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Sit-to-stand movement (STS) is a mundane activity, controlled by the central-nervous-system (CNS) via a complex neurophysiological mechanism that involves coordination of limbs for successful execution. Detailed analysis and accurate simulations of STS task have significant importance in clinical intervention, rehabilitation process, and better design for assistive devices. The CNS controls STS motion by taking inputs from proprioceptors. These input signals suffer delay in transmission to CNS making movement control and coordination more complex which may lead to larger body exertion or instability. This paper deals with the problem of STS movement execution in the presence of proprioceptive feedback delays in joint position and velocity. We present a high-gain observer (HGO) based feedback linearization control technique to mimic the CNS in controlling the STS transfer. The HGO estimates immeasurable delayed states to generate input signals for feedback. The feedback linearization output control law generates the passive torques at joints to execute the STS movement. TheH2dynamic controller calculates the optimal linear gains by using physiological variables. The whole scheme is simulated in MATLAB/Simulink. The simulations illustrate physiologically improved results. The ankle, knee, and hip joint position profiles show a high correlation of 0.91, 0.97, 0.80 with the experimentally generated reference profiles. The faster observer dynamics and global boundness of controller result in compensation of delays. The low error and high correlation of simulation results demonstrate (1) the reliability and effectiveness of the proposed scheme for customization of human models and (2) highlight the fact that for detailed analysis and accurate simulations of STS movement the modeling scheme must consider nonlinearities of the system.

Maintaining balance is an essential skill regulated by the central nervous system (CNS) that helps humans to function effectively. Developing a physiologically motivated computational model of a neural controller with good performance is a central component for a large range of potential applications, such as the development of therapeutic and assistive devices, diagnosis of balance disorders, and designing robotic control systems. In this paper, we characterize the biomechanics of postural control system by considering the musculoskeletal dynamics in the sagittal plane, proprioceptive feedback, and a neural controller. The model includes several physiological structures, such as the feedforward and feedback mechanism, sensory noise, and proprioceptive feedback delays. A high-gain observer (HGO)-based feedback linearization controller represents the CNS analog in the modeling paradigm. The HGO gives an estimation of delayed states and the feedback linearization control law generates the feedback torques at joints to execute postural recovery movements. The whole scheme is simulated in MATLAB/Simulink. The simulation results show that our proposed scheme is robust against larger perturbations, sensory noises, feedback delays and retains a strong disturbance rejection and trajectory tracking capability. Overall, these results demonstrate that the nonlinear system dynamics, the feedforward and feedback mechanism, and physiological latencies play a key role in shaping the motor control process.

Postural regulation and stability is a complex neuromuscular task and it requires coordination among different limbs and body parts for successful execution. The central nervous system (CNS) successfully controls this task. The proprioceptors provide feedback of fascicle length and fascicle velocity from joints to CNS which then regulates the motion. The muscle feedback by proprioceptors i.e. Muscle-Spindle (MS) and Golgi-Tendon-Organs (GTO) have neural transmission latencies that make control of CNS activity and computations an intricate issue to handle. This article discusses a robust nonlinear compensator design relying on vector filed method (feedback-linearization) in the presence of physiological delays for postural stability of a single link biomechanical model. We included small and medium delays in MS sensory feedback. We designed and implemented $H_{\infty}$ dynamic controller with feedback linearization to measure the joint torque or output to maintain postural stability. The joint torque makes up for the latencies and settles the movement profiles inside anatomical imperatives and demonstrates the applicability of feedback linearization with $H_{\infty}$ compensator in the presence of physiological latencies.

Postural balance includes keeping the selected body setup effectively against gravity and internal or external disturbances. The central nervous system (CNS) successfully controls this task. The proprioceptors provide feedback of fascicle length and fascicle velocity from joints to CNS which then regulates the motion. The muscle feedback by proprioceptors i.e. Muscle- Spindle (MS) and Golgi-Tendon-Organs (GTO) have neural transmission latencies that make control of CNS activity and computations an intricate issue to handle. This article discusses a robust nonlinear compensator design relying on vector filed method (feedback-linearization) in the presence of physiological delays for postural stability of a single link biomechanical model. We included small and medium delays in MS sensory feedback and GTO forced feedback. We designed and implemented $H_{\infty}$ dynamic controller with feedback linearization to measure the joint torque or output to maintain postural stability. The joint torque makes up for the latencies and settles the movement profiles inside anatomical imperatives and demonstrates the applicability of feedback linearization with $H_{\infty}$ compensator in the presence of physiological latencies.

