Conventional curved surface robot has a rectangular boundary, and kinematics theory has been constructed with the same premise. The authors have constructed the kinematics for the curved surface robot whose boundary does not depend on a roughly rectangular shape, but a robot to which the kinematics can be applied has not been realized. In this paper, we propose a new robot that does not actively control the curved surface shape and controls the shape of the boundary, thereby passively realizing a surface with the smallest area according to the boundary shape.

In this paper, we study a compact wheeled robot with high frequency repeated jumping. Jumping is not only expounding the explore field for the robot, but also express the robot emotion from the motion. We proposed that the robot can interact with a human for jump motion. Then, the robot required high frequency repeated the jumping motion. The robots were evaluated rapid jump frequency capability. The proposed robot has two wheels and a jumping mechanism based on snap-through buckling of an elastic strip. The proposed robot can jump about 5.9 cm high and repeated jumping at 1.9 Hz from the experimental result.

In this paper, we propose an algorithm for identifying the elastic property of an elastic rod along its body trunk. The proposed algorithm estimates the stiffness matrix for bending and torsion along the backbone curve of an elastic rod based on the measured information on its shape and the forces and torques applied at its base by making full use of the discretized Kirchhoff elastic rod model. We propose a system for identifying the elastic property as well. Experimental result using an elastic strip with a known elastic property shows that the proposed method can estimate the elastic property of the rod successfully by averaging the estimated elastic values for different rod poses with the weight where elastic values estimated from straight shapes are not considered to be accurate.

In this research, we propose a measurement system for surface undulation detection using a scanning soft haptic sensor. The scanning soft tactile sensor is a haptic device in which two long strain gauges are embedded in rubber layers. When the haptic sensor is pressed against the surface to be measured and traced, the haptic sensor outputs a signal corresponding to the shape of the surface. By learning the signal on machine learning and using the result, it is possible to detect the size of the surface undulation in real time. Furthermore, by aligning one of the embedded strain gauges by tilting, the position of the surface undulation can be measured from the phase difference of the two strain gauges and the tracing position. A measurement system that enables the detection of the position and size of the surface undulation on the measurement target surface by using the scanning soft haptic sensor is described.

Pneumatic artificial muscles have unique advantages such as high compliance, high ratio of power to mass, and easy manufacturing. Especially, the flexibility contributes to compose novel mechanisms. The flexibility of pneumatic artificial muscles releases us from the spatially strict design required for rigid mechanical elements: it could actualize compact mechanisms made of a fewer parts. The authors propose to manufacture the machine with uniformed structure of simple parts. We fabricated novel soft mechanisms that are composed of only woven strings and thin McKibben muscles. The structure is uniformed; nevertheless, the forms and movements of mechanisms are diverse. In this paper, we report the experiment to reveal the bending force characteristic of the active textile.

In this manuscript, we propose a fish-like underwater robot composed of a silicone resin. By utilizing a silicon resin, we can fabricate a small, lightweight underwater robot. This manuscript especially describes a fabrication method of a fish-like robot using a mold casting. By defoaming in the chamber of a vacuum packaging machine, the outer shell of the fish-like robot can be easily fabricated. The internal mechanism which is composed of a microcontroller, a drive circuit, a battery, a servomotor, and a fin is encapsulated into the outer surface. The outer surface is sealed using additional silicone resin after assembling. We finally assess the performance of our prototype through several locomotion tests in air and underwater.

With the biomechanical fusion system consisting of biological parts and artificial mechanical parts, we can incorporate the excellent properties of living organisms into the engineering system. The most important thing in such a system is how to interface biological and mechanical parts. In this research, in order to freely move the musculoskeleton of the living body, the purpose is to know what kind of stimulation should be given to the nerve. Using Xenopus as an experimental subject, we examined the relationship between the pattern of electrical stimulation and the posture of the lower extremity. Experimentally showed that we can make the lower limb in desired posture using the obtained relation.

In table tennis robots, a spinning ball is difficult to be returned to the opponent court because its direction of bound is dependent on the spinning direction and amount. We aimed to solve this problem by swing motion that is robust over a large range of spinning pattern without accurate recognition of spinning. Specifically, we examined the relation between swing speed and returning direction. When the racket speed was 7 m/s, the difference of returning direction reduced to 20 % compared to no swing against the spinning ball in the range from -20 rev/s to 20 rev/s. In addition, we focused on the flexibility of swinging arm to increase the swing speed. We found that a flexible arm swung faster than a rigid arm in the whole range of motion when exploiting the joint angle limit.

