<p> A key mechanism to maintain balance during walking is the foot placement strategy,  where the person steps in the direction of an impending fall. On a clear walkway, the foot  placement strategy translates to maintaining a consistent relationship between the center of mass  state and the base of support (a body-centric constraint on foot placement), which is reflected in  a consistent step length. However, to safely navigate in the community, foot placement must  maintain certain spatial relations with environmental features as well (environmental constraints on foot placement). For stepping over obstacles, the environmental constraint takes the form of  targeting. That is, the feet must be placed at precise locations relative to the obstacle to minimize  the likelihood of tripping.  My dissertation focused on proactive adaptations to foot placements while navigating  cluttered environments. I developed the interstep covariation (ISC) index that quantifies the covariation between consecutive foot placements relative to stationary, visible environmental  features (an obstacle and a visual target). The across-step (or group) changes in this index  indicate how the two constraints (body-centric and environmental) on foot placement are  managed during adaptive gait tasks. I quantified how the ISC index changed (1) across steps  while approaching and crossing an obstacle, (2) due to healthy aging and (3) when the proximity  of two environmental features was systematically altered. Specifically, in Study 1, the ISC index  was quantified for the obstacle crossing step for healthy younger and older adults. In Study 2, proactive changes in the ISC index as healthy young adults approached and crossed an obstacle were characterized. In Study 3, the changes in the dynamics of the across-step ISC index due to  an additional visual stepping target in the approach to the obstacle were identified.  I found that there exists a covariance strategy that healthy adults use to navigate the  environment safely and successfully. First, I found that individuals prioritize the environmental  constraint at the expense of the body-centric constraint when the environment poses a larger risk  to balance (the obstacle), or to satisfy a specified constraint (stepping on a visual target). Second,  I found that the shift in prioritization is proactive, i.e., it occurs while approaching an obstacle.  The strategy to shift priorities is influenced by age (Study 1), environmental features (Study 2  and Study 3), and the proximity of two environmental features (Study 3). These studies add to  the current understanding of foot placement control by demonstrating how this well-known and 15 fundamental strategy to maintain balance while walking is systematically influenced by the  environment and task constraints. These findings can be further extended to study proactive and  reactive adaptations during walking in different populations.   </p>

Foot placement prediction can be important for exoskeleton and prosthesis controllers, human-robot interaction, or body-worn systems to prevent slips or trips. Previous studies investigating foot placement prediction have been limited to predicting foot placement during the swing phase, and do not fully consider contextual information such as the preceding step or the stance phase before push-off. In this study, a deep learning-based foot placement prediction approach was proposed, where the deep learning models were designed to sequentially process data from three IMU sensors mounted on pelvis and feet. The raw sensor data are pre-processed to generate multi-variable time-series data for training two deep learning models, where the first model estimates the gait progression and the second model subsequently predicts the next foot placement. The ground truth gait phase data and foot placement data are acquired from a motion capture system. Ten healthy subjects were invited to walk naturally at different speeds on a treadmill. In cross-subject learning, the trained models had a mean distance error of 5.93 cm for foot placement prediction. In single-subject learning, the prediction accuracy improved with additional training data, and a mean distance error of 2.60 cm was achieved by fine-tuning the cross-subject validated models with the target subject data. Even from 25-81% in the gait cycle, mean distance errors were only 6.99 cm and 3.22 cm for cross-subject learning and single-subject learning, respectively / Master of Science / This study proposes a new approach for predicting where a person's foot will land during walking, which could be useful in controlling robots and wearable devices that work with humans to prevent events such as slips and falls and allow for more smooth human-robot interactions. Although foot placement prediction has great potential in various domains, current works in this area are limited in terms of practicality and accuracy. The proposed approach uses data from inertial sensors attached to the pelvis and feet, and two deep learning models are trained to estimate the person's walking pattern and predict their next foot placement. The approach was tested on ten healthy individuals walking at different speeds on a treadmill, and achieved state-of-the-arts results. The results suggest that this approach could be a promising method when sufficient data from multiple people are available.

Undesirable landing area (e. g. , a hole, a fragment of glass, a water puddle, etc) creates the necessity for an alternate foot placement planning and execution. Previous study has proposed that three determinants are used by the central nervous system (CNS) for planning an alternate foot placement: minimum foot displacement, stability and maintenance of forward progression. However, validation of these determinants is lacking. Therefore, the general purpose of the series of studies presented here is to validate and test the generality of the decision algorithm of alternate foot placement selection developed previously. The first study was designed to validate the use of a virtual planar obstacle paradigm and the economy assumption behind minimum foot displacement determinant. Participants performed two blocks of trials. In one block, they were instructed to avoid stepping in a virtual planar obstacle projected in the screen of a LCD monitor embedded in the ground. In another block, they were instructed to avoid stepping in a real hole present in walkway. Behavioral response was unaffected by the presence of a real hole. In addition, it was suggested that minimum foot displacement results in minimum changes in EMG activity which validates the economy determinant. The second study was proposed to validate the stability determinant. Participants performed an avoidance task under two conditions: free and forced. In the free condition participants freely chose where to land in order to avoid stepping in a virtual obstacle. In the forced condition, a green arrow was projected over the obstacle indicating the direction of the alternate foot placement. The data from the free condition was used to determine the preferred alternate foot placement whereas the data from the forced condition was used to assess whole body stability. It was found that long and lateral foot placements are preferred because they result in a more stable behavior. The third study was designed to validate the alternate foot placement model in a more complex terrain. Participants were required to avoid stepping in two virtual planar obstacles placed in sequence. It was found that participants used the strategy of planning the avoidance movement globally and additional determinants were used. One of the additional determinants was implementation feasibility. In the third study, gaze behavior was also monitored and two behaviors emerged from this data. One sub-group of participants fixated on the area stepped during adaptive step, whereas another sub-group anchor their gaze in a spot ahead of the area-to-be avoided and used peripheral vision for controlling foot landing. In summary, this thesis validates the three determinants for the alternate foot placement planning model and extends the previous model to more complex terrains.

