Model-Based Control of a 4-DOF Rehabilitation Parallel Robot with Online Identification of the Gravitational Term.

Parallel robots are being increasingly used as a fundamental component of lower-limb rehabilitation systems. During rehabilitation therapies, the parallel robot must interact with the patient, which raises several challenges to the control system: (1) The weight supported by the robot can vary from patient to patient, and even for the same patient, making standard model-based controllers unsuitable for those tasks since they rely on constant dynamic models and parameters. (2) The identification techniques usually consider the estimation of all dynamic parameters, bringing about challenges concerning robustness and complexity. This paper proposes the design and experimental validation of a model-based controller comprising a proportional-derivative controller with gravity compensation applied to a 4-DOF parallel robot for knee rehabilitation, where the gravitational forces are expressed in terms of relevant dynamic parameters. The identification of such parameters is possible by means of least squares methods. The proposed controller has been experimentally validated, holding the error stable following significant payload changes in terms of the weight of the patient's leg. This novel controller allows us to perform both identification and control simultaneously and is easy to tune. Moreover, its parameters have an intuitive interpretation, contrary to a conventional adaptive controller. The performance of a conventional adaptive controller and the proposed one are compared experimentally.

Vision-Based Hybrid Controller to Release a 4-DOF Parallel Robot from a Type II Singularity.

The high accuracy and dynamic performance of parallel robots (PRs) make them suitable to ensure safe operation in human-robot interaction. However, these advantages come at the expense of a reduced workspace and the possible appearance of type II singularities. The latter is due to the loss of control of the PR and requires further analysis to keep the stiffness of the PR even after a singular configuration is reached. All or a subset of the limbs could be responsible for a type II singularity, and they can be detected by using the angle between two output twist screws (OTSs). However, this angle has not been applied in control because it requires an accurate measure of the pose of the PR. This paper proposes a new hybrid controller to release a 4-DOF PR from a type II singularity based on a real time vision system. The vision system data are used to automatically readapt the configuration of the PR by moving the limbs identified by the angle between two OTSs. This controller is intended for a knee rehabilitation PR, and the results show how this release is accomplished with smooth controlled movements where the patient's safety is not compromised.

Passive Exercise Adaptation for Ankle Rehabilitation Based on Learning Control Framework.

Ankle injuries are among the most common injuries in sport and daily life. However, for their recovery, it is important for patients to perform rehabilitation exercises. These exercises are usually done with a therapist's guidance to help strengthen the patient's ankle joint and restore its range of motion. However, in order to share the load with therapists so that they can offer assistance to more patients, and to provide an efficient and safe way for patients to perform ankle rehabilitation exercises, we propose a framework that integrates learning techniques with a 3-PRS parallel robot, acting together as an ankle rehabilitation device. In this paper, we propose to use passive rehabilitation exercises for dorsiflexion/plantar flexion and inversion/eversion ankle movements. The therapist is needed in the first stage to design the exercise with the patient by teaching the robot intuitively through learning from demonstration. We then propose a learning control scheme based on dynamic movement primitives and iterative learning control, which takes the designed exercise trajectory as a demonstration (an input) together with the recorded forces in order to reproduce the exercise with the patient for a number of repetitions defined by the therapist. During the execution, our approach monitors the sensed forces and adapts the trajectory by adding the necessary offsets to the original trajectory to reduce its range without modifying the original trajectory and subsequently reducing the measured forces. After a predefined number of repetitions, the algorithm restores the range gradually, until the patient is able to perform the originally designed exercise. We validate the proposed framework with both real experiments and simulation using a Simulink model of the rehabilitation parallel robot that has been developed in our lab.

Dynamic Parameter Identification of Subject-Specific Body Segment Parameters Using Robotics Formalism: Case Study Head Complex.

