This study proposes a computational method for approximating the Minkowski sum of two ellipsoids in three-dimensional space using a superellipsoid. Computing the Minkowski sum using high-precision mesh generation is expensive. Therefore, methods for approximating the Minkowski sum using functional representations have been proposed. In particular, numerous approaches use ellipsoids for approximation but suffer from accuracy limitations. The shape matrix and exponents of the superellipsoid are derived through a closed-form computation with constant time complexity of O ( 1 ) , independent of any boundary sampling resolution. Moreover, because the superellipsoid is an implicit function, the inside–outside testing of points is straightforward and requires only the evaluation of an inequality. In our experiments, we evaluate various parameter combinations for two general ellipsoids. The results demonstrate that the superellipsoid approximates the Minkowski sum with small error. Additionally, a comparison with an existing method that approximates the Minkowski sum of rotational ellipsoids using superellipsoids shows comparable accuracy, while the proposed method generalizes the approach to arbitrary ellipsoids. Regarding execution time, the method exhibits consistently fast and stable performance, as it relies solely on closed-form computation. The theoretical framework of this method has the potential to be extended to N -dimensional spaces, and is expected to find applications not only in rigid body simulations in three dimensions but also in computational tasks, such as grasp stability evaluation for robotics in six dimensions.

Shape-changing garments have gained increasing attention in wearable technology due to their potential applications in adaptive wearables, assistive technology, and soft robotics. This paper presents the design, fabrication, and experimental evaluation of a flat tube bending actuator, focusing on air pressure, flat tube design, and resulting deformation. The study investigates the relationship between applied pressure and bending angles, the curvature per length, and air leakage for each design. Additionally, the actuators were integrated into a shape-changing garment with optimized flat tube designs. Various air-supplying methods were analyzed to optimize the supplying pressure to resist the leakage of the fabric. Experi-mental results demonstrate controllable shape transformations by each type of actuator, highlighting the actuator’s adaptability for wearable applications.

Abstract In this paper, we propose a fast and accurate method for approximating the Minkowski sum of two rotational ellipsoids with a superellipsoid. The Minkowski sum is used in a variety of applications such as robot motion planning and particle flow simulation requiring collision detection. Many of them are computed based on Minkowski sum, whose accuracy and processing time depend on how the mesh is created. We approximate Minkowski sum with a superellipsoid function. The superellipsoid has various shapes with the value of the exponents, and the computation of the parameters including the exponents is an algebraic computation with the time complexity $$\varvec{O}(1)$$ O ( 1 ) . As a result, approximation error is small and computation is fast in all combinations of rotational ellipsoids. In addition, collision is quickly detected by solving the inequality of superellipsoid.

This paper presents a stiffness-changeable soft finger using chain mail jamming. This finger can achieve adaptive grasping and in-hand manipulation by reshaping and exerting changeable gripping force. The jamming phenomenon happens when particles in a chamber get interlocked where confining pressure is exerted at their boundaries, which is widely used to construct mechanisms with changeable stiffness. Compared with the traditional granular media, chain mail has a lower packing fraction and provides a stronger tensile force. In this paper, we proposed to apply chain mail jamming to the field of robotic finger design. Especially, we propose the design of the finger, the fabrication process, the method of predicting gripping force, and the grasping strategies. The experiments quantitatively verify the model of gripping force prediction. The demonstrations validate the advantages of adaptive grasp by picking a variety of items including foods, goods, and industrial components, and show the application of in-hand manipulation.

This study presents a method for estimating the three-dimensional (3D) shapes of transparent objects from an RGB-D image using a statistical shape model. Statistical shape models compress the dimensions of multiple shapes to represent shape variations using fewer parameters. It is difficult to measure the depth of a transparent object using sensors. Therefore, the statistical shape model is deformed to fit the contour extracted from an RGB image and estimate the shape of the object. The depth image is used only to detect the plane on which the transparent objects are placed. Unlike other estimation methods, the proposed method estimates the whole shape of a transparent object. To validate the proposed method, the obtained estimation accuracy is compared with that of a machine-learning-based method. In addition, the estimated whole shape is compared with the measured data from a 3D scanner.

