Российский журнал биомеханики 2023, № 2, С. 47-54., 2023
Рассматривается метод диффузионного анализа результатов стабилометрии. Известно, что диффузионные... more Рассматривается метод диффузионного анализа результатов стабилометрии. Известно, что диффузионные функции стабилограмм для фронтального и сагиттального направлений различны и их графики в логарифмических осях имеют характерный излом. Предполагается, что этот излом связан с изменением свойств персистентности для различных интервалов времени движения при наличии обратной связи в системе поддержания человеком вертикальной позы. В статье рассмотрен вопрос о возможной связи описанных особенностей диффузионного анализа стабилограмм с наличием зоны нечувствительности сигнала вестибулярного аппарата. Рассмотрены модели управляемой стабилизации вертикальной позы для фронтального и cагиттального направлений. Эти модели используют модифицированные уравнения движения перевернутого маятника, стабилизируемого ПИД-регулятором по позиционным измерениям. Управление дополнено обратной связью по информации, поступающей от модели отолитового органа, имеющего зону нечувствительности. Предполагается, что сигнал вертикального канала отолитов и полукружных каналов являются подпороговыми и системой управления не воспринимаются. Приведены результаты диффузионного анализа для ансамбля реализаций численной модели удержания человеком вертикальной позы. Параметры системы управления скорректированы по итогам сопоставления результатов моделирования с натурными данными. Численное моделирование показало, что влияние отолитового органа при спокойном стоянии здорового человека в позе "ноги на ширине плеч" во фронтальной плоскости минимально или отсутствует, в сагиттальной же плоскости существуют значения коэффициента усиления сигнала отолита, при которых становится заметно влияние этой составляющей управления. Представленное моделирование позволяет наметить основные направления для анализа связи показателей диффузионного анализа стабилограмм с особенностями функционирования как вестибулярного аппарата, так и других сенсорных модальностей.
Биомеханика двигательных действий и биомеханический контроль в спорте: материалы X Всероссийской с международным участием научно-практической конференции, Москва, 24-25 Ноября 2022г. — МАЛАХОВКА МГАФК Москва, 2022., 2022
В работе рассматривается метод диффузионного анализа стабилограмм. Известно, что показатели таког... more В работе рассматривается метод диффузионного анализа стабилограмм. Известно, что показатели такого анализа реальных данных для фронтали и сагиттали различны, при этом диффузионные функции стабилограмм имеют характерный «изгиб». В докладе рассмотрен вопрос о возможной связи такого различия показателей диффузионного анализа с особенностями работы вестибулярного аппарата, обладающего зоной нечувствительности.
Описан подход к количественной оценке изменения функционального состояния человека за время полет... more Описан подход к количественной оценке изменения функционального состояния человека за время полета летательного аппарата. Для такой оценки предполагается использовать сравнение результатов стабилометриче-ских и окулографических обследований пассажира летательного аппарата, проведенные до и после полета. Проведена серия пробных полетов на легкомоторных летательных аппаратах, до и по окончании которых пассажиры проходили подобное обследование. Для имеющейся выборки добровольцев выявлены параметры, которые имеют устойчивую тенденцию к изменению. Эти параметры включают качество зрительного слежения и стабилометрические характеристики. У большинства добровольцев заметны изменения стабилометрических параметров для оптокинетической пробы и пробы с удержанием равновесия на неустойчивой опоре в виде пластины пенополиуретана. В большинстве случаев после полета изменялись скорости слежения, средняя скорость центра давления и показатель качества функции равновесия. Отмечено, что показатель Херста после полета снижался при вставании на пластину пенополиуретана у подавляющего числа испытателей, по сравнению с со значением в фоновой пробе, в то время как до полета изменение этого параметра носит разнонаправленный характер.
Статья в публикации: Международная научная конференция «Фундаментальные и прикладные задачи механ... more Статья в публикации: Международная научная конференция «Фундаментальные и прикладные задачи механики», Москва, 7–10 декабря 2021 г. Материалы конференции. В двух частях. Часть 1
The problem of stabilizing an inverted pendulum pivotally connected to a platform mounted on a viscoelastic base. This system is designed to simulate a test with maintaining equilibrium by a person standing on a foamed polyurethane plate used in biomechanical studies. The control in the system is the torque in the cylindrical hinge of the pendulum. This torque is limited in absolute value. The described model corresponds to the “ankle” strategy considered in biomechanical studies of the posture control by a person standing on an unstable support. It shows numerically that the linearized system, although it has a deficit in the number of control inputs, is controllable. The region of controllability of the system is found with a control torque limited in absolute value. A control is constructed that stabilizes an unstable equilibrium position with a maximum region of attraction. This control is such that all of its resources are used to suppress the only unstable mode. The boundaries of the region of attraction of the equilibrium state under this control are found. The behavior of the stabilized system has been studied. The results of the analysis allow us to compare the solution of the problem under consideration and the solution of the problem of maintaining equilibrium by a person standing on seesaw.