A soft gripper has the possibility to manipulate arbitrarily shaped objects by adapting its shape subject to the objects. The goal of this research is to develop a novel soft gripper which can manipulate plural objects simultaneously by one action. As the first step of this study, a soft gripper that can open and close by one action and that also can grasp plural object simultaneously is modeled, and its dynamic movements are simulated in order to investigate the effect of each joint stiffness to its motion. The stiffness parameters in the simulations are identified from the experiments. Through simulation results, it is shown that the desired final shape of the manipulator can be achieved using our model.

We propose an active bending thin scalpel mechanism capable of separating tissue into a three-dimensional curved surface. Many mechanical tools have been developed, however, it has been difficult to separate a tissue into a curved shape. In this paper, we develop a scalpel that can realize active bending motion with a thin structure. The basic principle of the bending is demonstrated, and the prototype scalpel is fabricated. The basic bending experiment is conducted, and the target tissue was separated using the proposed prototype.

In this paper, we present a multi-material 3D printed soft finger with an integrated bending sensor to measure its contact force. The bending sensor is made of polyurethane, and then inserted in to the inflation chamber of the soft finger. When the soft finger is contract with an object, it is possible to get the contact force from sensor curvature readings and finger inflation pressure. Experiments are carried out to calibrate the sensor curvature and inflation pressure response to the contact force between soft finger and objects. Results have proven the contact force measured by the bending sensor is accurate and reliable, with a maximum error of 0.1N.

We propose an axially-reinforced torus balloon mechanism that can grasp complex shape objects by wrapping and adapting its shape. Several soft grippers using a balloon have been proposed which consist of elastic rubber materials. However, since the traction force does not transmit efficiently due to its soft body, it had difficulty in grasping heavy objects. To solve this problem, we constructed a torus balloon that is axially reinforced by inextensible fibers. The fabrication method is presented, and the stress-strain property is measured of the torus membrane. A basic grasping test was conducted to show its effectiveness.

This paper presents a jellyfish soft robot to collect rubbish such as micro plastics floating around in the water. We focused on the flow of water caused by a behavior of real moon jellyfish and proposed the jellyfish soft robot using shape memory alloy (SMA) actuators. The cap body of jellyfish soft robot is 218 mm in diameter and 142 mm in height. We put the SMA actuators on its cap body. The cap body was bent into a circle like a motion of real jellyfish when the SMA actuator was operated by applying electric current. To investigate the response time of the bending motion, we monitored the cap body of jellyfish soft robot using a high speed camera. When 3.2 A 16.2 V electric current for 2.0 seconds was applied, the bending displacement was approximately 35.3 mm at maximum.

In order to move on uneven ground, control with sensor such as a force sensor is necessary. Thus, we propose a soft continuum leg robot. The continuum legs passively change the shape and improve the ground adaptability without using the sensor. Moreover, the development of the continuum legs referred to brittle star. Brittle star is a moving creature that uses thin, long and flexible legs. It has a high step climbing ability and omnidirectional movement ability with five legs interlocked. These abilities are useful for mobile robots. In this paper, we describe development of the elliptic ball joint and the prototype of continuum legs with reference to brittle star.

This paper proposes an image stabilization method for a braided-tube in-pipe locomotive device. A braided-tube device is a simple in-pipe locomotive device with pneumatic power. Its deformation to locomote shakes a view from a camera which is attached at a device tip and a view from the camera. This study synchronizes an image update with a periodical deformation of a device. A synchronized update can acquire images which have the same field of view and succeeds to stabilize acquired images.

In this research, we aim to realize omnidirectional movement operation by developing flexible deformable body using 3D printer. However, the bending module developed in the previous study confirmed the problem of requiring air leakage and bending motion requiring high pressure, and a large number of tubes as a flow path. We developed an injection mechanism capable of injecting two-component curing type silicone called PDMS, which is a highly flexible material. In addition, since the number of tubes serving as flow paths is large, it is greatly affected by the movement operation in the omni-directional movement operation. Therefore, we developed a pneumatic self-excited valve aiming at reducing the number of flow channels.