Quickness, preciseness and robustness are required in manipulation tasks of robotic hands for automation of manufacturing sites. Previous researches have found that sensing from fingertips equipped with proximity sensors is available for the requirements, because it complements blind areas of vision sensors. In this paper, we develop a novel optical proximity sensor for robot fingertips which provides two levels of proximity information with different purposes, sampling rates, information quantity and quality. The lower-level information from the sensor is for high-speed feedback control of a robotic hand, and the higher-level information is for recognizing the shape and size of an object. A prototype of the sensor with 5 × 5 matrix of photo detectors is presented, and its availability is shown through basic characteristic tests. A motion experiment using a robotic hand equipped with the prototype sensors is also conducted. The result confirms that the robotic hand can adjust the position and orientation of the fingertips to various objects and then correct the grasping form according to the object size within 1s.

This paper presents methodologies for dexterous manipulation by an underactuated robotic soft gripper with a low DOF. While the softness and passive joints provide a stable grasp, the manipulations become challenging owing to the complexities of modeling and state estimation. To investigate the drawbacks, target manipulations using a support surface and gravity are defined in this study. By realizing the target manipulations, methodologies for utilizing both the support surface and gravity in manipulation are validated. For manipulation utilizing the support surface, the key states - at which the type of gripper motion primitive changes - are defined, and gripper motion at the key states is produced with a DNN-based motion generator. For manipulation utilizing gravity, the fall risk of the object is formulated as a constraint for a criterion function, and a parameters-online-exploration based methodology is adopted. The validity of the methodologies is demonstrated through several experiments.

The human fingertip has very high density of the receptor to accept sense of touch stimulation. The corresponding somatic sensory area in a brain is very large, and considered to be a specialized part for palpation. A lot of haptic display system then have been developed with the investigation of human haptic perception. However, the researches about the human perception for pulling force at grasping, namely static frictional force are limited. This paper investigated it, aiming at a future development of pulling and grasping force feedback system for neurosurgical robotic systems. For the purpose, this paper explored the possibility of displaying pulling force to an index finger during grasping. The absolute and difference thresholds for pulling sense were the targets. The results showed that grasping disturbs the pulling sense, and the sides of index fingertip can be used to display pulling sense, relatively large force, namely scaled force feedback is required for the perception. The results provide an important insight at a hardware and controller design of force feedback systems.

In this study, we experimentally investigated the effect of robot fingertip stiffness on the maximum resistible force. The maximum resistible force is defined as the maximum tangential force at which the fingertip can maintain contact when applying and increasing tangential/shearing force. We include in the definition of this term the effect of fingertip deformation. In contrast to our previous study [11], cylindrical fingertips with flat surfaces were used in this study so that the contact area would remain the same when there was no tangential/shearing force. This made it possible to see the effect of fingertip stiffness more clearly. We also investigated the effect of curvature of the contact surface, which was not investigated in depth in [11]. The main findings are as follows. 1) Harder fingertips produce larger resistible forces, irrespective of the shape of the contact surface (flat or curved). 2) For harder fingertips, the maximum resistible force depends largely on the shape of the contact surface, while for softer fingertips, the shape has little effect. 3) For softer fingertips, the magnitude of the resistible force changes little even when the normal force increases.

In this study, we experimentally investigated the process leading to fracture in tofu grasping by deformable fingertips filled with a fluid. In our previous papers [1, 2], we developed deformable fingertips using a rubber bag filled with a viscoelastic fluid, and presented a strategy for delicate tofu grasping without any advance knowledge about fracture. However, the predication point was close to fracture, and the prediction was then still a gamble. In order to realize fracture prediction at an earlier stage, we examined the process leading to fracture when pushing tofu by the deformable fingertips. The stiffness of the fingertips can be controlled with the pressure of the fluid inside the fingertips. The pushing force and fluid pressure were examined for different levels of stiffness of the fingertips. The main findings and contributions are as follows. 1) The convergence of the ratio of the contact force to fluid pressure gives an indication of dent occurrence. This convergence could be seen when fingertip rubber bag was not filled (low stiffness). 2) It was easier for a dent to occur when the fingertip rubber bag was not filled than when it was filled (high stiffness). 3) Changes in the rate of increase of the fluid pressure as the tofu was pushed were repeatedly observed. We defined this as a phase change and present a method for detecting such changes. The phase change points were detected by comparing the fitting accuracies of different approximation models. 4) The last and second to the last phase changes before fracture were detected by detecting the first phase change (after the convergence of the rate of the contact force to fluid pressure if the fingertip bag was not completely filled). The detected points can be regarded as alert points indicating a fracture risk that is not close to the fracture point.