Models of the motion of person who undergoes the stabilometric "test with visual step in... more Models of the motion of person who undergoes the stabilometric "test with visual step input" are considered. At the beginnings of the test person stand on the stabilometric force plate. Center of pressure (COP) image and target are displayed on the screen in front of the person. Center of target is superposed with the mean COP position on the basic plane. During test the target changes position jump-like and the person’s asked to change quickly his ankle angle to superpose COP image with the center of a target on the screen and to hold it hereafter in target region. For test results analyses it is suggested to use the solution of optimal control of position of the inverted pendulum with actuator in a pivot. The speed-of-response control and LQ stabilization optimal problems are considered. Possibility of usage of optimal solutions for generation of test indexes is discussed.
At present, the theory of wheeled robotic systems is being actively developed. In modeling the mo... more At present, the theory of wheeled robotic systems is being actively developed. In modeling the motion of wheeled robots, one mostly uses the classical nonholonomic motion model, which does not take into account the slip of deformable wheels. Meanwhile, for robots with deformable wheels, nonholonomic models can be inadequate for the design and analysis of control algorithms. This can be the case for statically unstable balancing robots with coaxial wheels, similar in design with such vehicles as Segway. Thus, modeling the motion of a two-wheeled robot taking into account the possibility of wheels slip and analysis of applicability of simplified models are of interest. Such models can be used to develop new control algorithms in active maneuvering, and for preliminary estimates of robustness of algorithms designed using approximate nonholonomic models. This paper focuses on modeling the motion of balancing robots, on analyzing their steady-state motion, and on possibilities of their stabilization. It is shown that for models with deformable wheels in the steady-state motion the body has a forward pitch. Such a pitch is not found in most nonholonomic models.
Abstract—Problems of optimal control were analyzed for a human motion model for stabilometric tes... more Abstract—Problems of optimal control were analyzed for a human motion model for stabilometric tests where the posture changes under a stepwise input action. The presence of a prominent “swing” and an “overshoot” are characteristic of the center-of-pressure trajectories recorded in the test. A one-dimensional inverted pendulum model was used in the study. The solution of the optimal control for the inverted pendulum motion controlled by coupling torque was put in correspondence with the test results. The problems of optimal speed-of-response control and linear–quadratic regulator were considered. The solution of these optimum problems was compared with the stabilometric test results. A modified algorithm was proposed for stabilometric data processing. This motion was shown to reach a stable motor pattern. The swing and overshoot were found to correspond to the acceleration and deceleration stages, respectively.
Journal of Applied Mathematics and Mechanics, 2016
Abstract A very simple model of the process of maintaining balance by a person standing on a sees... more Abstract A very simple model of the process of maintaining balance by a person standing on a seesaw is considered. The model consists of a planar single-link inverted pendulum, which is connected by means of a cylindrical hinge, i.e., an “ankle joint”, to a support in the form of a segment of cylinder, whose axis is perpendicular to the pendulum. The support can oscillate by rolling on a horizontal surface, and the pendulum can oscillate in a plane that is perpendicular to the cylinder axis. The control is a torque applied on the axis of the hinge. This torque is assumed to have a restricted absolute value. A control law is constructed in the form of feedback along a single “unstable” coordinate of the open system in such a manner that the region of attraction of the linearized system would be the maximum possible. Several characteristic trajectories of the system for the control constructed are considered.
In this study, we discuss the lost data recovery in videoanalysis (motion capture) of human movem... more In this study, we discuss the lost data recovery in videoanalysis (motion capture) of human movement based on measures of two-component accelerometer. The algorithm uses mathematical model of movement and consists of two stages: identification of unknown parameters and proper stage of recovery of lost information. Both problems are reduced to solution of overdetermined systems of linear equations. Two approaches to recovery problem solution are compared. The first one uses traditional non-recurrent procedure of the least-squares method The second one uses the procedure of suboptimal algorithm of smoothing based on Kalman filtering. These algorithms are applied to recovery of lost values of the angle between the shin of a person and the horizontal.
SPECIFIC CHARACTERISTICS OF FREQUENCY ANALYSIS OF FORCETORQUE SENSORS DATA IN THE PHYSIOLOGICAL T... more SPECIFIC CHARACTERISTICS OF FREQUENCY ANALYSIS OF FORCETORQUE SENSORS DATA IN THE PHYSIOLOGICAL TREMOR RESEARCH
The problem of the control synthesis to stabilize the double inverted pendulum installed on the s... more The problem of the control synthesis to stabilize the double inverted pendulum installed on the seesaw is considering. The movement in the vertical plane of such kind of the pendulums is studying. The seesaw is a segment of the cylinder whose axis is horizontal. This cylindrical segment oscillates while rolling on the horizontal surface without any slipping. The lower (first) link of the pendulum is fastened to the seesaw by the cylindrical joint. The axis of this joint is parallel to the axis of the cylinder and to the axis of the inter-link joint also. The limited in the absolute value torque is applied to the pendulum in the inter-link joint. Thus, the described above system has three degrees of freedom and the single control action only. The open-loop system has an unstable equilibrium position with the both links of the pendulum directed vertically upwards. The seesaw in this equilibrium position is not tilted. The control stabilizing the desired unstable equilibrium is constructed in the feedback form on two "unstable" Jordan variables of an open-loop linearized system. By this way we design the feedback control with maximal as possible the attraction domain of the equilibrium position. Some properties of the controllability and attraction domains are studied. The results of the numerical studies are presented.