Undesirable landing area (e. g. , a hole, a fragment of glass, a water puddle, etc) creates the necessity for an alternate foot placement planning and execution. Previous study has proposed that three determinants are used by the central nervous system (CNS) for planning an alternate foot placement: minimum foot displacement, stability and maintenance of forward progression. However, validation of these determinants is lacking. Therefore, the general purpose of the series of studies presented here is to validate and test the generality of the decision algorithm of alternate foot placement selection developed previously. The first study was designed to validate the use of a virtual planar obstacle paradigm and the economy assumption behind minimum foot displacement determinant. Participants performed two blocks of trials. In one block, they were instructed to avoid stepping in a virtual planar obstacle projected in the screen of a LCD monitor embedded in the ground. In another block, they were instructed to avoid stepping in a real hole present in walkway. Behavioral response was unaffected by the presence of a real hole. In addition, it was suggested that minimum foot displacement results in minimum changes in EMG activity which validates the economy determinant. The second study was proposed to validate the stability determinant. Participants performed an avoidance task under two conditions: free and forced. In the free condition participants freely chose where to land in order to avoid stepping in a virtual obstacle. In the forced condition, a green arrow was projected over the obstacle indicating the direction of the alternate foot placement. The data from the free condition was used to determine the preferred alternate foot placement whereas the data from the forced condition was used to assess whole body stability. It was found that long and lateral foot placements are preferred because they result in a more stable behavior. The third study was designed to validate the alternate foot placement model in a more complex terrain. Participants were required to avoid stepping in two virtual planar obstacles placed in sequence. It was found that participants used the strategy of planning the avoidance movement globally and additional determinants were used. One of the additional determinants was implementation feasibility. In the third study, gaze behavior was also monitored and two behaviors emerged from this data. One sub-group of participants fixated on the area stepped during adaptive step, whereas another sub-group anchor their gaze in a spot ahead of the area-to-be avoided and used peripheral vision for controlling foot landing. In summary, this thesis validates the three determinants for the alternate foot placement planning model and extends the previous model to more complex terrains.