In this study, we experimentally investigated the effect of robot fingertip stiffness on friction during grasping of an object. To make robots more human-friendly, robotic hands with soft surfaces have been developed. A soft fingertip, i.e., one with low stiffness, is considered desirable because it produces high friction. However, in our experiments, we were able to obtain high friction from a stiff fingertip under a certain condition. We initially investigated the maximum resistible force when solid objects with different angled surfaces were grasped by spherical fingertips of different stiffness. When the contact surface was flat, a stiffer fingertip produced larger frictional force. When the contact surface was highly convex, the maximum frictional force increased with decreasing fingertip stiffness. Secondly, we examined the relationships among the contact area, the load, and the maximum frictional force. We reformulated the relationship between the load and the maximum frictional force and, together with our experimental results, used it to determine the factor that increased the maximum frictional force.

This paper presents a gripper with fingertips constructed from incompressible fluid covered by rubber with the aim of grasping very fragile objects. Owing to the incompressibility, simply closing the gripper allows the fingertips to approach the target object with low stiffness; after contact, the contact stiffness increases with increasing fingertip deformation, and grasping with high stiffness can be realized. The adaptation of the fingertips to the object shape and a uniform contact pressure are further benefits of the proposed system. Fragile and brittle objects can be grasped by controlling the contact pressure so that it does not exceed the fracture stress/pressure. We found that the initial sign of fracture appears before total fracture when soft and ductile objects are grasped. Based on this phenomenon, we developed a strategy for grasping ductile objects without any advance knowledge of fracture. The proposed fingertips have a rigid layer inside the fluid to grasp objects with normal rigidity. The effectiveness of the fingertips was confirmed experimentally.

This paper investigates how visual cues affect human performance at a line drawing task. Line drawing is a primitive and fundamental task using tools such as pens, (soldering) irons, and cutters. Many situations (for example, home, office, studio, and workshop) require drawing lines with tools. Assistive tools for improving performance might be especially useful for unskilled people. As a first step, we focus on visual cues as assistive tools and determine the kinds of visual cues that are effective for good performance. We asked subjects to draw a line on a displayed dotted line while the spacing and shape of the dots is changed, and we then analyzed the data. The results indicate that the cue that should be displayed for good performance should change according to subjects' performance: for good performers the cue whose geometrical center is easy to detect, and for not-good performers the cues whose occupied area is large. We also discussed the possibility of controlling performance in line drawing, and presented a strategy for displaying visual cues for good line drawing performance.

This paper presents a novel approach for grasp optimization considering contact position and object information uncertainties. In practice, it is hard to grasp an object at the designated or planned contact positions, as errors in measurement, estimation, and control usually exist. Therefore, we first formulate the influences of contact uncertainties on joint torques, contact wrenches, and frictional condition. We then include external wrench uncertainties in the required external wrenches set. Based on this formulation, we define the linear grasp optimization problem for two kinds of frictional contact models-frictional point contact and soft finger contact-so that we can successfully grasp an object even if deviations in contact point, object weight, and center of mass occur. The validity of our approach is shown by means of numerical examples and the result of experiments.

This paper presents a novel analysis for the effects of softness at the fingertip on the manipulability and stability of grasping. The stability for grasping can be regarded that how much magnitude of external wrench we can balance. We formulate manipulability and the set of generable object wrenches for grasping system, taking deformation of the fingertips into consideration, and show that the increase of the softness decreases the manipulability while it increases generable object wrench. The validity of our analysis is shown by numerical examples.

This paper presents new manipulability measures to evaluate how much easily the robot manipulates the grasped object, simultaneously taking how much magnitude of joint torque we need to keep grasping into consideration. For the purpose, we use operation range. The operation range is for actuator attached to every joint of robot and provides generable joint torque and velocity and their relation (between generating torque/velocity and addable velocity/torque). While we introduced a manipulability measure using the operation range in our previous paper, it was for a limited class due to large computational effort and we could not evaluate whole space of object velocity and could not consider whole space of external wrench. This paper proposes new manipulability measures which can evaluate whole space of object velocity, taking the effect of external wrench in whole space into consideration.