In this paper, we discuss a possibility of evaluating a part of the energy cost for maintaining a... more In this paper, we discuss a possibility of evaluating a part of the energy cost for maintaining a vertical posture by a person. We use the stabilometric data (center of pressure (CoP) postural sway measurements) only. The application of an inverted pendulum model for calculating the components of the mechanical work of particular groups of leg muscles is described. We use integral of the modulus of the power of total torques developed by the antagonists. For the sagittal direction, the mechanical work of muscles of the ankle is make an estimate mainly, and for the frontal directionof the pelvic muscles. The possibility of using approximate estimates of energy indicators for the slow components of human movement is discussed. To analyze the correlations of various indicators, the results of postural stability tests were used. During these tests the subjects stood with their eyes open in an upright posture. Moreover, in several tests, they were presented with various visual illusions. It was causing a change in postural characteristics and, accordingly, stabilometric parameters. The correlations between the introduced energetical indicators and indicators traditionally used in stabilometry are analyzed. The next indicators: CoP trajectory range of oscillations along the frontal and sagittal, the average CoP velocity and its projection on the frontal and sagittal axes, as well as an indicator called the "total energy density of statokinesiogram" and its components for the frontal and sagittal directions were considered. A correlation between the used indicator of mechanical work and the stabilogram range was developed. It is shown that the change in a part of the energy corresponding to an indicator called the "total energy density of statokinesiogram" is small and, apparently, does not adequately characterize the change in mechanical energy.
Full text: https://rdcu.be/cDPVb The approaches to determining the horizontal coordinates... more Full text: https://rdcu.be/cDPVb The approaches to determining the horizontal coordinates of the center of mass (CoM) applicablefor force plate are compared. The force plate for which only vertical forces are the measurements takes into account. The first of these approaches uses the information not only about the initial position and rate of CoM, but also about its terminal state. The second is associated with the use of the assumption about the absence of unstable components in the movement and uses frequency filtering methods. Known algorithms were modified to solve the problem in conditions of sufficiently intense movements by a person. The considered modified algorithms were compared for recordings movement of the subjects who performed a “test with a stepwise visual disturbance” on a force plate. A system of video cameras was simultaneously used to determine the coordinates of a marker fixed approximately at the CoM height. The working capacity of all modified algorithms was demonstrated. It was noted that the error of the estimation method using a double filtration in forward and reverse time was lower than in other procedures.
The problem of the control synthesis to stabilize the double inverted pendulum installed on the s... more The problem of the control synthesis to stabilize the double inverted pendulum installed on the seesaw is considering. The movement in the vertical plane of such kind of the pendulums is studying. The seesaw is a segment of the cylinder whose axis is horizontal. This cylindrical segment oscillates while rolling on the horizontal surface without any slipping. The lower (first) link of the pendulum is fastened to the seesaw by the cylindrical joint. The axis of this joint is parallel to the axis of the cylinder and to the axis of the inter-link joint also. The limited in the absolute value torque is applied to the pendulum in the inter-link joint. Thus, the described above system has three degrees of freedom and the single control action only. The open-loop system has an unstable equilibrium position with the both links of the pendulum directed vertically upwards. The seesaw in this equilibrium position is not tilted. The control stabilizing the desired unstable equilibrium is constructed in the feedback form on two "unstable" Jordan variables of an open-loop linearized system. By this way we design the feedback control with maximal as possible the attraction domain of the equilibrium position. Some properties of the controllability and attraction domains are studied. The results of the numerical studies are presented.
The test and correcting calibration capability of a portable acceleration re-corder under orbita... more The test and correcting calibration capability of a portable acceleration re-corder under orbital flight conditions is discussed. This recorder includes a 3-axis accelerometer. Determination its scale factors is the most difficult test cali-bration stage. The main difficulty of calibration is the lack of special equipment on the space station. It is proposed to use a standard mass meter installed on the ISS for testing accelerometers. The algorithms considered in the article use, in addition to the recorder readings, data of the mass meter platform motion and the video camera records processing. To test the algorithms in ground conditions, recordings were made that simulate the situation of an orbital flight. The proposed algorithms showed 2% error in the accelerometers scale factors
The paper is devoted to the simplified models of force plate measurements. The traditional models... more The paper is devoted to the simplified models of force plate measurements. The traditional models are used to describe the motion of a person. Human motion in the sagittal plane is described by the inverted pendulum model. Simplified three link model is used to frontal plane motion description. Two links of this model are parallel and support on the floor. These units model the legs, and the third link simulates the body, arms and head, which do not change the mutual arrangement. Links pivotally connected at the hip joints. It is assumed that the force plate (stabilograph) is a rigid body. These models are used to express force plate measurements through body model angles and ankle and hip torques. The approximate analysis shows that changes in the sagittal and frontal coordinates of the centre of pressure mostly characterize the change of ankle and hip torques, respectively. The obtained estimation is valid for arbitrary tempo of human movements, and it allows us to explain “deteri...
