Neural adaptive control of nonlinear multivariable systems with application to a class of inverted pendulums

In this paper multilayer neural networks (MNNs) are used to control the balancing of a class of inverted pendulums. Unlike normal inverted pendulums, the pendulum discussed here has two degrees of rotational freedom and the base-point moves randomly in three-dimensional space. The goal is to apply control torques to keep the pendulum in a prescribed position in spite of the random movement at the base-point. Since the inclusion of the base-point motion leads to a non-autonomous dynamic system with time-varying parametric excitation, the design of the control system is a challenging task. A feedback control algorithm is proposed that utilizes a set of neural networks to compensate for the effect of the system's nonlinearities. The weight parameters of neural networks updated on-line, according to a learning algorithm that guarantees the Lyapunov stability of the control system. Furthermore, since the base-point movement is considered unmeasurable, a neural inverse model is employed to estimate it from only measured state variables. The estimate is then utilized within the main control algorithm to produce compensating control signals. The examination of the proposed control system, through simulations, demonstrates the promise of the methodology and exhibits positive aspects, which cannot be achieved by the previously developed techniques on the same problem. These aspects include fast, yet well-maintained damped responses with reasonable control torques and no requirement for knowledge of the model or the model parameters. The work presented here can benefit practical problems such as the study of stable locomotion of human upper body and bipedal robots.     

Modelling 3D control of upright stance using an optimal control strategy

A 3D balance control model of quiet upright stance is presented, based on an optimal control strategy, and evaluated in terms of its ability to simulate postural sway in both the anterior–posterior and medial–lateral directions. The human body was represented as a two-segment inverted pendulum. Several assumptions were made to linearise body dynamics, for example, that there was no transverse rotation during upright stance. The neural controller was presumed to be an optimal controller that generates ankle control torque and hip control torque according to certain performance criteria. An optimisation procedure was used to determine the values of unspecified model parameters including random disturbance gains and sensory delay times. This model was used to simulate postural sway behaviours characterised by centre-of-pressure (COP)-based measures. Confidence intervals for all normalised COP-based measures contained unity, indicating no significant differences between any of the simulated COP-based measures and corresponding experimental references. In addition, mean normalised errors for the traditional measures were < 8%, and those for most statistical mechanics measures were ～3–66%. On the basis these results, the proposed 3D balance control model appears to have the ability to accurately simulate 3D postural sway behaviours.     

Modelling 3D control of upright stance using an optimal control strategy

A 3D balance control model of quiet upright stance is presented, based on an optimal control strategy, and evaluated in terms of its ability to simulate postural sway in both the anterior-posterior and medial-lateral directions. The human body was represented as a two-segment inverted pendulum. Several assumptions were made to linearise body dynamics, for example, that there was no transverse rotation during upright stance. The neural controller was presumed to be an optimal controller that generates ankle control torque and hip control torque according to certain performance criteria. An optimisation procedure was used to determine the values of unspecified model parameters including random disturbance gains and sensory delay times. This model was used to simulate postural sway behaviours characterised by centre-of-pressure (COP)-based measures. Confidence intervals for all normalised COP-based measures contained unity, indicating no significant differences between any of the simulated COP-based measures and corresponding experimental references. In addition, mean normalised errors for the traditional measures were 相似文献   

Behaviour-based modelling of hexapod locomotion: linking biology and technical application

Walking in insects and most six-legged robots requires simultaneous control of up to 18 joints. Moreover, the number of joints that are mechanically coupled via body and ground varies from one moment to the next, and external conditions such as friction, compliance and slope of the substrate are often unpredictable. Thus, walking behaviour requires adaptive, context-dependent control of many degrees of freedom. As a consequence, modelling legged locomotion addresses many aspects of any motor behaviour in general. Based on results from behavioural experiments on arthropods, we describe a kinematic model of hexapod walking: the distributed artificial neural network controller walknet. Conceptually, the model addresses three basic problems in legged locomotion. (I) First, coordination of several legs requires coupling between the step cycles of adjacent legs, optimising synergistic propulsion, but ensuring stability through flexible adjustment to external disturbances. A set of behaviourally derived leg coordination rules can account for decentralised generation of different gaits, and allows stable walking of the insect model as well as of a number of legged robots. (II) Second, a wide range of different leg movements must be possible, e.g. to search for foothold, grasp for objects or groom the body surface. We present a simple neural network controller that can simulate targeted swing trajectories, obstacle avoidance reflexes and cyclic searching-movements. (III) Third, control of mechanically coupled joints of the legs in stance is achieved by exploiting the physical interactions between body, legs and substrate. A local positive displacement feedback, acting on individual leg joints, transforms passive displacement of a joint into active movement, generating synergistic assistance reflexes in all mechanically coupled joints.     