Our previous paper presented a method for reducing adhesion forces by oscillation and showed the adhesion state can be checked by analyzing the data obtained by laser displacement meter. However, there are several problems in this method. 1) The end-effector must be located at the specific point where laser displacement meter can measure oscillation. 2) The adhesion state can not be checked if something blocks the light/laser or the target leaves the measuring point. 3) The total system becomes very large. To resolve these problems, this paper firstly presents a method for checking the adhesion state by piezo-transducer. Next, to achieve more precise manipulation, we propose a method to deform the end-effector by adding DC input to the piezo actuator which is also oscillated simultaneously to reduce adhesion forces. Furthermore, we find that the first mode resonance frequency shifts with the increase of the pushing force applied to the object by the end-effector. Using the shift amount, we develop a method for checking the adhesion state.

This paper provides a new approach of manipulability for general grasping system. While conventional manipulability is analysis in velocity domain and can not include force effect such as gravitational force, the proposing approach can include the force effect to keep grasping. For the purpose, an operation range is introduced. The operation range is for actuator attached with every joint of robot and provides generable joint torque and velocity and their relation (between generating torque/velocity and addable velocity/torque). Using the operation range, we derive manipulability set and measure in velocity domain, including force effect. The proposing method can evaluate not only the performance in velocity domain but also effects of friction, contact state, and external forces, which were not obtained in conventional studies.

In our previous paper, we proposed a method for reducing adhesion forces by oscillation. However, the following problems have not been still resolved: (1) Since adhesion state was checked by analyzing the data obtained by laser displacement meter, this method is available in only limited situations. (2) Automatic checking system for adhesion state was not developed. (3) Automatic micro manipulation system was not developed. Considering the above, in this paper, we propose a method to automatically check adhesion state by vision. Firstly, we develop a method to estimate the amplitude of the oscillation using the blur resulted from the oscillation. We call the estimated amplitude AIV (amplitude indicating value). Then, we develop a method for checking adhesion state by AIV. Based on the checking method, we develop a automatic micro manipulation system for pick and place operation. The validity of our method is shown by experiments.

In this paper, we investigate optimal grasp points on an arbitrary-shaped grasped object using a required external force set. The required external force set is given based on a task, and consists of the external forces and moments, which must be balanced by virtue of contact forces applied by a robotic hand. When the origin is in the interior of the set, a force-closure grasp is required. When the dimension of the set is one, an equilibrium grasp is required. Therefore, we can investigate whatever the desired grasp is, such as when the desired grasp is a force closure and equilibrium grasps. Also, we only have to consider the forces contained in a given required external force set, not the whole set of possible resulting forces. Furthermore, we can avoid the frame-invariant problem (the criterion value changes with the change of the task (object) coordinate frame). We consider an optimization problem from the viewpoint of decreasing the magnitudes of the contact forces needed to balance any external force and moment contained in a given required external force set. In order to solve the problem, we present an algorithm based on a branch-and-bound method. We also present some numerical examples to show the validity of our approach. Note to Practitioners-This paper is concerned with grasping an object by a robotic hand. This article address how to grasp the object, namely, how to position every finger on the object. Recently, robots are desired to be used in housekeeping and in caring for elderly people. For this purpose, robot (multifingered) hands are equipped with the robots as general-purpose end effectors. The robot hands are required to automatically move to accomplish such tasks. In this case, the most fundamental issue for robot hands is to grasp the object. At home, there are many various-shaped objects. Consider the case where the robot (hand) is commanded to perform a certain task, such as putting the object into a box. In this case, the robot (hand) must grasp such an object (of any arbitrary shape) with appropriate grasp positions for completing the task. Therefore, the appropriate grasp positions must be calculated automatically. This article addresses a method to solve this problem. But to complete the grasping task, the following problems remain: calculation and control of the appropriate grasping forces