Animals with soft bodies, such as snail and caterpillars, often exhibit excellent adaptivity to various terrain. For the purpose to clarify their excellence , the authors take a synthetic approach by constructing flexible robots which resemble their motion. In this paper, we develop a soft-bodied mobile robot using gel in which multiple shape memory alloy actuators in V-shaped arrangement. By applying periodic voltage with certain phase difference, we show that a surface wave appears on the robots belly, which results in its forward locomotion.

The goal of this research is to develop a novel manufacturing method for soft robots. In this article, we develop an initial prototype of hydrogel that is made from fish myofibrillar proteins. It is known that a kind of elastic hydrogel can be produced by adding salt to screw-pressed fresh muscles of animals and heating it. This phenomenon has long been exploited in the field of food manufacturing, and a wide variety of fish jelly products has been made from whitefish paste that is high in the myofibrillar proteins. A few manufacturing method such as a manual 3D printing are proposed by focusing on a mechanical property of the whitefish paste that has viscosity and shape retaining ability even before curing process by heating.

In this study, we focused on C.elegans and aimed to clarify its swarm search behavior mechanism. In this research we propose a method to quantify the complex trajectories of C.elegans. The proposed method is divided into three parts. First, the distance from the chemical source was derived from the coordinate frame data obtained by carrying out experiments. Second, we fitted this data using polynomial linear regression. Third, from this fitting we classified a pattern of the actions of C.elegans. Based on our proposed method, we could quantitatively analyze complex trajectories for all experimental trials after we classified them. This result suggests that the swarm search behavior can be quantified by comparing it with the classification result when experimenting with multiple specimens.

Foraging behavior to collect objects distributed in the field is one important task suitable for multirobot system. For effective performance, proper cooperation should be introduced into the robots. In this study, we propose a novel method for cooperative collective behavior of swarm robots. Once the robot finds an object, it stops there and broadcasts its position to other robots. The robots which receive the signal try to move towards the signal source and to search for another object. In our proposal, we introduce a “doubt point”, which is incremented when the robot fails to find another object. If the point exceeds given limitation, the robot ignores the signal even if it detects the signal from other robots. In this paper, we confirm the effectiveness of this algorithm in several different types of object distribution by computer simulation.

Autonomous vehicles have been developed to reduce traffic accidents and use as means of transporting the elderly. Autonomous vehicles require surrounding environment recognition with LIDAR to detect obstacles. In the conventional method, if dynamic obstacles are detected, dynamic state is estimated using Kalman filter, and if static obstacles are detected, map of static environment is made. However, this method sometimes cannot be consistent between dynamic obstacles and static obstacles. Therefore, this paper introduce Dynamic Occupancy Grid Map using LIDAR information. In Dynamic Occupancy Grid Map, the environment is represented by 2D grid, and this method is able to estimate velocity and object existence probability on each grid, so it is possible to recognize dynamic obstacles and static obstacles at the same time. In this paper, after making the map using actual driving data, we consider the estimation results of dynamic objects and static objects.

If one robot system can take various shapes, it can play various roles and be useful. Modular robots are robot systems in which multiple modules construct a robot by uniting, and it is possible to construct robots of other shapes by changing combinations of uniting of modules. In a conventional modular robot, there is a constraint on shape construction by gravity and some shapes are not able to be constructed. In this study, We propose a gravity compensation modular robot in order to solve this problem. This paper describes the design and prototyping of the gravity compensation modular robot and example of robot shapes by the gravity compensation modules and motion experiments of the robots.

In recent years, some studies have been conducted on algorithms to construct various shapes autonomously using a large number of robots. Such researches need to use many robots, external power sources by power lines are not realistic, therefore it is inevitably driven by batteries. However, charging and maintenance of batteries of many robots is not easy from the viewpoint of cost. To overcome this issue, we made a prototype of an ultra-compact wireless power supply system, which makes the operating time practically infinite, and we performed rudimentary operation testing. As a result, it was determined that a sufficient power supply to operate a single cleaning robot can be achieved.

This study tackles the task for swarm robotics where robots explore the environment to detect many targets. When a robot detects a target, the robot must be connected with a base station via intermediate relay robots for wireless communication. In our previous results, we confirmed that Lévy flight outperformed the usual random walk for exploration strategy in real robot experiments. This paper investigated the performance of Lévy flight varying minimum movement in navigation through a series of computer simulations. The results suggest that the search efficiency of Lévy flight has an optimal value for minimum movement and the overall target detection rate was not significantly different between environments with uniformly and non-uniformly distributed targets.