The approaches to determining the horizontal coordinates of the center of mass (CoM) applicable f... more The approaches to determining the horizontal coordinates of the center of mass (CoM) applicable for force plate are compared. The force plate for which only vertical forces are the measurements takes into account. The first of these approaches uses the information not only about the initial position and rate of CoM, but also about its terminal state. The second is associated with the use of the assumption about the absence of unstable components in the movement and uses frequency filtering methods. Known algorithms were modified to solve the problem in conditions of sufficiently intense movements by a person. The сonsidered modified algorithms were compared for recordings movement of the subjects who performed a “test with a stepwise visual disturbance” on a force plate. A system of video cameras was simultaneously used to determine the coordinates of a marker fixed approximately at the CoM height. The working capacity of all modified algorithms was demonstrated. It was noted that the error of the estimation method using a double filtration in forward and reverse time was lower than in other procedures.
Российский журнал биомеханики 2023, № 2, С. 47-54., 2023
Рассматривается метод диффузионного анализа результатов стабилометрии. Известно, что диффузионные... more Рассматривается метод диффузионного анализа результатов стабилометрии. Известно, что диффузионные функции стабилограмм для фронтального и сагиттального направлений различны и их графики в логарифмических осях имеют характерный излом. Предполагается, что этот излом связан с изменением свойств персистентности для различных интервалов времени движения при наличии обратной связи в системе поддержания человеком вертикальной позы. В статье рассмотрен вопрос о возможной связи описанных особенностей диффузионного анализа стабилограмм с наличием зоны нечувствительности сигнала вестибулярного аппарата. Рассмотрены модели управляемой стабилизации вертикальной позы для фронтального и cагиттального направлений. Эти модели используют модифицированные уравнения движения перевернутого маятника, стабилизируемого ПИД-регулятором по позиционным измерениям. Управление дополнено обратной связью по информации, поступающей от модели отолитового органа, имеющего зону нечувствительности. Предполагается, что сигнал вертикального канала отолитов и полукружных каналов являются подпороговыми и системой управления не воспринимаются. Приведены результаты диффузионного анализа для ансамбля реализаций численной модели удержания человеком вертикальной позы. Параметры системы управления скорректированы по итогам сопоставления результатов моделирования с натурными данными. Численное моделирование показало, что влияние отолитового органа при спокойном стоянии здорового человека в позе "ноги на ширине плеч" во фронтальной плоскости минимально или отсутствует, в сагиттальной же плоскости существуют значения коэффициента усиления сигнала отолита, при которых становится заметно влияние этой составляющей управления. Представленное моделирование позволяет наметить основные направления для анализа связи показателей диффузионного анализа стабилограмм с особенностями функционирования как вестибулярного аппарата, так и других сенсорных модальностей.
Биомеханика двигательных действий и биомеханический контроль в спорте: материалы X Всероссийской с международным участием научно-практической конференции, Москва, 24-25 Ноября 2022г. — МАЛАХОВКА МГАФК Москва, 2022., 2022
В работе рассматривается метод диффузионного анализа стабилограмм. Известно, что показатели таког... more В работе рассматривается метод диффузионного анализа стабилограмм. Известно, что показатели такого анализа реальных данных для фронтали и сагиттали различны, при этом диффузионные функции стабилограмм имеют характерный «изгиб». В докладе рассмотрен вопрос о возможной связи такого различия показателей диффузионного анализа с особенностями работы вестибулярного аппарата, обладающего зоной нечувствительности.
Описан подход к количественной оценке изменения функционального состояния человека за время полет... more Описан подход к количественной оценке изменения функционального состояния человека за время полета летательного аппарата. Для такой оценки предполагается использовать сравнение результатов стабилометриче-ских и окулографических обследований пассажира летательного аппарата, проведенные до и после полета. Проведена серия пробных полетов на легкомоторных летательных аппаратах, до и по окончании которых пассажиры проходили подобное обследование. Для имеющейся выборки добровольцев выявлены параметры, которые имеют устойчивую тенденцию к изменению. Эти параметры включают качество зрительного слежения и стабилометрические характеристики. У большинства добровольцев заметны изменения стабилометрических параметров для оптокинетической пробы и пробы с удержанием равновесия на неустойчивой опоре в виде пластины пенополиуретана. В большинстве случаев после полета изменялись скорости слежения, средняя скорость центра давления и показатель качества функции равновесия. Отмечено, что показатель Херста после полета снижался при вставании на пластину пенополиуретана у подавляющего числа испытателей, по сравнению с со значением в фоновой пробе, в то время как до полета изменение этого параметра носит разнонаправленный характер.
Статья в публикации: Международная научная конференция «Фундаментальные и прикладные задачи механ... more Статья в публикации: Международная научная конференция «Фундаментальные и прикладные задачи механики», Москва, 7–10 декабря 2021 г. Материалы конференции. В двух частях. Часть 1
The problem of stabilizing an inverted pendulum pivotally connected to a platform mounted on a viscoelastic base. This system is designed to simulate a test with maintaining equilibrium by a person standing on a foamed polyurethane plate used in biomechanical studies. The control in the system is the torque in the cylindrical hinge of the pendulum. This torque is limited in absolute value. The described model corresponds to the “ankle” strategy considered in biomechanical studies of the posture control by a person standing on an unstable support. It shows numerically that the linearized system, although it has a deficit in the number of control inputs, is controllable. The region of controllability of the system is found with a control torque limited in absolute value. A control is constructed that stabilizes an unstable equilibrium position with a maximum region of attraction. This control is such that all of its resources are used to suppress the only unstable mode. The boundaries of the region of attraction of the equilibrium state under this control are found. The behavior of the stabilized system has been studied. The results of the analysis allow us to compare the solution of the problem under consideration and the solution of the problem of maintaining equilibrium by a person standing on seesaw.
