Intermittent Feedback-Control Strategy for Stabilizing Inverted Pendulum on Manually Controlled Cart as Analogy to Human Stick Balancing

The stabilization of an inverted pendulum on a manually controlled cart (cart-inverted-pendulum; CIP) in an upright position, which is analogous to balancing a stick on a fingertip, is considered in order to investigate how the human central nervous system (CNS) stabilizes unstable dynamics due to mechanical instability and time delays in neural feedback control. We explore the possibility that a type of intermittent time-delayed feedback control, which has been proposed for human postural control during quiet standing, is also a promising strategy for the CIP task and stick balancing on a fingertip. Such a strategy hypothesizes that the CNS exploits transient contracting dynamics along a stable manifold of a saddle-type unstable upright equilibrium of the inverted pendulum in the absence of control by inactivating neural feedback control intermittently for compensating delay-induced instability. To this end, the motions of a CIP stabilized by human subjects were experimentally acquired, and computational models of the system were employed to characterize the experimental behaviors. We first confirmed fat-tailed non-Gaussian temporal fluctuation in the acceleration distribution of the pendulum, as well as the power-law distributions of corrective cart movements for skilled subjects, which was previously reported for stick balancing. We then showed that the experimental behaviors could be better described by the models with an intermittent delayed feedback controller than by those with the conventional continuous delayed feedback controller, suggesting that the human CNS stabilizes the upright posture of the pendulum by utilizing the intermittent delayed feedback-control strategy

Stabilization of a Cart Inverted Pendulum: Improving the Intermittent Feedback Strategy to Match the Limits of Human Performance

Stabilization of the CIP (Cart Inverted Pendulum) is an analogy to stick balancing on a finger and is an example of unstable tasks that humans face in everyday life. The difficulty of the task grows exponentially with the decrease of the length of the stick and a stick length of 32 cm is considered as a human limit even for well-trained subjects. Moreover, there is a cybernetic limit related to the delay of the multimodal sensory feedback (about 230 ms) that supports a feedback stabilization strategy. We previously demonstrated that an intermittent-feedback control paradigm, originally developed for modeling the stabilization of upright standing, can be applied with success also to the CIP system, but with values of the critical parameters far from the limiting ones (stick length 50 cm and feedback delay 100 ms). The intermittent control paradigm is based on the alternation of on-phases, driven by a proportional/derivative delayed feedback controller, and off-phases, where the feedback is switched off and the motion evolves according to the intrinsic dynamics of the CIP. In its standard formulation, the switching mechanism consists of a simple threshold operator: the feedback control is switched off if the current (delayed) state vector is closer to the stable than to the unstable manifold of the off-phase and is switched on in the opposite case. Although this simple formulation is effective for explaining upright standing as well as CIP balancing, it fails in the most challenging configuration of the CIP. In this work we propose a modification of the standard intermittent control policy that focuses on the explicit selection of switching times and is based on the phase reset of the estimated state vector at each switching time and on the simulation of an approximated internal model of CIP dynamics. We demonstrate, by simulating the modified intermittent control policy, that it can match the limits of human performance, while operating near the edge of instability

Comparison of Pixel-based Position Input and Direct Acceleration Input for Virtual Stick Balancing Tests

A virtual stick balancing environment is developed using a computer mouse as input device. The development process is presented both on the hardware and software level. Two possible concepts are suggested to obtain the acceleration of the input device: discrete differentiation of the cursor position measured in pixels on the screen and by direct measurements via an Inertial Measurement Unit (IMU). The comparison of the inputs is carried out with test measurements using a crank mechanism. The measured signals are compared to the prescribed motion of the mechanism and it is shown that the IMU-based input signal fits better to the prescribed motion than the pixel-based input signal. The pixel-based input can also be applied after additional filtering, but this presents an extra computational delay in the feedback loop

The Critical Length is a Good Measure to Distinguish between Stick Balancing in the ML and AP Directions

Seven novice subjects participated in experiments of stick balancing on a linear track in the anterior-posterior (AP) and the medio-lateral (ML) directions. The goal of the experiments was to test how the depth perception in the subjects' AP direction affects balancing performance compared to balancing in the ML direction, where depth perception does not play a role. It is easier to balance longer sticks than shorter ones, therefore balancing performance is measured by the length of the shortest stick that subjects can balance. Subjects were found to be able to balance shorter sticks in the ML direction than in the AP direction: the ratio of the shortest stick lengths in the ML direction relative to the AP direction was in average 0.53. Thus, the additional challenge posed by depth perception in the AP direction is clearly observable. Additionally, repeated trials were carried out for 5 consecutive days to assess the development of balancing skill by using stabilometry analysis. The maximal balance time of the subjects significantly increased with the days of practice