Regulation of postural balance and equilibrium is a complicated neurophysiological process that involves movement coordination for effective execution. The central nervous system (CNS) effectively regulates this task. The proprioceptors impart feedback of fascicle length and fascicle velocity from joint to CNS which then controls the movement. The muscle feedback by proprioceptors i.e. Muscle-Spindle (MS) and Golgi-Tendon-Organs (GTO) have neural transmission latencies that make control of CNS activity and computations an intricate issue to handle. This article discusses a robust nonlinear compensator design relying on vector filed method (feedback-linearization) in the presence of physiological delays for postural stability of a single link biomechanical model. We included small and medium delays in MS sensory feedback and GTO forced feedback. We designed and implemented H 2 dynamic controller with feedback linearization to measure the joint torque or output to maintain postural stability. The joint torque makes up for the latencies and settles the movement profiles inside anatomical imperatives and demonstrates the applicability of feedback linearization with H 2 compensator in the presence of physiological latencies.

Postural stability is the capability of an individual to maintain the position of a human body in upright posture, more specifically to balance its center of mass (COM) within precise limitations of physiological space and stability limits. In this paper, we study an application of nonlinear control of a single link biomechanical model relating to postural stability. We construct feedback compensator to regulate and estimate the movement of biomechanical model for postural stability and fall prevention. The compensator design utilizes the strength of feedback linearization method to regulate the 2nd order system equations. Moreover, feedback estimator mimics a nonlinear estimation of central-nervous-system (CNS) to investigate the stability of biomechanical movements. We simulate this scheme in MATLAB/Simulink environment and observe that the compensator with optimal gains resulted in optimized torques in the presence of noisy measurements from joint sensor.

The Physiological studies illustrate that human sit-to-stand STS movement consists of different phases that are distinguishable by their kinematics constraints and stability requirements. We propose to use a fuzzy TSK biomechanical model to analyze, integrate, and study biomechanical STS movement. The fuzzy model combines two local linear models defined at the initiation and termination points of STS using Gaussian membership functions that operate on measurement of knee flexion. Further, we develop TSK fuzzy controllers that employ H2 and H∞ optimal control techniques for effective regulation of biomechanical STS. The fuzzy controllers similarly combine knowledge from local linear optimal controllers via membership functions. Our simulation results show that fuzzy TSK modeling is useful for the synthesis of STS movement because of its relevance with physiological principles and the use of localized control strategies for the joint torques.

Successful execution of biomechanical sit-to-stand (STS) task combines a forward thrust phase with an upward extension phase and stable movement termination. We have previously developed a fuzzy dynamic model to analyze the STS task by joining two local linear models, defined at the equilibrium positions, via Gaussian membership functions. The local linear models were obtained from a four-segment biomechanical representation of the human body dynamics in the sagittal plane. Our fuzzy controller model uses an observer to reconstruct velocity data from noisy observation of joint positions. In this study, we propose a reduced order observer with an optimal controller design for the STS task. The fuzzy optimal controller generates feedback and feedforward components of joint torques, whereby the latter are derived from a reference trajectory. Our movement control strategy employing fuzzy reduced order observer with fuzzy controller leads to physiologically tractable simulation of the STS movement with results that are superior to those previously obtained with full order compensators.

State Space formulation of a system belongs to vector space either in real or complex vector fields. The solution of second-order or higher order state space requires concept of linear (matrix) algebra for understanding. First-order state space system solves by simple theorems of calculus and algebra. The first-order equation may be homogenous or non-homogenous and both require the standard solution.

A control system is usually defined as a device or set of devices in order to manage, direct, regulate, or command the other set of devices. Typically everything in nature is working under some control mechanisms because every single item is controlled by some higher authority for desired objectives. The objectives or goals are the desired outputs of the system, and whatever resources are needed in order to achieve these objectives are inputs to the system. The authority that manages the resources to achieve desired objective for the system is called the “control system.” Here we are talking about two systems, one system that is being controlled normally called a “plant,” and another system that is controlling called the “controller.” Both are defined as a complete system individually because of different inputs and outputs. In reality, the outputs of a control system become the inputs of the plant and the outputs of the plant become the inputs to the control system. So, this loop works the objectives are achieved, or the resources are depleted. The overall system in this loop configuration, as shown in Fig. 8.1, is called the feedback system, closed loop system, or automatic system.