Postural control model interpretation of stabilogram diffusion analysis

Collins and De Luca [Collins JJ, De Luca CJ (1993) Exp Brain Res 95: 308–318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior. Received: 13 August 1998 / Accepted in revised form: 12 November 1999     

A mathematical model of the stability control of human thorax and pelvis movements during walking

A mathematical model is developed to study the human thorax and pelvis movements in the frontal plane during normal walking. The model comprises of two-link base-excited inverted pendulums with one-degree of rotational freedom for each link. Since the linear motion of the pelvis has a significant effect on the upper body stability, this effect is included in the model by having a base point moving in the frontal plane in a general way. Furthermore, because the postural stability is the primary requirement of normal human walking, the control law is developed based on Lyapunov's stability theory, which guarantees the stability of the pendulum system around the up-right position. To evaluate the model, the simulation results, including the angular displacement of each link and the torque applied on each link, are compared with those from gait measurements. It is shown that the simulation results match those from gait measurements closely. These results suggest that the proposed model can provide a useful framework for analysis of postural control mechanisms.     

Non-linear stimulus-response behavior of the human stance control system is predicted by optimization of a system with sensory and motor noise

We developed a theory of human stance control that predicted (1) how subjects re-weight their utilization of proprioceptive and graviceptive orientation information in experiments where eyes closed stance was perturbed by surface-tilt stimuli with different amplitudes, (2) the experimentally observed increase in body sway variability (i.e. the “remnant” body sway that could not be attributed to the stimulus) with increasing surface-tilt amplitude, (3) neural controller feedback gains that determine the amount of corrective torque generated in relation to sensory cues signaling body orientation, and (4) the magnitude and structure of spontaneous body sway. Responses to surface-tilt perturbations with different amplitudes were interpreted using a feedback control model to determine control parameters and changes in these parameters with stimulus amplitude. Different combinations of internal sensory and/or motor noise sources were added to the model to identify the properties of noise sources that were able to account for the experimental remnant sway characteristics. Various behavioral criteria were investigated to determine if optimization of these criteria could predict the identified model parameters and amplitude-dependent parameter changes. Robust findings were that remnant sway characteristics were best predicted by models that included both sensory and motor noise, the graviceptive noise magnitude was about ten times larger than the proprioceptive noise, and noise sources with signal-dependent properties provided better explanations of remnant sway. Overall results indicate that humans dynamically weight sensory system contributions to stance control and tune their corrective responses to minimize the energetic effects of sensory noise and external stimuli.     

Implementation of controlling strategy in a biomechanical lower limb model with active muscles for coupling multibody dynamics and finite element analysis

Computational biomechanics for human body modeling has generally been categorized into two separated domains: finite element analysis and multibody dynamics. Combining the advantages of both domains is necessary when tissue stress and physical body motion are both of interest. However, the method for this topic is still in exploration. The aim of this study is to implement unique controlling strategies in finite element model for simultaneously simulating musculoskeletal body dynamics and in vivo stress inside human tissues. A finite element lower limb model with 3D active muscles was selected for the implementation of controlling strategies, which was further validated against in-vivo human motion experiments. A unique feedback control strategy that couples together a basic Proportion-Integration-Differentiation (PID) controller and generic active signals from Computed Muscle Control (CMC) method of the musculoskeletal model or normalized EMG singles was proposed and applied in the present model. The results show that the new proposed controlling strategy show a good correlation with experimental test data of the normal gait considering joint kinematics, while stress distribution of local lower limb tissue can be also detected in real-time with lower limb motion. In summary, the present work is the first step for the application of active controlling strategy in the finite element model for concurrent simulation of both body dynamics and tissue stress. In the future, the present method can be further developed to apply it in various fields for human biomechanical analysis to monitor local stress and strain distribution by simultaneously simulating human locomotion.     