Models of the motion of person who undergoes the stabilometric "test with visual step in... more Models of the motion of person who undergoes the stabilometric "test with visual step input" are considered. At the beginnings of the test person stand on the stabilometric force plate. Center of pressure (COP) image and target are displayed on the screen in front of the person. Center of target is superposed with the mean COP position on the basic plane. During test the target changes position jump-like and the person’s asked to change quickly his ankle angle to superpose COP image with the center of a target on the screen and to hold it hereafter in target region. For test results analyses it is suggested to use the solution of optimal control of position of the inverted pendulum with actuator in a pivot. The speed-of-response control and LQ stabilization optimal problems are considered. Possibility of usage of optimal solutions for generation of test indexes is discussed.
At present, the theory of wheeled robotic systems is being actively developed. In modeling the mo... more At present, the theory of wheeled robotic systems is being actively developed. In modeling the motion of wheeled robots, one mostly uses the classical nonholonomic motion model, which does not take into account the slip of deformable wheels. Meanwhile, for robots with deformable wheels, nonholonomic models can be inadequate for the design and analysis of control algorithms. This can be the case for statically unstable balancing robots with coaxial wheels, similar in design with such vehicles as Segway. Thus, modeling the motion of a two-wheeled robot taking into account the possibility of wheels slip and analysis of applicability of simplified models are of interest. Such models can be used to develop new control algorithms in active maneuvering, and for preliminary estimates of robustness of algorithms designed using approximate nonholonomic models. This paper focuses on modeling the motion of balancing robots, on analyzing their steady-state motion, and on possibilities of their stabilization. It is shown that for models with deformable wheels in the steady-state motion the body has a forward pitch. Such a pitch is not found in most nonholonomic models.
Abstract—Problems of optimal control were analyzed for a human motion model for stabilometric tes... more Abstract—Problems of optimal control were analyzed for a human motion model for stabilometric tests where the posture changes under a stepwise input action. The presence of a prominent “swing” and an “overshoot” are characteristic of the center-of-pressure trajectories recorded in the test. A one-dimensional inverted pendulum model was used in the study. The solution of the optimal control for the inverted pendulum motion controlled by coupling torque was put in correspondence with the test results. The problems of optimal speed-of-response control and linear–quadratic regulator were considered. The solution of these optimum problems was compared with the stabilometric test results. A modified algorithm was proposed for stabilometric data processing. This motion was shown to reach a stable motor pattern. The swing and overshoot were found to correspond to the acceleration and deceleration stages, respectively.
Journal of Applied Mathematics and Mechanics, 2016
Abstract A very simple model of the process of maintaining balance by a person standing on a sees... more Abstract A very simple model of the process of maintaining balance by a person standing on a seesaw is considered. The model consists of a planar single-link inverted pendulum, which is connected by means of a cylindrical hinge, i.e., an “ankle joint”, to a support in the form of a segment of cylinder, whose axis is perpendicular to the pendulum. The support can oscillate by rolling on a horizontal surface, and the pendulum can oscillate in a plane that is perpendicular to the cylinder axis. The control is a torque applied on the axis of the hinge. This torque is assumed to have a restricted absolute value. A control law is constructed in the form of feedback along a single “unstable” coordinate of the open system in such a manner that the region of attraction of the linearized system would be the maximum possible. Several characteristic trajectories of the system for the control constructed are considered.
In this study, we discuss the lost data recovery in videoanalysis (motion capture) of human movem... more In this study, we discuss the lost data recovery in videoanalysis (motion capture) of human movement based on measures of two-component accelerometer. The algorithm uses mathematical model of movement and consists of two stages: identification of unknown parameters and proper stage of recovery of lost information. Both problems are reduced to solution of overdetermined systems of linear equations. Two approaches to recovery problem solution are compared. The first one uses traditional non-recurrent procedure of the least-squares method The second one uses the procedure of suboptimal algorithm of smoothing based on Kalman filtering. These algorithms are applied to recovery of lost values of the angle between the shin of a person and the horizontal.
SPECIFIC CHARACTERISTICS OF FREQUENCY ANALYSIS OF FORCETORQUE SENSORS DATA IN THE PHYSIOLOGICAL T... more SPECIFIC CHARACTERISTICS OF FREQUENCY ANALYSIS OF FORCETORQUE SENSORS DATA IN THE PHYSIOLOGICAL TREMOR RESEARCH
The problem of the control synthesis to stabilize the double inverted pendulum installed on the s... more The problem of the control synthesis to stabilize the double inverted pendulum installed on the seesaw is considering. The movement in the vertical plane of such kind of the pendulums is studying. The seesaw is a segment of the cylinder whose axis is horizontal. This cylindrical segment oscillates while rolling on the horizontal surface without any slipping. The lower (first) link of the pendulum is fastened to the seesaw by the cylindrical joint. The axis of this joint is parallel to the axis of the cylinder and to the axis of the inter-link joint also. The limited in the absolute value torque is applied to the pendulum in the inter-link joint. Thus, the described above system has three degrees of freedom and the single control action only. The open-loop system has an unstable equilibrium position with the both links of the pendulum directed vertically upwards. The seesaw in this equilibrium position is not tilted. The control stabilizing the desired unstable equilibrium is constructed in the feedback form on two "unstable" Jordan variables of an open-loop linearized system. By this way we design the feedback control with maximal as possible the attraction domain of the equilibrium position. Some properties of the controllability and attraction domains are studied. The results of the numerical studies are presented.