Search methods which search victims in accident at sea by using some drones are receiving a lot of attention. This paper compares some search strategies, such as parallel search pattern, expanding square search pattern, Lévy flight and so on, by using a multi-agent simulation. And we investigate an optimal search strategy for multi-agent systems.

Swarm robotics is the study of a large group of autonomous robots that emerges collective behavior from local interactions. This paper investigated the relationship between the cognition ability of a robotic swarm and the probability distribution of random walk. The task of the robotic swarm is to achieve consensus on the color that occupies more of the two-colored environment. The robot performs a random walk to explore the environment and disseminate its opinion. Three different probability distributions are employed for generating the random walk to investigate the effect on cognition ability of the robotic swarm. The results show that the random walk which travels the longer distance has better cognition ability to achieve faster consensus.

Multi-agent system (MAS) is constructed by many autonomous agents. Conflicts occur in MAS because of complex interactions among many agents. An agent needs to carry out a task and to avoid conflicts at same time. That is, each agent has to achieve the contradicting purposes. Therefore, this paper proposes a new approach by using multi-objective reinforcement learning as decision making system of an agents. We investigate the efficiency of the proposed approach through a simulation experiment that two agents pass each other in the narrow path.

Swarm robotics is the field of study that aims to generate a collective behavior of a large number of robots. In this paper, we applied deep reinforcement learning to design a controller for a robotic swarm. Deep reinforcement learning is a combination of reinforcement learning with deep neural networks that contain convolution layers. With the help of convolution layers, robots are able to learn from the camera image as the input of a deep neural network. When using deep reinforcement learning, however, it is difficult to understand the mechanism of improving performance. This paper analyses the convolution layers of the controller to understand the learning mechanism of a robotic swarm.

With the progress of technology, the realization of a symbiotic society with human beings and robots sharing the same environment has become an important subject. An example of this kind of systems is soccer game. Soccer is a multi-agent game that requires strategies by taking into account each member’s position and actions. The behavior of a player changes depending on the game situation, such as the score gap, the remaining time and the importance of the match. In this paper, a futsal game played by agents is observed and analyzed to find a mapping relationship. The strategy in the team is analyzed based on the state vector parameters using a Self-Organizing Map (SOM) and different behaviors are analyzed and compared to achieve, in the future, the best possible result cooperation in a real game.

Home service robots have begun attracting attention due to decreasing birthrate and increasing aging population. We,“Hibikino-Musashi@Home”team, develop home service robots, and participate international competitions; RoboCup@Home and World Robot Challenge (WRC), which are established to realize that robots will work and live with people in domestic environments. In this paper, we introduce our robots and technologies, especially an object recognition and manipulation system. We use You Only Look Once (YOLO) for object recognition. To train YOLO, a big dataset which is difficult to prepare in a short term is required. For this, we develop an automatic annotation system for YOLO which can generate 1.7 million training data, and we can complete training of YOLO in a day. To grasp objects, estimation of object orientations is required. Our system can detect the orientations by processing point clouds of objects. By using the system, we obtained about 30% of scores in Tidy Up Task in the WRC.

We study on a gait pattern generator with kick motion to perform walk-kick. The developed gait pattern generator calculates the trajectory of the center of gravity (COG) by using preview control. It can calculate the trajectory of COG such that the target ZMP is always near the center of the supporting foot, including when performing the kicking motion. As a result, it is possible to flexibly change the ground contact position and timing of the foot, so that it is possible to perform a kick motion at the swing leg. In this paper, after describing the developed walking pattern generator, we verify its effectiveness by experiment using a real humanoid robot.

In this paper, we describe the rover control method which our SuperNOVA team won in the Tanegashima rocket contest and won the distance of 0 m to the goal. In the past CanSat contest, our rover has approached the goal to about 5.81 m, due to the running control to the goal by GPS. However, according to the log file, in the GPS positioning information, our rover approached 0.4 m distance to the goal. This is due to GPS positioning accuracy. Therefore, with the running control using only GPS, it is not possible to reliably control the running of the rover to the goal to a distance of 0 m. Therefore, we propose a method to reliably guide the goal to the distance of 0 m by goal cone recognition by camera image and actually won the competition by achieving guidance up to 0 m in the Tanegashima rocket contest 2018.