MECHANICAL MODEL FOR HUMAN BALANCING ON ROLLING BALANCE BOARD

A two-degree-of-freedom mechanical model was developed to analyze human balancing on rolling balance board in the frontal plane. The human nervous system is modeled as a proportionalderivative controller with constant feedback delay. The radius R of the wheels and the board distance h measured from the center of the wheel are adjustable parameters. Simulation results using the mechanical model were compared with real balancing trials recorded by an OptiTrack motion capture system. The goal of the paper is to investigate whether the two-degree-of-freedom model is accurate enough to model the balancing task and to introduce a stabilometry parameter in order to characterize balancing skill in case of different set of R and h. The conclusion is that the angle of the upper body and the angle of the head also play an important role in the balancing process therefore a three- or four-degree-of-freedom model is more appropriate

Understanding motor control in humans to improve rehabilitation robots

Recent reviews highlighted the limited results of robotic rehabilitation and the low quality of evidences in this field. Despite the worldwide presence of several robotic infrastructures, there is still a lack of knowledge about the capabilities of robotic training effect on the neural control of movement. To fill this gap, a step back to motor neuroscience is needed: the understanding how the brain works in the generation of movements, how it adapts to changes and how it acquires new motor skills is fundamental. This is the rationale behind my PhD project and the contents of this thesis: all the studies included in fact examined changes in motor control due to different destabilizing conditions, ranging from external perturbations, to self-generated disturbances, to pathological conditions. Data on healthy and impaired adults have been collected and quantitative and objective information about kinematics, dynamics, performance and learning were obtained for the investigation of motor control and skill learning. Results on subjects with cervical dystonia show how important assessment is: possibly adequate treatments are missing because the physiological and pathological mechanisms underlying sensorimotor control are not routinely addressed in clinical practice. These results showed how sensory function is crucial for motor control. The relevance of proprioception in motor control and learning is evident also in a second study. This study, performed on healthy subjects, showed that stiffness control is associated with worse robustness to external perturbations and worse learning, which can be attributed to the lower sensitiveness while moving or co-activating. On the other hand, we found that the combination of higher reliance on proprioception with \u201cdisturbance training\u201d is able to lead to a better learning and better robustness. This is in line with recent findings showing that variability may facilitate learning and thus can be exploited for sensorimotor recovery. Based on these results, in a third study, we asked participants to use the more robust and efficient strategy in order to investigate the control policies used to reject disturbances. We found that control is non-linear and we associated this non-linearity with intermittent control. As the name says, intermittent control is characterized by open loop intervals, in which movements are not actively controlled. We exploited the intermittent control paradigm for other two modeling studies. In these studies we have shown how robust is this model, evaluating it in two complex situations, the coordination of two joints for postural balance and the coordination of two different balancing tasks. It is an intriguing issue, to be addressed in future studies, to consider how learning affects intermittency and how this can be exploited to enhance learning or recovery. The approach, that can exploit the results of this thesis, is the computational neurorehabilitation, which mathematically models the mechanisms underlying the rehabilitation process, with the aim of optimizing the individual treatment of patients. Integrating models of sensorimotor control during robotic neurorehabilitation, might lead to robots that are fully adaptable to the level of impairment of the patient and able to change their behavior accordingly to the patient\u2019s intention. This is one of the goals for the development of rehabilitation robotics and in particular of Wristbot, our robot for wrist rehabilitation: combining proper assessment and training protocols, based on motor control paradigms, will maximize robotic rehabilitation effects

Dynamic Determinants of the Uncontrolled Manifold during Human Quiet Stance

Human postural sway during stance arises from coordinated multi-joint movements. Thus, a sway trajectory represented by a time-varying postural vector in the multiple-joint-angle-space tends to be constrained to a low-dimensional subspace. It has been proposed that the subspace corresponds to a manifold defined by a kinematic constraint, such that the position of the center of mass (CoM) of the whole body is constant in time, referred to as the kinematic uncontrolled manifold (kinematic-UCM). A control strategy related to this hypothesis (CoM-control-strategy) claims that the central nervous system (CNS) aims to keep the posture close to the kinematic-UCM using a continuous feedback controller, leading to sway patterns that mostly occur within the kinematic-UCM, where no corrective control is exerted. An alternative strategy proposed by the authors (intermittent control-strategy) claims that the CNS stabilizes posture by intermittently suspending the active feedback controller, in such a way to allow the CNS to exploit a stable manifold of the saddle-type upright equilibrium in the state-space of the system, referred to as the dynamic-UCM, when the state point is on or near the manifold. Although the mathematical definitions of the kinematic- and dynamic-UCM are completely different, both UCMs play similar roles in the stabilization of multi-joint upright posture. The purpose of this study was to compare the dynamic performance of the two control strategies. In particular, we considered a double-inverted-pendulum-model of postural control, and analyzed the two UCMs defined above. We first showed that the geometric configurations of the two UCMs are almost identical. We then investigated whether the UCM-component of experimental sway could be considered as passive dynamics with no active control, and showed that such UCM-component mainly consists of high frequency oscillations above 1 Hz, corresponding to anti-phase coordination between the ankle and hip. We also showed that this result can be better characterized by an eigenfrequency associated with the dynamic-UCM. In summary, our analysis highlights the close relationship between the two control strategies, namely their ability to simultaneously establish small CoM variations and postural stability, but also make it clear that the intermittent control hypothesis better explains the spectral characteristics of sway