Compliant Axis Research Articles

Imitation learning-based framework for learning 6-D linear compliant motions

We present a novel method for learning from demonstration 6-D tasks that can be modeled as a sequence of linear motions and compliances. The focus of this paper is the learning of a single linear primitive, many of which can be sequenced to perform more complex tasks. The presented method learns from demonstrations how to take advantage of mechanical gradients in in-contact tasks, such as assembly, both for translations and rotations, without any prior information. The method assumes there exists a desired linear direction in 6-D which, if followed by the manipulator, leads the robot’s end-effector to the goal area shown in the demonstration, either in free space or by leveraging contact through compliance. First, demonstrations are gathered where the teacher explicitly shows the robot how the mechanical gradients can be used as guidance towards the goal. From the demonstrations, a set of directions is computed which would result in the observed motion at each timestep during a demonstration of a single primitive. By observing which direction is included in all these sets, we find a single desired direction which can reproduce the demonstrated motion. Finding the number of compliant axes and their directions in both rotation and translation is based on the assumption that in the presence of a desired direction of motion, all other observed motion is caused by the contact force of the environment, signalling the need for compliance. We evaluate the method on a KUKA LWR4+ robot with test setups imitating typical tasks where a human would use compliance to cope with positional uncertainty. Results show that the method can successfully learn and reproduce compliant motions by taking advantage of the geometry of the task, therefore reducing the need for localization accuracy.

Directional Stiffness Control Through Geometric Patterning and Localized Heating of Field’s Metal Lattice Embedded in Silicone

This research explores a new realm of soft robotic materials where the stiffness magnitude, directionality, and spatial resolution may be precisely controlled. These materials mimic biological systems where localized muscle contractions and adjustment of tissue stiffness enables meticulous, intelligent movement. Here we propose the use of a low-melting-point (LMP) metal lattice structure as a rigid frame using localized heating to allow compliance about selectable axes along the lattice. The resulting shape of the lattice is modeled using product of exponentials kinematics to describe the serial chain of tunably compliant axes; this model is found to match the behavior of the physical test piece consisting of a Field’s metal (FM) lattice encased in silicone rubber. This concept could enable highly maneuverable robotic structures with significantly improved dexterity.

The Principal Axes Decomposition of Spatial Stiffness Matrices

This paper presents an alternative decomposition of spatial stiffness matrices based on the concept of compliant axes. According to the congruence transformation of spatial stiffness, the coordinate-invariant aspects, which are referred to as the central principal components of the $6\times 6$ symmetric positive semidefinite matrices, can be derived uniquely. The proposed decomposition is free from the eigenvalue problems of the $6\times 6$ stiffness matrices so that both Plucker's ray and axis coordinates can be utilized to characterize the elastic system's force–deflection behavior. Hence, an arbitrary spatial stiffness matrix can be uniquely decomposed into two sets of orthogonal spring wrenches with finite and infinite pitches, respectively. The decomposed wrenches with finite pitches correspond to the stiffness’ wrench-compliant axes, along which linear deformations produce only wrenches parallel to them. As a result, three torsional and three screw springs are required, at the most, to realize a given spatial stiffness. Using the principal axes decomposition, some physical appreciations, such as the center of stiffness, the wrench-compliant axes, and the correspondence of compliance and stiffness, can be derived to reveal the inherent structure of spatial stiffness in an intuitive manner. In order to verify the effectiveness of the proposed method, two numerical examples are intensively studied with comparison to the eigenscrew decomposition. In addition, a potential application of the proposed stiffness decomposition method is also provided for the structural compliance modeling of flexible links in robot manipulators.

Design and Experimental Study of a 6-DOF Material Testing Machine

A six degrees-of-freedom (DOF) parallel material testing machine (PMTM), which is based on Stewart Platform, is first proposed in this paper. Several essential issues including prototyping, compliant axis determination and controller design are investigated with specific methods or technologies. The compliant axis, along which the proposed machine has a better performance, is determined by the eigenscrew decomposition method. The proposed force controller incorporates the simplified inverse dynamic model output as a model-based portion of the controller and its validity is verified by means of simulations. Evaluation tests are performed to examine the practicability of the proposed controller and to determine the loading accuracy of the PMTM. Tensile tests and preliminary multiaxial loading tests are performed to verify the performance of the proposed PMTM. The experimental results illustrate that the proposed PMTM is capable of performing multiaxial loading tests of materials and thus a suitable candidate for multiaxial material testing machine.

Mechanical Response of the Herniated Human Abdomen to the Placement of Different Prostheses

This paper describes a method designed to model the repaired herniated human abdomen just after surgery and examine its static mechanical response to the maximum intra-abdominal pressure provoked by a physiological movement (standing cough). The model is based on the real geometry of the human abdomen bearing a large incisional hernia with several anatomical structures differentiated by MRI. To analyze the outcome of hernia repair, the surgical procedure was simulated by modeling a prosthesis placed over the hernia. Three surgical meshes with different mechanical properties were considered: an isotropic heavy-weight mesh (Surgipro®), a slightly anisotropic light-weight mesh (Optilene®), and a highly anisotropic medium-weight mesh (Infinit®). Our findings confirm that anisotropic implants need to be positioned such that the most compliant axis of the mesh coincides with the craneo-caudal direction of the body.