In the robotic swarm using a large number of robots, there is a trade-off relationship between rapid robot manufacturing and robot stand-alone function improvement. In this research, we have developed the robotic swarm using real robots for real environments and considered construction of optimal real robot by using rapid prototyping method. Furthermore, the actual small mobile robot we proposed has a large number of sensors and image processing devices, and it is suitable for robotic swarm. We propose to emerge more flexible behavior by fusing multiple sensors mounted on actual robots.

In this paper, a line-trace robot is described. This robot is applied for robot contest in the practicum class of creative challenge of robotics in department of robotics. Rules of the robot contest and lecture contents are confirmed by making this robot.

One of the college students project of Nagasaki Institute of Applied Science has been participated in robot contest named the Micom Car Rally from 2010. In this paper, the history of the Micom Car Rally are explained, and the results of the project named MCR2.0 are described. In 2018, MCR2.0 was participated two conpetitions, and we got the third prize. Moreover, we proposed the soft material bumper made by 3D printer. This bumper will be able to adjust the shape and hardness.

Robot competition is holding with the theme of decommissioning of nuclear reactor organized by Ministry of Education, Culture, Sports, Science and Technology: MEXT since 2016. The competition is called ”HIRO creative RoboCon”. The first and second year, the targets of the competition were performances of the robots mobility. The this third year in 2018, the targets are changed total performance for decommissioning of nuclear reactor of the Fukushima Dai-ich. This report summarizes the outline of the three times competitions. We show that summary mainly the this third competition and simply the first and second.

This paper describes the robot contest produce competition and its purpose on creativity education. In this competition, participants plan an original robot contest for children including the rule book, the field, the robots for demonstration and the promotion video. Then, they present the robot contest as the trial management. This competition aims to promote their creativity, especially the problem-setting ability and the problem dividing ability, and presentation ability too. In this paper we report the results of robot contest produce competition 2018 conducted as a civic forum in the JSME annual conference.

In this research, we develop a new driving source using fluid pressure. Therefore, we propose a method called magnet flow in which a magnet is placed in a tube and the inside magnet is moved by air pressure. By using the magnet flow, it is thought that three operations of propulsion, rotation, and movement in the radial direction of the tube become possible. First, we examine the tube and magnet conditions that can be used for magnet flow. Second, we realize the propulsion motion, examine the propulsion force, and make a tube type propulsion robot. Finally, we realize the rotational motion and describe the development to the unidirectional rotation method.

Many products of small and high-performance computers have got easily-available in the market of recent years. In this paper, we examine the system architecture on humanoids equipped with these computers for high-performance and low-latency control of robot hardware. We developed and evaluated a few types of control systems which employ the FPGA boards with the recent popular high-speed communication links such as USB 2.0, EtherCAT, and Gigabit Ethernet. It is demonstrated that lower-latency control of humanoids can be achieved with FPGAs and high-speed communication links.

Slide-ring material (SRM) is a unique polymer that has ring-shaped cross-linking points, which lead to superior mechanical characteristics. Our previous work reported that a SRM sheet sandwiched by two compliant electrodes shows large bending deformation when subjected to a large electric field. This paper proposes a U-shaped structure to obtain linear displacement from the bending motion. In the proposed U-shaped actuator, an SRM sheet is bent into U-shape, whose tip linearly moves as the SRM sheet bends. The paper reports on its motion characteristics.

Steel plates are used for many products as the main material in the traveling line of the steelworks, the steel plate is contact-supported and traveled by rollers. However, the roller comes into contact with the steel plate, there occurs a problem that the surface quality deteriorates. In order to solve this problem, a noncontact guide system has been proposed which makes it possible to change the traveling direction by applying electromagnetic force from the direction of the edge of the running steel plate.In this study, we made a basic study on the difference of the damping effect that appears by changing the running shape of the steel plate.