In this paper, we discuss a possibility of evaluating a part of the energy cost for maintaining a... more In this paper, we discuss a possibility of evaluating a part of the energy cost for maintaining a vertical posture by a person. We use the stabilometric data (center of pressure (CoP) postural sway measurements) only. The application of an inverted pendulum model for calculating the components of the mechanical work of particular groups of leg muscles is described. We use integral of the modulus of the power of total torques developed by the antagonists. For the sagittal direction, the mechanical work of muscles of the ankle is make an estimate mainly, and for the frontal directionof the pelvic muscles. The possibility of using approximate estimates of energy indicators for the slow components of human movement is discussed. To analyze the correlations of various indicators, the results of postural stability tests were used. During these tests the subjects stood with their eyes open in an upright posture. Moreover, in several tests, they were presented with various visual illusions. It was causing a change in postural characteristics and, accordingly, stabilometric parameters. The correlations between the introduced energetical indicators and indicators traditionally used in stabilometry are analyzed. The next indicators: CoP trajectory range of oscillations along the frontal and sagittal, the average CoP velocity and its projection on the frontal and sagittal axes, as well as an indicator called the "total energy density of statokinesiogram" and its components for the frontal and sagittal directions were considered. A correlation between the used indicator of mechanical work and the stabilogram range was developed. It is shown that the change in a part of the energy corresponding to an indicator called the "total energy density of statokinesiogram" is small and, apparently, does not adequately characterize the change in mechanical energy.
Full text: https://rdcu.be/cDPVb The approaches to determining the horizontal coordinates... more Full text: https://rdcu.be/cDPVb The approaches to determining the horizontal coordinates of the center of mass (CoM) applicablefor force plate are compared. The force plate for which only vertical forces are the measurements takes into account. The first of these approaches uses the information not only about the initial position and rate of CoM, but also about its terminal state. The second is associated with the use of the assumption about the absence of unstable components in the movement and uses frequency filtering methods. Known algorithms were modified to solve the problem in conditions of sufficiently intense movements by a person. The considered modified algorithms were compared for recordings movement of the subjects who performed a “test with a stepwise visual disturbance” on a force plate. A system of video cameras was simultaneously used to determine the coordinates of a marker fixed approximately at the CoM height. The working capacity of all modified algorithms was demonstrated. It was noted that the error of the estimation method using a double filtration in forward and reverse time was lower than in other procedures.
The problem of the control synthesis to stabilize the double inverted pendulum installed on the s... more The problem of the control synthesis to stabilize the double inverted pendulum installed on the seesaw is considering. The movement in the vertical plane of such kind of the pendulums is studying. The seesaw is a segment of the cylinder whose axis is horizontal. This cylindrical segment oscillates while rolling on the horizontal surface without any slipping. The lower (first) link of the pendulum is fastened to the seesaw by the cylindrical joint. The axis of this joint is parallel to the axis of the cylinder and to the axis of the inter-link joint also. The limited in the absolute value torque is applied to the pendulum in the inter-link joint. Thus, the described above system has three degrees of freedom and the single control action only. The open-loop system has an unstable equilibrium position with the both links of the pendulum directed vertically upwards. The seesaw in this equilibrium position is not tilted. The control stabilizing the desired unstable equilibrium is constructed in the feedback form on two "unstable" Jordan variables of an open-loop linearized system. By this way we design the feedback control with maximal as possible the attraction domain of the equilibrium position. Some properties of the controllability and attraction domains are studied. The results of the numerical studies are presented.
The test and correcting calibration capability of a portable acceleration re-corder under orbita... more The test and correcting calibration capability of a portable acceleration re-corder under orbital flight conditions is discussed. This recorder includes a 3-axis accelerometer. Determination its scale factors is the most difficult test cali-bration stage. The main difficulty of calibration is the lack of special equipment on the space station. It is proposed to use a standard mass meter installed on the ISS for testing accelerometers. The algorithms considered in the article use, in addition to the recorder readings, data of the mass meter platform motion and the video camera records processing. To test the algorithms in ground conditions, recordings were made that simulate the situation of an orbital flight. The proposed algorithms showed 2% error in the accelerometers scale factors
The paper is devoted to the simplified models of force plate measurements. The traditional models... more The paper is devoted to the simplified models of force plate measurements. The traditional models are used to describe the motion of a person. Human motion in the sagittal plane is described by the inverted pendulum model. Simplified three link model is used to frontal plane motion description. Two links of this model are parallel and support on the floor. These units model the legs, and the third link simulates the body, arms and head, which do not change the mutual arrangement. Links pivotally connected at the hip joints. It is assumed that the force plate (stabilograph) is a rigid body. These models are used to express force plate measurements through body model angles and ankle and hip torques. The approximate analysis shows that changes in the sagittal and frontal coordinates of the centre of pressure mostly characterize the change of ankle and hip torques, respectively. The obtained estimation is valid for arbitrary tempo of human movements, and it allows us to explain “deteri...