Components and elements bond the system, which define the relationship between two consecutive ports. These bonding elements follow constitutive laws for equating power between bonds. These elements are analogues in different energy systems as we discussed effort and flow variables in Chap. 3. If a bond or port has only one element at either end and does not require any other element to define it, then it is a 1-port element. If an element requires two bonds for defining relationship, then it is a 2-port element. If three or more bonds connect for a constitutive law, then these elements are called junctions. It is important to note that these 1-port and 2-port elements and junctions are different than vector bond graphs, which will be discussed later.

Dynamical systems are classified by the form of energy consumed or delivered, e.g., electrical, mechanical, chemical, and hydraulic systems. There are different physical laws dealing with different energy systems and therefore different modeling schemes formulate the differential equations accordingly. Universally there is only one source of energy behind all sources as our understanding, but modern day’s physics is still not able to prove the unification of all forces together. The law of conversation of energy has the same units of energy consumption as well as the rate of change of energy in all forms. This law helps to form a unified modeling approach for different types of energy systems. Modeling of an electromechanical system requires modeling through electrical laws as well as mechanical laws, with governing equations between energy transfers. Some examples are electromagnetic relays, servo control hydraulic systems, pressure valves, and many other similar systems. In the 1960s a professor named Henry M. Paynter of MIT introduced this scheme by modeling through power transformation. A graphical bond represents the power flow or transformation from one end to other end. A bond represents a single power transformation between two ports or ends. The interconnection of these bonds leads us to develop a complete model of a required system. A half arrow is a graphical representation to show the direction of power flow in the model as shown in Fig. 3.1.

A system is an isolated part of the Universe that is of interest due to a specific reason for an appropriate time. This isolated reality can be used for discussion, study, analysis, improvement, betterment, protection, or any other objective. The isolated part in which we take interest actually becomes the system and everything else is surroundings, environment, or the rest of the Universe. For example, an astrophysicist wants to study the gravitational forces of the sun and its planets, so this isolated interest becomes a solar system for him. The rest of the galaxies, and even relatively small events on the earth and planets, become surroundings for him. An oceanographer analyzing the waves and currents in the Pacific is only interested in his isolated reality and the rest of the happenings in the world are collectively an environment. Similarly, an engineer working on a comparatively small problem whether designing, studying, or discussing is a system for him and everything else in the world becomes an environment or surroundings to him till he stops working. A car is a system, an isolated part of reality for a buyer. But this car itself is a combination of many other systems such as a combustion system, braking system, fuel injection system, electrical system, steering systems, etc. A buyer at a time is interested in all including the color of car, financial value in the market, fuel consumption, etc. He is overall looking for an appropriate driving system that suits his needs. But several different types of engineers are interested in several subsystems of the same car. This car in turn is a collection of subsystems. A subsystem is a complete system when one develops an interest in it and other subsystems of the same car become an environment or surroundings for it. This example is similar to the human body system with several subsystems like the respiratory system, digestive system, reproductive system, central nervous system, etc. A body needs all subsystems at a time but an orthopedic surgeon usually only focuses on the skeletal system, and a gastroenterologist is only interested in the digestive system.

Bond graph modeling is used in diverse engineering applications due to its universality between energy systems. Every year the number of research papers and publications in the domain of modeling and engineering using this technique is on rise. Lagrangian modeling is a popular method, especially in robotic manipulators, but with the help of bond graphs these models can be extended with electromechanical systems of actuators and sensors. In the last decade, numerous papers in conferences and journals have appeared for bond graph modeling and simulation. It is being taught at undergraduate and graduate level courses in different universities showing the developing interest in this technique. Bioengineering or biomedical engineering is a key area of interest for research and development for its applications. Bond graph modeling made its way to this area by providing an alternative paradigm for modeling and simulation. In this chapter, we will focus on the recent applications of bond graph in biomedical engineering followed by some applications in a few other fields.

We obtain the biggest advantage of bond graph when a system is composed of different energy domains. In this chapter, we will cover some examples of bond graph modeling in different energy systems with advanced and more practical concepts in addition to the details covered in the last chapter. In the last chapter, basic bond graph formulation and state space representation were discussed. In this chapter, we will discuss the concepts of algebraic loops, additional two port elements known as fields, the effect of derivative causality, and bond graph in the vector notation.