Simulation studies on the control of posture and movement in a multi-jointed limb

Simulation studies were performed to evaluate the effectiveness of different control schemes in stabilizing a multi-jointed limb (human arm) in response to force perturbations. The mechanical properties of the arm were modeled as a linear visco-elastic system and the effectiveness of negative feedback of angular position and torque was evaluated. The effectiveness of a given amount of position feedback depended strongly on the initial position of the arm and on the perturbation, while torque feedback was much more consistently effective in damping the motion of the limb.     

Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator

The central pattern generators (CPGs) in the spinal cord strongly contribute to locomotor behavior. To achieve adaptive locomotion, locomotor rhythm generated by the CPGs is suggested to be functionally modulated by phase resetting based on sensory afferent or perturbations. Although phase resetting has been investigated during fictive locomotion in cats, its functional roles in actual locomotion have not been clarified. Recently, simulation studies have been conducted to examine the roles of phase resetting during human bipedal walking, assuming that locomotion is generated based on prescribed kinematics and feedback control. However, such kinematically based modeling cannot be used to fully elucidate the mechanisms of adaptation. In this article we proposed a more physiologically based mathematical model of the neural system for locomotion and investigated the functional roles of phase resetting. We constructed a locomotor CPG model based on a two-layered hierarchical network model of the rhythm generator (RG) and pattern formation (PF) networks. The RG model produces rhythm information using phase oscillators and regulates it by phase resetting based on foot-contact information. The PF model creates feedforward command signals based on rhythm information, which consists of the combination of five rectangular pulses based on previous analyses of muscle synergy. Simulation results showed that our model establishes adaptive walking against perturbing forces and variations in the environment, with phase resetting playing important roles in increasing the robustness of responses, suggesting that this mechanism of regulation may contribute to the generation of adaptive human bipedal locomotion.     

Evolving experience-dependent robust behaviour in embodied agents

In this work, based on behavioural and dynamical evidence, a study of simulated agents with the capacity to change feedback from their bodies to accomplish a one-legged walking task is proposed to understand the emergence of coupled dynamics for robust behaviour. Agents evolve with evolutionary-defined biases that modify incoming body signals (sensory offsets). Analyses on whether these agents show further dependence to their environmental coupled dynamics than others with no feedback control is described in this article. The ability to sustain behaviours is tested during lifetime experiments with mutational and sensory perturbations after evolution. Using dynamical systems analysis, this work identifies conditions for the emergence of dynamical mechanisms that remain functional despite sensory perturbations. Results indicate that evolved agents with evolvable sensory offset depends not only on where in neural space the state of the neural system operates, but also on the transients to which the inner-system was being driven by sensory signals from its interactions with the environment, controller, and agent body. Experimental evidence here leads discussions on a dynamical systems perspective on behavioural robustness that goes beyond attractors of controller phase space.     

Stability and Control of Human Trunk Movement During Walking

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov's stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.     

Stability and Control of Human Trunk Movement During Walking

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov' stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.     

Stabilization of human standing posture using functional neuromuscular stimulation

Functional neuromuscular stimulation (FNS)/functional electrical stimulation (FES) is a potential way to restore some functionality to the limbs of patients with spinal cord injury through direct/indirect stimulation of the motoneuron. One of the constraints for wider use of FNS on paraplegic patients is the lack of efficient control algorithm. Most of the published works on FNS/FES control are based on oversimplified models of human body dynamics. An innovative control strategy for stabilizing the standing posture of paraplegic patients is proposed here which is a combination of a proportional-plus-derivative controller for motions of the skeletal system and a control action prediction mechanism to produce musculotendon activation. The goal is to produce musculotendon torque which can approximate those demanded by the controller for the skeletal system. In computer simulations, using a detailed skeletal–musculotendon–muscle activation dynamics model of human body, this FNS/FES control approach can stabilize a paraplegic patient's standing posture with the minimum number of musculotendon groups. Also, it is found that this control strategy can maintain stability even in the presence of reasonable variations in the controller's musculotendon parameters.     