The approaches to determining the horizontal coordinates of the center of mass (CoM) applicable f... more The approaches to determining the horizontal coordinates of the center of mass (CoM) applicable for force plate are compared. The force plate for which only vertical forces are the measurements takes into account. The first of these approaches uses the information not only about the initial position and rate of CoM, but also about its terminal state. The second is associated with the use of the assumption about the absence of unstable components in the movement and uses frequency filtering methods. Known algorithms were modified to solve the problem in conditions of sufficiently intense movements by a person. The сonsidered modified algorithms were compared for recordings movement of the subjects who performed a “test with a stepwise visual disturbance” on a force plate. A system of video cameras was simultaneously used to determine the coordinates of a marker fixed approximately at the CoM height. The working capacity of all modified algorithms was demonstrated. It was noted that the error of the estimation method using a double filtration in forward and reverse time was lower than in other procedures.
Optimal control problems for human movement patterns often contain the parameters for which infor... more Optimal control problems for human movement patterns often contain the parameters for which information is missing. This complicates the direct use of optimal trajectories for the assessment of the quality of motion control. However, some properties can be used for such an evaluation. In this report is considered given approach by example of stabilometric test with step visual input. While completing test a person stands on the force plate in front of the computer screen, which shows the target and image of the person center of pressure. During the test target changes its position stepwise and person is supposed change quickly the body position in order to match the image of the center of pressure with target and held it in vicinity of the latter target position. In the sagittal plane required motion can be achieved only by changing the ankle angle and the person must carry this motion out, stay whole foot on. Person motion is associated with the movement of the inverted pendulum controlled by torque in the ankle joint. The problem of speed of response control when the person must change the angle of the pendulum and LQG stabilization problem are solved. The properties of optimal trajectories for these problems are: the presence of “swing-up”; the equality of “swing-up” and “overshoot” amplitudes. These properties are suggested for designing of performance indexes of movement. It seems that the use of these parameters when evaluating the perfect motion can simplify of work statement given for the athlete to improve the simulated movement. The parameters describing “swing-up” and “overshoot” characterize the intensity of muscular effort during acceleration at the start of the movement and in the final braking. Using the ratio values will allow comparing them to the values for the dimensionless optimal control problems.
Models of the motion of person who undergoes the stabilometric "test with visual step input" are ... more Models of the motion of person who undergoes the stabilometric "test with visual step input" are considered. At the beginnings of the test person stand on the stabilometric force plate. Center of pressure (COP) image and target are displayed on the screen in front of the person. Center of target is superposed with the mean COP position on the basic plane. During test the target changes position jump-like and the person’s asked to change quickly his ankle angle to superpose COP image with the center of a target on the screen and to hold it hereafter in target region. For test results analyses it is suggested to use the solution of optimal control of position of the inverted pendulum with actuator in a pivot. The speed-of-response control and LQ stabilization optimal problems are considered. Possibility of usage of optimal solutions for generation of test indexes is discussed.
В настоящей статье рассмотрены примеры достаточно простых задач, иллюстрирующие взаимосвязь прибл... more В настоящей статье рассмотрены примеры достаточно простых задач, иллюстрирующие взаимосвязь приближенных моделей описывающих силы, действующие при качении деформируемого колеса. Основные причины, побудившие автора представить настоящий материал, состоят в следующем. Во-первых, вопросы теории качения деформируемого колеса как правило не находят отражения в курсах теоретической механики. В этих курсах обсуждаются упрощенные сигнатурные модели контактных сил, но при этом не поясняется, от знака какой именно величины зависят силы в контакте колеса с дорогой. Во-вторых, в настоящее время широкое распространение получила теория поликомпонентного сухого трения [4], результаты которой на первый взгляд не согласуются с известными моделями качения деформируемого колеса. В тоже время подход к моделированию контактных сил c использованием модели cухого трения для деформируемого колеса известен давно и изложен, например, в книге [1]. Различные приближения построенных моделей используются при описании таких явлений как, например, увод колеса, шимми управляемых колес автомобиля и самолета и т.д. Недостатком этого изложения следует считать отсутствие аккуратного обоснования для пренебрежения «моментом трения верчения». Наконец, в русскоязычной литературе, обсуждающей особенности современных моделей качения деформируемых колёс, подобные вопросы обсуждаются крайне редко.
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Papers by Pavel Kruchinin
человеком вертикальной позы. В статье рассмотрен вопрос о возможной связи описанных особенностей диффузионного анализа стабилограмм с наличием зоны нечувствительности сигнала вестибулярного аппарата. Рассмотрены модели управляемой стабилизации вертикальной позы для фронтального и cагиттального направлений. Эти модели используют модифицированные уравнения движения перевернутого маятника, стабилизируемого ПИД-регулятором по позиционным измерениям. Управление дополнено обратной связью по информации, поступающей от модели отолитового органа, имеющего зону нечувствительности.