Bond graph modeling possesses more applicability towards systems with different energy domains. It is easier to model electrical systems with electrical theories using KCL or KVL. It is easier to model mechanical systems using Newtonian mechanics, Lagrangian mechanics, etc. Similarly, for electromagnetic systems there are Maxwell laws to deal with both electrical and magnetic forces; in hydraulics systems, there are Bernoulli’s /Stroke’s law to deal with pressure and forces. But now, with the advent of modern technologies, there are systems which are now amalgams of electrical, mechanical, hydraulics, electromagnetic systems, etc. Bond graph modeling provides help to these modeling schemes, and dealing with systems in their energy domains provides an easier and technically mature approach. Bond graph provides a unified approach to model a system comprised of two or more energy systems. On the other hand it is difficult to provide a universal methodology that is applicable to all systems. In electrical and hydraulic systems, nodes appear where generalized flow distributes between them whereas, in mechanical systems, nodes appear where forces act together both in series or parallel configurations. As we discussed in previous chapters, that series and parallel combination is not a universal phenomenon for modeling. So there arises a problem in formulating a unified procedure for modeling at system level. A generalized set of procedures are written for modeling the systems that is applicable for modeling systems within same energy domain as well as modeling in multi-energy domain. It needs careful attention when a series or parallel combinations of different energy systems are modeled as a single system.

The neurophysiological mechanisms involved in postural stabilization are not well understood. Active and passive mechanisms at muscle and spinal levels as well as visual and vestibular processes are known to contribute toward postural stabilization and coordination of voluntary movement. The motivation for this research is to use a modeling–simulation framework to achieve two aims: (a) to ascertain viability of a physiologically motivated optimal controller design in the maintenance of posture and coordination of voluntary movement and (b) to study the relative contribution from active (feedforward) and passive (feedback) mechanisms in the execution of said movement. We employ a multi-segment sagittal model built on anatomical proportions with three degrees of freedom, including rotation at the ankle, knee, and hip joints. The behavior of the biomechanical model is controlled by an optimal linear quadratic regulator whose state and control weights are derived from physiological considerations. Representative postural and voluntary movements are simulated to illustrate the analysis–synthesis framework of biomechanical movement. Our analytical and simulation results support an active–passive model of postural stabilization and movement coordination. Besides expanding our understanding of the physiological stabilization processes in the body, the insight gained from this study promotes awareness of the existence of optimizing controllers in the central nervous system.

Human movement, postural stability and physiological models have been subjects of interest for several centuries. Physiological models for postural stability are studied in this paper with bond graph modelling and optimal control techniques. The bond graph models of a physiological motor control system provide a new prospective to analyze stability and movement of biomechanical models. The bond graphs of the musculoskeletal feedback system are used with linear H 2 optimal controller for analysis of different physiological parameters. Simulation results are obtained for various physiological parameters to analyze overall robustness of the model. These results demonstrate the applicability of bond graph modelling with robust control theory for physiological systems.

Physiologists, scientists and biomechanical engineers have all used modelling tools to study motor functions in humans using a variety of techniques ranging from rigid-body mechanics to finite element methods. We present a theoretical framework to apply bond graph modelling techniques for obtaining biomechanical system model comprising inertia, muscle, Golgi tendon organ and spindle dynamics. The bond graph modelling tracks the flow of power from system input to output, thus providing an alternative perspective to analyse physiological motor control functions. In this study, bond graph models of skeletal muscle, muscle spindle and Golgi tendon organ are developed and combined into a musculoskeletal model with proprioceptive feedback. This modelling scheme demonstrates the applicability of bond graph modelling to the physiological subsystems and their integration into the anatomical system for analysis and controller design.

Human biomechanical Sit-to-stand (STS) movement is a complex physiological task which requires movement coordination, balance and skillful termination. In previous studies we proposed the STS movement with different control strategies for physiologically relevant and optimized movements. These control techniques allowedus to optimize control systems designs for cost and robust performance. In this paper we used a four link biomechanical model with mixed H 2 /H ∞ control theory for STS transfer. We solved a biomechanical control problem with Linear Matrix Inequalities (LMI) for better physiological results by optimizing cost and bounds. Introducing LMIs for STS transfer provides a diverse perspective to physiological understand the movement. We compared these results with previous studies for H 2 and H ∞ control problems, and discussed the validity of LMI for human STS problem. Our simulation results shows that the biomechanical model with LMI control will provide a robust framework to analyze STS movement with physiological relevant control objectives.