Feasibility and Design of a Low-Cost Prosthetic Knee Joint Using a Compliant Member for Stance-Phase Control

This paper is concerned with the feasibility and design of a low-cost prosthetic knee joint that uses a compliant member for stance-phase control. A mechanical locking mechanism was used in conjunction with a compliant control axis to achieve automatic stance-phase locking. The concept was developed with the aid of computer-aided engineering software and was validated through the fabrication and testing of a simplified prototype made of an injection moldable polymer. A prosthetic knee joint was then designed, incorporating the compliant member concept. After modeling, fabrication, and laboratory testing, a pilot study was conducted in a clinical setting. A simple gait analysis showed asymmetric gait patterns that demonstrated the need for improved swing-phase control and damping, while qualitative feedback indicated the desire to reduce the noise produced by the knee. The knee provided the automatic stance-phase control for which it was designed and shows significant potential to evolve into a highly functioning, low-cost knee.

Stiffness analysis for a 3-PUU parallel kinematic machine

This paper presents the stiffness characteristics of a three-prismatic-universal–universal (3-PUU) translational parallel kinematic machine (PKM). The stiffness matrix is derived intuitively based upon an alternative approach considering actuations and constraints, and the compliances subject to both actuators and legs are involved in the stiffness model. The stiffness performance of the manipulator is evaluated by utilizing the extremum stiffness values, and the influences of design parameters on the stiffness properties are presented, which will be valuable for the architecture design of a 3-PUU PKM. Moreover, the stiffness behavior of the PKM is investigated via the eigenscrew decomposition of the stiffness matrix, which provides a physical interpretation of the PKM stiffness and allows the identification of the stiffness center and compliant axis.

Determination of the dynamics of micromachined lateral suspensions in the scanning electron microscope

A lateral suspension, suitable for a microseismometer application, has been fabricated using deep reactive-ion etching. The critical dynamic parameters of the suspension, namely the normal modes along the compliant axis and the damping, have been determined from slow-scan imaging in an environmental scanning electron microscope. The results show the presence of an unwanted spurious mode which can be attributed to the finite mass of the suspension. An analytical solution yields good agreement with observations. Damping is shown to be dominated by viscous effects, with the suspension material only limiting performance at high vacuum.

Realization of those elastic behaviors that have compliant axes in compact elastic mechanisms

AbstractIn this article, we address the synthesis and realization of a subset of spatial elastic behaviors, those with compliant axes, in compact parallel mechanisms. Using the procedures developed, a geometric description of the layout of a compact mechanism of springs connected in parallel is obtained. In each of these mechanisms, each spring axis is restricted to intersect a single point in space. The variation in the orientation of the intersecting spring axes is also restricted. The degree of restriction in axis orientation is determined by the number of “compliant axes” associated with the specified elastic behavior. Also, as part of this work, a physical appreciation of the different classes of stiffnesses that have compliant axes is identified and interpreted in different types of concurrent parallel mechanisms. © 2002 Wiley Periodicals, Inc.

Results in position/force control of flexible link/joint manipulators

The experimental validation of a position/force control strategy for industrial manipulators with elastic joints and links is presented. The manipulator is modelled as a multibody system having rigid and elastic bodies. The control algorithm consists of a feedforward action to perform the classical nonlinear decoupling of the system equations and a feedback action to reduce the reference path deviations and, simultaneously, to damp the system vibrations due to elasticities in joint and links. This control strategy is simulated and experimentally tested on a laboratorial robot with 5- compliant axis and 2 elastic links, with tridimensional flexibility, for a constrained endless trajectory.

A Classification of Robot Compliance

The concept of compliant axes is developed from the compliance matrix eigenvalue problem. It is shown that the necessary and sufficient conditions for the existence of a compliant axis are two collinear eigenscrews with eigenvalues of equal magnitude and opposite sign. This leads to a new classification of compliance matrices based on the number of compliant axes. Selected matrices from the literature illustrate both the compliant axis concept and the classification.

Structure of Robot Compliance

The structure of nonsingular robot compliance is investigated by applying screw theory to two eigenvalue problems. For the first problem the eigenscrews are demonstrated to be Ball’s (1990) principal screws of the potential. Several new propositions are presented characterizing compliance matrix eigenstructure. Using a novel formulation, the second eigenvalue problem generalizes the three wrench-compliant axes of Dimentberg (1965) to include three twist-compliant axes. These two types of compliant axes are shown to be reciprocal and define conjugate screw systems. The wrench- and twist-compliant axes are demonstrated to the general elements of a compliant axis hierarchy.

Efficiency calculations for a Salter's duck on a compliant axis

Efficiency calculations for a Salter's duck on a compliant axis