Предполагается, что сигнал вертикального канала отолитов и полукружных каналов являются подпороговыми и системой управления не воспринимаются. Приведены результаты
диффузионного анализа для ансамбля реализаций численной модели удержания человеком вертикальной позы. Параметры системы управления скорректированы по итогам сопоставления результатов моделирования с натурными данными. Численное моделирование показало, что влияние отолитового органа при спокойном стоянии здорового человека в позе "ноги на ширине плеч" во фронтальной плоскости минимально или отсутствует, в сагиттальной же плоскости существуют значения коэффициента усиления сигнала отолита, при которых становится заметно влияние этой составляющей управления. Представленное моделирование позволяет наметить основные направления для анализа связи показателей диффузионного анализа стабилограмм с особенностями функционирования как вестибулярного аппарата, так и других сенсорных модальностей.
The problem of stabilizing an inverted pendulum pivotally connected to a platform mounted on a viscoelastic base. This system is designed to simulate a test with maintaining equilibrium by a person standing on a foamed polyurethane plate used in biomechanical studies. The control in the system is the torque in the cylindrical hinge of the pendulum. This torque is limited in absolute value. The described model corresponds to the “ankle” strategy considered in biomechanical studies of the posture control by a person standing on an unstable support. It shows numerically that the linearized system, although it has a deficit in the number of control inputs, is controllable. The region of controllability of the system is found with a control torque limited in absolute value. A control is constructed that stabilizes an unstable equilibrium position with a maximum region of attraction. This control is such that all of its resources are used to suppress the only unstable mode. The boundaries of the region of attraction of the equilibrium state under this control are found. The behavior of the stabilized system has been studied. The results of the analysis allow us to compare the solution of the problem under consideration and the solution of the problem of maintaining equilibrium by a person standing on seesaw.
algorithms was demonstrated. It was noted that the error of the estimation method using a double filtration in forward and reverse time was lower than in other procedures.
человеком вертикальной позы. В статье рассмотрен вопрос о возможной связи описанных особенностей диффузионного анализа стабилограмм с наличием зоны нечувствительности сигнала вестибулярного аппарата. Рассмотрены модели управляемой стабилизации вертикальной позы для фронтального и cагиттального направлений. Эти модели используют модифицированные уравнения движения перевернутого маятника, стабилизируемого ПИД-регулятором по позиционным измерениям. Управление дополнено обратной связью по информации, поступающей от модели отолитового органа, имеющего зону нечувствительности.
Предполагается, что сигнал вертикального канала отолитов и полукружных каналов являются подпороговыми и системой управления не воспринимаются. Приведены результаты
диффузионного анализа для ансамбля реализаций численной модели удержания человеком вертикальной позы. Параметры системы управления скорректированы по итогам сопоставления результатов моделирования с натурными данными. Численное моделирование показало, что влияние отолитового органа при спокойном стоянии здорового человека в позе "ноги на ширине плеч" во фронтальной плоскости минимально или отсутствует, в сагиттальной же плоскости существуют значения коэффициента усиления сигнала отолита, при которых становится заметно влияние этой составляющей управления. Представленное моделирование позволяет наметить основные направления для анализа связи показателей диффузионного анализа стабилограмм с особенностями функционирования как вестибулярного аппарата, так и других сенсорных модальностей.
The problem of stabilizing an inverted pendulum pivotally connected to a platform mounted on a viscoelastic base. This system is designed to simulate a test with maintaining equilibrium by a person standing on a foamed polyurethane plate used in biomechanical studies. The control in the system is the torque in the cylindrical hinge of the pendulum. This torque is limited in absolute value. The described model corresponds to the “ankle” strategy considered in biomechanical studies of the posture control by a person standing on an unstable support. It shows numerically that the linearized system, although it has a deficit in the number of control inputs, is controllable. The region of controllability of the system is found with a control torque limited in absolute value. A control is constructed that stabilizes an unstable equilibrium position with a maximum region of attraction. This control is such that all of its resources are used to suppress the only unstable mode. The boundaries of the region of attraction of the equilibrium state under this control are found. The behavior of the stabilized system has been studied. The results of the analysis allow us to compare the solution of the problem under consideration and the solution of the problem of maintaining equilibrium by a person standing on seesaw.
algorithms was demonstrated. It was noted that the error of the estimation method using a double filtration in forward and reverse time was lower than in other procedures.
Person motion is associated with the movement of the inverted pendulum controlled by torque in the ankle joint. The problem of speed of response control when the person must change the angle of the pendulum and LQG stabilization problem are solved. The properties of optimal trajectories for these problems are: the presence of “swing-up”; the equality of “swing-up” and “overshoot” amplitudes. These properties are suggested for designing of performance indexes of movement. It seems that the use of these parameters when evaluating the perfect motion can simplify of work statement given for the athlete to improve the simulated movement. The parameters describing “swing-up” and “overshoot” characterize the intensity of muscular effort during acceleration at the start of the movement and in the final braking. Using the ratio values will allow comparing them to the values for the dimensionless optimal control problems.
For test results analyses it is suggested to use the solution of optimal control of position of the inverted pendulum with actuator in a pivot. The speed-of-response control and LQ stabilization optimal problems are considered. Possibility of usage of optimal solutions for generation of test indexes is discussed.