Accurate knowledge of body segment inertia parameters (BSIP) improves the assessment of dynamic analysis based on biomechanical models, which is of paramount importance in fields such as sport activities or impact crash test. Early approaches for BSIP identification rely on the experiments conducted on cadavers or through imaging techniques conducted on living subjects. Recent approaches for BSIP identification rely on inverse dynamic modeling. However, most of the approaches are focused on the entire body, and verification of BSIP for dynamic analysis for distal segment or chain of segments, which has proven to be of significant importance in impact test studies, is rarely established. Previous studies have suggested that BSIP should be obtained by using subject-specific identification techniques. To this end, our paper develops a novel approach for estimating subject-specific BSIP based on static and dynamics identification models (SIM, DIM). We test the validity of SIM and DIM by comparing the results using parameters obtained from a regression model proposed by De Leva (1996, "Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters," J. Biomech., 29(9), pp. 1223-1230). Both SIM and DIM are developed considering robotics formalism. First, the static model allows the mass and center of gravity (COG) to be estimated. Second, the results from the static model are included in the dynamics equation allowing us to estimate the moment of inertia (MOI). As a case study, we applied the approach to evaluate the dynamics modeling of the head complex. Findings provide some insight into the validity not only of the proposed method but also of the application proposed by De Leva (1996, "Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters," J. Biomech., 29(9), pp. 1223-1230) for dynamic modeling of body segments.

Model of soft tissue artifact propagation to joint angles in human movement analysis.

This work describes the kinematic laws that govern the transmission of soft tissue artifact errors to kinematic variables in the analysis of human movements. Artifacts are described as relative translations and rotations of the marker cluster over the bone, and a set of explicit expressions is defined to account for the effect of that relative motion on different representations of rotations: the rotation around the screw axis, or rotation vector, and three Euler angle sequences (XY'Z, YX'Y″, ZX'Y″). Although the error transmission is nonlinear in all cases, the effect of artifacts is greater on Euler sequences than on the rotation vector. Specifically, there are crosstalk effects in Euler sequences that amplify the errors near singular configurations. This fact is an additional source of variability in studies that describe artifacts by comparing the Euler angles obtained from skin markers, with the angles of an artifact-free gold standard. The transmission of errors to rotation vector coordinates is less variable or dependent on the type of motion. This model has been tested in an experiment with a deformable mechanical model with a spherical joint.

Point of optimal kinematic error: improvement of the instantaneous helical pivot method for locating centers of rotation.

This paper proposes a variation of the instantaneous helical pivot technique for locating centers of rotation. The point of optimal kinematic error (POKE), which minimizes the velocity at the center of rotation, may be obtained by just adding a weighting factor equal to the square of angular velocity in Woltring׳s equation of the pivot of instantaneous helical axes (PIHA). Calculations are simplified with respect to the original method, since it is not necessary to make explicit calculations of the helical axis, and the effect of accidental errors is reduced. The improved performance of this method was validated by simulations based on a functional calibration task for the gleno-humeral joint center. Noisy data caused a systematic dislocation of the calculated center of rotation towards the center of the arm marker cluster. This error in PIHA could even exceed the effect of soft tissue artifacts associated to small and medium deformations, but it was successfully reduced by the POKE estimation.

Kinematic description of soft tissue artifacts: quantifying rigid versus deformation components and their relation with bone motion.

This paper proposes a kinematic approach for describing soft tissue artifacts (STA) in human movement analysis. Artifacts are represented as the field of relative displacements of markers with respect to the bone. This field has two components: deformation component (symmetric field) and rigid motion (skew-symmetric field). Only the skew-symmetric component propagates as an error to the joint variables, whereas the deformation component is filtered in the kinematic analysis process. Finally, a simple technique is proposed for analyzing the sources of variability to determine which part of the artifact may be modeled as an effect of the motion, and which part is due to other sources. This method has been applied to the analysis of the shank movement induced by vertical vibration in 10 subjects. The results show that the cluster deformation is very small with respect to the rigid component. Moreover, both components show a strong relationship with the movement of the tibia. These results suggest that artifacts can be modeled effectively as a systematic relative rigid movement of the marker cluster with respect to the underlying bone. This may be useful for assessing the potential effectiveness of the usual strategies for compensating for STA.

Representation of planar motion of complex joints by means of rolling pairs. Application to neck motion.