In this paper, we analyze the mechanism of the phenomenon between an end effector, a micro object and a substrate during a micro manipulation. In a micro range, the attracting forces such as the van der Waals, capillary, and electrostatic forces dominate and course adhesion between the object and the end-effector. The adhesion makes the manipulation of an object difficult. Recently, we developed a method to reduce the attracting/adhesion effect. When bringing an oscillating end-effector close to a micro object on a substrate, the attracting force between the object and the end-effector is reduced, attracting the object to the substrate. Then, it becomes easy to remove the end-effector from the object. Using this method, a micro object can be easily manipulated. However, the mechanism of the phenomenon is still unclear. In this paper, we develop the theoretical model of the system to analyze the phenomenon, and simulate the dynamical motion of the system. Comparing the experimental results, we show the validity of our approach. Using simulation and experiment, we show that the oscillation of the end-effector can reduce the adhesion effect between the end-effector and the object, attracting the object to the substrate

This paper discusses the whole arm manipulation allowing the contact state transition. For manipulation of an object under fully constrained, the contact state transition becomes necessary. In order to realize the object manipulation, we first derive the feasible direction of the object manipulation by analyzing the active/passive closure properties for every combination of contact states. Second, we derive the set of joint torque to move the object in the feasible direction. These analyses also provide the joint torque to realize the manipulation at the planned contact states. Effectiveness of the proposed method is confirmed by some simulation results

In this paper, we discuss the manipulation of an object under hybrid active/passive closure. We show the orthogonality between the directions of active and passive force closures for general grasping systems. Based on the orthogonality, we decompose the dynamics of grasping system into the” active part” and the” passive part”. By using the decomposition, we show that the grasped object can be manipulated only by considering the dynamics of the active part. We also consider how to determine the desired internal forces in order to satisfy frictional constraints during the manipulation. In order to verify the validity of our approach, some simulation results are shown.

In this paper, we discuss the directions of active and passive force closures in hybrid active/passive-closure grasps. We show the directions are orthogonal to each other. We also discuss the magnitudes of the internal forces in the manipulation of the object. In hybrid active/passive-closure grasps, there exist two kinds of magnitudes of internal forces. One is the magnitude of internal forces, which changes if the object moves and the geometry of the fingers changes. The other is the one which don't change even when the object moves. We derive these two magnitudes.

In this paper, we proposed a novel strategy for pick and place operation in a micro range, by using a squeeze effect. In a micro range, the attracting forces such as the van der Waals, capillary, and electrostatic forces are dominate due to the scaling effect. The attracting forces make a release of an object difficult. In this paper, by vibrating the finger, we generate the gas film (the squeeze effect) between the object and the finger and relax the attracting forces. Some experimental results are shown to verify our approach.

In this paper, we consider an optimization of grasping by using a required external force set. Using the set, we cannot only deal with whatever a desired grasp is, such as force closure or equilibrium grasp, but also evaluate the magnitudes of the resistible external forces and moments. Then, we define an optimization problem from the viewpoint of decreasing the magnitudes of the contact forces required to resist the required external force, and show that we can solve the problem by using a branch-and-bound method. Lastly we present some numerical simulations to show the validity of our approach.

Power grasp is a grasp that can hold objects stably without changing the joint torques of fingers. Almost all studies on power grasp deal with one object, but it is more efficient to hold multiple objects at the same time. This paper derives a condition for power grasp for multiple objects, and defines an optimal power grasp from the viewpoint of decreasing the work of joint torques. Finally, we show some numerical examples to verify the validity of our approach.

This paper deals with the control of a 3-link planar underactuated manipulator whose most distal joint is unactuated. This system is known as a second order nonholonomic system. In a previous paper (1996), we proposed a control law that guarantees the convergence of its state to a given desirable trajectory and to any desired final point, and we also gave a design method of the desirable trajectory. However, this method has a limitation on the location of the initial state. In this paper, we propose a design method of a desirable trajectory that starts from any given initial point, converges to any given desired final point, and on the way passes through any given desired passing point that can be specified rather freely. By this new design method, one can derive a desirable trajectory that satisfies given requirements much better than the previous method.

We propose a dynamic control method of soft-finger hands for pivoting an object in contact with the environment. This pivoting operation is often observed when a human moves a large or heavy object such as furniture. Different from the conventional manipulation of the object by only fingers, the characteristic of the pivoting operation is that we can use the reaction force from the environment. By using this reaction force, we can expect the magnitude of the forces applied to the object by the fingers to be smaller than the conventional manipulation of the object by only fingers. Taking this characteristic of the reaction force into consideration, we propose a dynamic control method for pivoting. To verify our approach, the simulation result is also presented.