In the steel plate production line, noncontact magnetic levitation conveyance of a thin steel plate using the attraction force of the electromagnet against the deterioration of the surface quality caused by contact with the roller is proposed. However, since the thin steel plate to be levitated is very flexible, deflection occurs at a place where the attraction force of the electromagnet does not reach, which is a cause of falling of the thin steel plate. Therefore、it is confirmed that by applying a magnetic field from the edge direction of the thin steel plate, the deflection of the thin steel plate is suppressed, and the levitation stability improves. We have considered levitation performance when the attraction force of the electromagnet, the transportation velocity, and the thickness of steel plate are changed. However, we have not examined the support position of the electromagnet installed at the edge of the steel plate. In this study, we conducted a basic study on the influence of supporting position on conveyance performance.

Humans have bi-articular muscles acting on two joints, and bi-articular muscles play a very important role in human action. For those reasons, the robot arms having a drive system based on the function of bi-articular muscles have been developed. In these robot, DOF for the control is lower than the DOF for the mechanism. Therefore, since that system depends on some kind of external force, it is necessary to know the characteristics for design the control. This study reports the mechanical characteristics of bi-articular muscle hydraulic actuator and robot arm using it. The hydraulic actuator consists of parallel connected master and slave cylinder. The slave cylinder is a differential mechanism with 3 ports. We examined the function as a bi-articular muscles actuator and confirmed the motion of the robot arm which depends on external force in the experiment.

Pneumatic artificial muscles have characteristics that are not found in motors such as lightweight and flexible. However, it is difficult to accurately sensing of state due to large deformation during operation and nonlinearity. To solve the problem, authors focus on a piezoelectric wire sensor which can sense change of shape. In this paper, we investigated the output characteristics of the piezoelectric wire sensor when changing collision speed, load and contact surface shape for sensing of artificial muscle. Results show that while the collision speed and the output are in a proportional trend, the load and the contact surface shape have less influence on the output.

We focused on the high elasticity of elastomer, and proposed a model for forming a three-dimensional structure using its characteristics. Furthermore, by exploiting elastomer as a dielectric elastomer actuator (DEA), we developed prototypes of a self-assembled actuator which can be driven by voltage application. We attempted several experiments to investigate basic characteristics of the actuator. Finally, we propose applications of the proposed actuator to the robots based on the experimental results.

Collaborative robots are expected to be applied in many fields in the near future, while high rigidity and high backdrivability are needed. A low friction gear is a good candidate for hightening backdrivability, but backlash on the gear is an issue for such a gear. In this paper, we therefore propose a two inertia model including nonlinear elements and tortion torque feedback using encoders. We showed that degradation of control accuracy due to internal deadzone, which is a demerit of the reduction gear, can be conpensated.

We develop a multi-legged robot with wire-driven telescopic legs. When a load is applied to the legs, length of the leg is shortened because the wire is stretched. In this paper, we develop a mechanism to estimate an amount of contraction of the legs. The mechanism consists mainly of a force sensor and urethane rubber. However, a problem is that a measurement range of force sensor is restriction. A measurement range is expanded by using urethane rubber. The amount of contraction depends on the length of the leg and the applied load. We construct an formula to estimate the amount of contraction depending on the value of the length and applied load by an experiment. We compare estimation of the mechanism with true value to evaluate the usefulness of the developed mechanism.

The current elevator is driven mainly by lifting and pulling up the wire with a pulley. However, deterioration and wear are caused by contact between the pulley and the cable in the conventional method. It is more difficult for maintenance and replacement of cable due to deterioration and abrasion, especially when long cable such as high-rise building is used. Therefore, reduction the number of maintenance and replacement become to be more important problem in the future. In this report, we propose a non-contact elevator using a linear induction motor that can move up and down in a noncontact manner with a wire without requiring a pulley. We carried out electromagnetic analysis to investigate thrust characteristics of proposed actuator and considered possibility of the elevator.

When an thin and flexible steel plate is to be levitated, levitation control becomes difficult because the thin steel plate undergoes increased flexure. We propose a levitation of an thin steel plate that is bent to the extent that the plate does not induce plastic deformation. It has been confirmed that vibrations are suppressed, and levitation performance is improved by bending levitation. In this study, we applied sliding mode control theory to the bending levitation system using 1DOF model and carried out levitation experiments. We conducted experiments on levitation performance when the electromagnet was displaced by frame vibration in the bending levitation system. We conducted experiments on levitation performance when the electromagnet was displaced by frame vibration in the bending levitation system. As a result, it is possible to realize stable levitation in the face of an input external disturbance when levitating at the optimum bending angle.