Human biomechanical movements are complex physiological tasks which are efficiently regulated by the central nervous system (CNS). Proprioceptors (muscle spindles) provide feedback of fascicle length and velocity from a joint to CNS, which then control the entire movement. These feedbacks have delays which are accounted for by the required output command. In this study, we used a four-link sagittal plane nonlinear biomechanical model with three joint angles, to simulate human sit-to-stand (STS) movement in the presence of these physiological latencies. Ankle, knee and hip joint angles have delays for angular and velocity feedbacks. We linearized the whole model using pade approximation at sitting and standing positions which resulted in two eighteenth order linear systems. We integrated these local models into a fuzzy model with Gaussian membership function. The knee flexion angle during sit to stand movement provides the criterion for determining the weights of fuzzy membership functions. We developed a H 2 dynamic optimal controller for each local linear model and integrated with the fuzzy model. This controller computed the joint's torque or inputs for biomechanical STS task. We also introduced a reference trajectory to track the knee flexion angle error for smooth and physiological relevant sit to stand transfer. Simulation results of angular profiles and kinematics variables demonstrate the applicability of the fuzzy modeling with H 2 controller in the presence of feedback latencies.

Sit-to-stand (STS) movement is a common human task which involves combination of a musculoskeletal structure integrated with neural control. We present a conceptual 3D bipedal nonlinear model for STS task with optimal controller design for exoskeleton torques. This model has 7 sagittal plane angles, 3 frontal plane angles, and 3 foot translational variables with 3 position based holonomic constraints. We regulate the model with optimal controller design by coupled torque optimization due to muscular interaction between ankle, knee and hip joints. Our simulation results show the improvement in the results from previous controller design schemes. We further obtain experimental data for STS task on a force plate to compare the ground reaction forces of experimental data with our mathematical framework. This proves the validity of the model to extend this mathematical framework for further analysis of healthy and neuro-deficient subjects and accordingly designs of ergonomics and rehabilitation robotics.

Human biomechanical movements are complex physiological tasks efficiently regulated by the central nervous system (CNS). Proprioceptors (muscle spindles) provide feedback of fascicle length and velocity from a joint to CNS, which then control the entire movement. These feedbacks have delays which are accounted for by the required output command. In this study, we are using a four-link sagittal plane nonlinear biomechanical model with three joint angles, to simulate human sit-to-stand (STS) movement in the presence of these physiological latencies. Ankle, knee and hip joint angles have delays for angular and velocity feedbacks. We linearize the whole model using pade approximation which results in eighteenth order linear system. Then, we subject this system to optimal controller design scheme for three joint torques using eighteenth order compensator with physiological cost optimization. We provide simulation results for linear and nonlinear models which show the suitability of this scheme for further analysis of STS task, feedback latencies and their effects on controller gains.

We present the development of a 3D bipedal robotic model with thirteen generalized coordinates, and decoupled optimal controller design for the control of biomechanical sit-to-stand (STS) transfer. The non-linear model developed in Maple DynaFlexPro environment has three frontal and seven sagittal degrees of freedom (DOF). Three holonomic constraints ensure stationary foot placement during performance of the STS task. The controller design proceeds by decoupling the constrained and unconstrained DOF. We propose H2 and Hinfin optimal control designs for feedback control of joint torques in the constrained and unconstrained planes, respectively. We provide analytical and computer simulation results to show the applicability and performance of the decoupling controller for the control of STS task.

The neuro-physiological mechanisms involved in postural stabilization are not well understood. Human body mechanically resembles an inverted pendulum that is inherently unstable. Active and passive mechanisms at muscle and spinal level as well as visual and vestibular processes are attributed to postural stabilization. At the same time, intrinsic delays in the reflex pathways and the low-pass characteristics of the muscle response tend to limit the effectiveness of active mechanisms of stabilization. The motivation for this research was to study the relative contribution from active control (feedforward mechanisms) and passive stiffness (feedback mechanisms) in maintenance of posture and coordination of voluntary movement. We develop a multi-segment sagittal model with three degrees of freedom that included the rotation at ankle, knee, and hip joints. We propose an optimal LQR controller as the central nervous system analog in posture and movement coordination. We present analytical and simulation results to support an active-passive model of postural stabilization. Besides expanding our understanding of the stabilization processes in the body, the insight gained from this study is expected to promote awareness of the existence of optimal trajectories in the coordination of skilled voluntary movements.

Researchers have analyzed human movement coordination in a variety of ways using different optimization variables and functions. In this study we used a 4-link sagittal plane biomechanical model of sit-to-stand transfer to study physiological cost optimization. We regulated the movement with optimal controller design emulating central nervous system decision making. In such scheme the state and inputs were weighted by penalty functions derived from physiological variables, i.e., center of mass and ground reaction forces. We tracked the position variables through reference trajectories, which were also used to generate active components of joint torques. Net torque comprising feedback and feedforward components resulted in stable STS transfer. Our results shows that analytical model with physiological cost functions provides efficient framework for the study of STS movement.