We propose to model planar movements between two human segments by means of rolling-without-slipping kinematic pairs. We compute the path traced by the instantaneous center of rotation (ICR) as seen from the proximal and distal segments, thus obtaining the fixed and moving centrodes, respectively. The joint motion is then represented by the rolling-without-slipping of one centrode on the other. The resulting joint kinematic model is based on the real movement and accounts for nonfixed axes of rotation; therefore it could improve current models based on revolute pairs in those cases where joint movement implies displacement of the ICR. Previous authors have used the ICR to characterize human joint motion, but they only considered the fixed centrode. Such an approach is not adequate for reproducing motion because the fixed centrode by itself does not convey information about body position. The combination of the fixed and moving centrodes gathers the kinematic information needed to reproduce the position and velocities of moving bodies. To illustrate our method, we applied it to the flexion-extension movement of the head relative to the thorax. The model provides a good estimation of motion both for position variables (mean R(pos)=0.995) and for velocities (mean R(vel)=0.958). This approach is more realistic than other models of neck motion based on revolute pairs, such as the dual-pivot model. The geometry of the centrodes can provide some information about the nature of the movement. For instance, the ascending and descending curves of the fixed centrode suggest a sequential movement of the cervical vertebrae.

A procedure for estimating the relevant forces in the human knee using a four-bar mechanism.

Knee injuries, especially those that affect the cruciate and lateral ligaments, are one of the most serious and frequent pathologies that affect the lower human extremity. Hence, the aim of this study is to develop a dynamic model for the lower extremity capable of estimating forces, forces in the cruciate and collateral ligaments and those normal to the articular cartilage, generated in the knee. The proposed model considers a four-bar mechanism in the knee, a spherical joint in the pelvis and a revolute one in the ankle. The four-bar mechanism is obtained by a synthesis process. The dynamic model includes the inertial properties of the femur, tibia, patella and the foot, the ground reaction force and the most important muscles in the knee. Muscle forces are estimated using an optimisation technique. Results from the application of the model on a real human task are presented.

Optimal average path of the instantaneous helical axis in planar motions with one functional degree of freedom.

This paper presents a model for determining the path of the instantaneous helical axis (IHA) that optimally represents human planar motions with one functional degree of freedom (fDOF). A human movement is said to have one fDOF when all degrees of freedom (DOFs) are coordinated such that all the kinematic variables can be expressed, across movement repetitions, as functions of only one independent DOF, except for a small natural intercycle variability quantified as lower than a prespecified value. The concept of fDOF allows taking into account that, due to motor coordination, human movements are executed in a repeatable manner. Our method uses the measurement of several repetitions of a given movement to obtain the optimal average IHA path. The starting point is a change of variables, from time to a joint position magnitude (generally an angle). In this way, instead of operating with the time-dependent single-valued trajectory of the successive cycles, our model permits the representation of any motion variable (e.g. positions and their time derivatives) as a cloud of points dependent on the joint angle. This allows the averaging to be performed over the displacements and their derivatives before determining the mean IHA path. We thus avoid the nonlinear magnification of errors and variability inherent in the IHA computation. Moreover, the IHA path can be considered as a geometric attribute of the joint and the type of motion, rather than of each single movement execution. An experiment was performed that show the accuracy and usefulness of the method.

Kinematics of the trunk in sitting posture: an analysis based on the instantaneous axis of rotation.

This paper presents a new approach for analysing trunk kinematics in sitting posture based on the characterisation of thorax and pelvis motion by means of ranges of motion and instantaneous axes of rotation (IAR). These variables are estimated from videophotogrammetric data. An experiment was carried out in order to analyse three motions associated with the flexion-extension movement: the absolute motions of the pelvis and thorax and the relative motion between the thorax and pelvis. The results obtained suggest a sequential activation of lumbar vertebrae in the flexion-extension motion. On the other hand, the location of the pelvis IAR shows that the movement of the pelvis on the seat is not just a rolling motion but a rolling with some level of sliding. Finally, the location of the IAR in the thorax-pelvis relative motion shows a mismatch between the trunk IAR and the backrest axis of rotation in several office chairs. The proposed technique provides a new approach for the kinematic analysis of sitting posture. The results can be applied to the improvement of biomechanical models of seated posture as well as to define some design criteria of work seats based on the fit between the trunk and backrest movements.