A Mathematical Model of the Stability Control of Human Thorax and Pelvis Movements During Walking

A mathematical model is developed to study the human thorax and pelvis movements in the frontal plane during normal walking. The model comprises of two-link base-excited inverted pendulums with one-degree of rotational freedom for each link. Since the linear motion of the pelvis has a significant effect on the upper body stability, this effect is included in the model by having a base point moving in the frontal plane in a general way. Furthermore, because the postural stability is the primary requirement of normal human walking, the control law is developed based on Lyapunov's stability theory, which guarantees the stability of the pendulum system around the up-right position. To evaluate the model, the simulation results, including the angular displacement of each link and the torque applied on each link, are compared with those from gait measurements. It is shown that the simulation results match those from gait measurements closely. These results suggest that the proposed model can provide a useful framework for analysis of postural control mechanisms.     

Mechanical interaction of center of pressure and force direction in the upright human

Humans maintain upright bipedal posture by producing appropriate force against the environment through the interaction of neural controlled muscle force with the mechanics of the skeletal system. Characterizing these mechanics facilitates understanding of the neural control. We used a mechanical model of an upright human to analyze how the mechanical linkage aspects of the human body affect the force between the feet and the ground (F). Key parameters of F that directly regulate upright body posture are the direction of F (θ(F)) and its point of application (x(CP), anterior-posterior position of the center of pressure). Instantaneous analysis of the equations of motion demonstrated that θ(F) varied systematically with x(CP) such that the F vectors intersected at a point called the Posture-specific force Intersection point or PI (Π). The Π was located above the center of mass when the hip and knee joints were modeled as rigid and was located near the knee when the hip and knee torques were held constant. Limb posture and the knee torque affected the location of Π. This Π behavior quantifies the purely mechanical effect of anterior-posterior center of pressure shifts on the direction of F, which has consequences for the control of whole body posture.     

Velocity Control of a Bounding Quadruped via Energy Control and Vestibular Reflexes

In this paper a bio-inspired approach of velocity control for a quadruped robot running with a bounding gait on compliant legs is set up. The dynamic properties ofa sagittal plane model of the robot are investigated. By analyzing the stable fixed points based on Poincare map, we find that the energy change of the system is the main source for forward velocity adjustment. Based on the analysis of the dynamics model of the robot, a new simple linear running controller is proposed using the energy control idea, which requires minimal task level feedback and only controls both the leg torque and ending impact angle. On the other hand, the functions of mammalian vestibular reflexes are discussed, and a reflex map between forward velocity and the pitch movement is built through statistical regression analysis. Finally, a velocity controller based on energy control and vestibular reflexes is built, which has the same structure as the mammalian nervous mechanism for body posture control. The new con- troller allows the robot to run autonomously without any other auxiliary equipment and exhibits good speed adjustment capa- bility. A series simulations and experiments were set to show the good movement agility, and the feasibility and validity of the robot system.     

Modeling biological motor control for human locomotion with functional electrical stimulation

This paper develops a novel control system for functional electrical stimulation (FES) locomotion, which aims to generate normal locomotion for paraplegics via FES. It explores the possibility of applying ideas from biology to engineering. The neural control mechanism of the biological motor system, the central pattern generator, has been adopted in the control system design. Some artificial control techniques such as neural network control, fuzzy logic, control and impedance control are incorporated to refine the control performance. Several types of sensory feedback are integrated to endow this control system with an adaptive ability. A musculoskeletal model with 7 segments and 18 muscles is constructed for the simulation study. Satisfactory simulation results are achieved under this FES control system, which indicates a promising technique for the potential application of FES locomotion in future.