we are able to classify all required assumptions and properties by system qualities as, e.g., zeros of the reduced model or boundary-layer system. This is in contrast to other authors.

Design and Modeling of a Snake Robot Based on Worm-Like Locomotion

In this paper we restrict our attention to worm-like, vertical traveling wave locomotion and present detailed kinematics and dynamics of a planar multi-link snake robot. Lagrange's method is used to obtain the robot dynamics. Webots software is used for simulation and to experimentally investigate the effects of link shape on motor torques. Using the dynamics model and Webots simulation, a nine-link snake robot is designed and constructed. Physical experiments are carried out to validate the mathematical model. Webots software is also used to perform simulation and further validate theoretical results. Finally, stability of the snake robot is experimentally investigated.

Gait generation considering dynamics for artificial segmented worms

This paper deals with terrestrial worm-like locomotion systems living in a straight line. They are modeled as chains of mass points having ground interaction via spikes which make the velocities unidirectional. A method is presented to construct gaits with any desired time pattern of resting mass points (which are acted on by the propulsive forces). Taking the dynamics into consideration, conclusions about the choice and shift of gaits in connection with actuator data are given.

Adaptive control of straight worms without derivative measurement

In this paper we consider an adaptive control problem of finite DoF worm-like locomotion systems (WLLS) which contact the ground with Coulomb dry friction. Using a rough mathematical friction law the system is shown to belong to a system class that allows adaptive control. Gaits from the kinematic theory can be tracked by means of adaptive controllers. For this we introduce two different adaptive controllers for λ-tracking and focus on that one which is not based on the derivative of the output. We pay attention to the analysis of such systems and present some theoretical control investigations including proofs. Numerical simulations of tracking different reference signals under arbitrary choice of the system parameters demonstrate and illustrate that the introduced simple adaptive controllers work successfully and effectively. Current experiments are aimed at the justification of theoretical results.

Oscillation induced worm-like locomotion of carbon nanotubes

Harmonic oscillation of a doubly clamped single-walled carbon nanotube rope is significantly damped by the resistive force of friction at intertube contacts and the energy transmission rate has been estimated to be lower than that on a metal wire excited at similar frequency and vibrating length by one order of magnitude.

Simulation of reiterated mechanical load of silicone rubber

A Peristaltically Actuated Device for Minimally Invasive Surgery (PADeMIS) is being developed at Technical University of Ilmenau. The device consists of compliant segments with cushions. Periodical filling of the cushions leads to a worm-like locomotion. To prevent injuries of the patient PADeMIS has to be compliant and silicone rubber is chosen as the material. During locomotion, some parts of the device will be subject to some thousand load cycles. Optimizing the design with FEA needs a constitutive law of the silicone rubber used. But the mechanical behaviour of this elastomer changes from loading to loading up to some thousand cycles. Hence, simulating the deformation of silicone rubber structures is problematic—because the stress–strain relation is furthermore not only dependent on the present strain. This work shows a possibility to describe the complex mechanical behaviour of the used silicone rubber with modelling the Mullins effect and the decreasing of the maximum stress, reached at same stretch with increasing number of load cycles, called stress softening. The resulting equations were implemented in the FEA program MSC.Marc2005r2 and the results are shown.

Adaptive [formula omitted]-tracking for locomotion systems

This paper deals with the (adaptive) control of mechanical systems, which are inspired by biological ideas. We introduce a certain type of mathematical models of worm-like locomotion systems and present some theoretical control investigations. Only discrete straight worms will be considered in this paper: chains of point masses moving along a straight line. We introduce locomotion systems in the form of a straight chain of k = 3 interconnected point masses, where we focus on interaction which emerges from a surface texture as asymmetric Coulomb friction. We consider two different types of drives: (i) The point masses are under the action of external forces, which can be regarded as external force control inputs. (ii) We deal with massless linear springs of fixed stiffnesses and controllable original spring lengths, which can be regarded as internal control inputs. The locomotion systems with these two types of drive mechanisms are described by mathematical models, which fall into the category of nonlinearly perturbed, multi-input, multi-output systems (MIMO-systems), where the outputs of the system are, for instance, the positions of the point masses or the displacements of the point masses. The goal is to simply control these systems in order to track given reference trajectories to achieve movement of the system. Because one cannot expect to have complete information about a sophisticated mechanical or biological system, but instead only structural properties are known, we deal with uncertain systems. Therefore, the method of adaptive control is chosen in this paper. Since we deal with nonlinearly perturbed MIMO-systems, we focus on the adaptive λ - tracking control objective to achieve our goal. This means tracking of a given reference signal for any pre-specified accuracy λ > 0 . The objective is not to obtain information about the characteristics of the system or about system parameters, but simply to control the unknown system. This control objective allows us to design simple adaptive controllers, which achieve λ -tracking. Numerical simulations of tracking different reference signals, for an arbitrary choice of the system parameters, will demonstrate and illustrate, that the introduced, simple adaptive controller works successfully and effectively.