A predictive, forward-dynamic model and computer simulation of human gait has important medical and research applications. Most human simulation work has focused on inverse dynamics studies to quantify bone on bone forces and muscle loads. Inverse dynamics is not predictive - it works backwards from experimentally measured motions in an effort to find the forces that caused the motion. In contrast, forward dynamics determines how a mechanism will move without the need for experimentation. Most of the forward dynamic gait simulations reported consider only one step, foot contact is not modeled, and balance controllers are not used. This thesis addresses a few of the shortcomings of current human gait simulations by contributing an experimentally validated foot contact model, a model-based stance controller, and an experimentally validated model of the relationship between foot placement location and balance. The goal of a predictive human gait simulation is to determine how a human would walk under a condition of interest, such as walking across a slippery floor, using a new lower limb prosthesis, or with reduced leg strength. To achieve this goal, often many different gaits are simulated and the one that is the most human-like is chosen as the prediction for how a person would move. Thus it is necessary to quantify how `human-like' a candidate gait is. Human walking is very efficient, and so, the metabolic efficiency of the candidate gait is most often used to measure the performance of a candidate gait. Muscles consume metabolic energy as a function of the tension they develop and the rate at which they are contracting. Muscle tension is developed, and contractions are made in an effort generate torques about joints in order to make them move. To predict human gait, it is necessary for the simulation to be able to walk in such a way that the simulated leg joints use similar joint torques and kinematics as a human leg does, all while balancing the body. The joint torques that the legs must develop to propel the body forward, and balance it, are heavily influenced by the ground reaction forces developed between the simulated foot and the ground. A predictive gait simulation must be able to control the model so that it can walk, and remain balanced while generating ground reaction force profiles that are similar to experimentally observed human ground reaction force profiles. Ground reaction forces are shaped by the way the foot interacts with the ground, making it very important to model the human foot accurately. Most continuous foot contact models present in the literature have been experimentally validated using pendulum impact methods that have since been shown to produce inaccurate results. The planar foot contact model developed as part of this research was validated in-vivo using conventional force plates and optical tracking markers. The experimental data was also highly useful for developing a computationally efficient foot model by identifying the dominant contact properties of a real foot (during walking), without the complexity of modelling the 26 bones, 33 joints, over 90 ligaments, and the network of muscles that are in a real foot. Both ground reaction forces and the balance of the model are heavily influenced by the way the stance limb is controlled. Anthropomorphic multibody models typically have a fragile sense of balance, and ground reaction force profiles that do not look similar to experimentally measured human ground reaction force profiles. In contrast, the simple point-mass spring-loaded-inverted-pendulum (SLIP) can be made to walk or run in a balanced manner with center-of-mass (COM) kinematics and ground reaction force profiles that could be mistaken for the equivalent human data. A stance limb controller is proposed that uses a planar SLIP to compute a reference trajectory for a planar anthropomorphic multibody gait model. The torso of the anthropomorphic model is made to track the computed trajectory of the SLIP using a control system. The aim of this partitioned approach to gait simulation is to endow the anthropomorphic model with the human-like gait of the simpler SLIP model. Although the SLIP model-based stance-controller allows an anthropomorphic gait model to walk in more human-like manner, it also inherits the short comings of the SLIP model. The SLIP can walk or run like a human, but only at a fixed velocity. It cannot initiate or terminate gait. Fall preventing movements, such as gait termination and compensatory stepping, are of particular relevance to kinesiologists and health care professionals. Kinesiologists have known for nearly a decade that humans restore their balance primarily by systematically altering their foot placement location. This thesis presents a human experimental validation of a planar foot placement algorithm that was originally designed to restore the balance of bipedal robots. A three-dimensional (3D) theoretical extension to the planar foot placement algorithm is also presented along with preliminary human experimental results. These models of foot placement can be used in the future to improve the capabilities of gait simulations by giving simple models human-like compensatory stepping abilities. The theoretical extension also provides some insight into how instability and balance performance can be quantified. The instability and balance performance measures have important applications for diagnosing and rehabilitating balance problems. Despite all of the progress that has been made, there is still much work to be done. Work needs to be continued to find methods that allow the anthropomorphic model to emulate the SLIP model more faithfully. Experimental work needs to be completed to realize the potential diagnostic and rehabilitation applications of the foot placement models. With continued effort, a predictive, balanced, multi-step gait simulation can be developed that will give researchers the time-saving capability of computerized hypothesis testing, and medical professionals improved diagnostic and rehabilitation methods.

A predictive, forward-dynamic model and computer simulation of human gait has important medical and research applications. Most human simulation work has focused on inverse dynamics studies to quantify bone on bone forces and muscle loads. Inverse dynamics is not predictive - it works backwards from experimentally measured motions in an effort to find the forces that caused the motion. In contrast, forward dynamics determines how a mechanism will move without the need for experimentation. Most of the forward dynamic gait simulations reported consider only one step, foot contact is not modeled, and balance controllers are not used. This thesis addresses a few of the shortcomings of current human gait simulations by contributing an experimentally validated foot contact model, a model-based stance controller, and an experimentally validated model of the relationship between foot placement location and balance. The goal of a predictive human gait simulation is to determine how a human would walk under a condition of interest, such as walking across a slippery floor, using a new lower limb prosthesis, or with reduced leg strength. To achieve this goal, often many different gaits are simulated and the one that is the most human-like is chosen as the prediction for how a person would move. Thus it is necessary to quantify how `human-like' a candidate gait is. Human walking is very efficient, and so, the metabolic efficiency of the candidate gait is most often used to measure the performance of a candidate gait. Muscles consume metabolic energy as a function of the tension they develop and the rate at which they are contracting. Muscle tension is developed, and contractions are made in an effort generate torques about joints in order to make them move. To predict human gait, it is necessary for the simulation to be able to walk in such a way that the simulated leg joints use similar joint torques and kinematics as a human leg does, all while balancing the body. The joint torques that the legs must develop to propel the body forward, and balance it, are heavily influenced by the ground reaction forces developed between the simulated foot and the ground. A predictive gait simulation must be able to control the model so that it can walk, and remain balanced while generating ground reaction force profiles that are similar to experimentally observed human ground reaction force profiles. Ground reaction forces are shaped by the way the foot interacts with the ground, making it very important to model the human foot accurately. Most continuous foot contact models present in the literature have been experimentally validated using pendulum impact methods that have since been shown to produce inaccurate results. The planar foot contact model developed as part of this research was validated in-vivo using conventional force plates and optical tracking markers. The experimental data was also highly useful for developing a computationally efficient foot model by identifying the dominant contact properties of a real foot (during walking), without the complexity of modelling the 26 bones, 33 joints, over 90 ligaments, and the network of muscles that are in a real foot. Both ground reaction forces and the balance of the model are heavily influenced by the way the stance limb is controlled. Anthropomorphic multibody models typically have a fragile sense of balance, and ground reaction force profiles that do not look similar to experimentally measured human ground reaction force profiles. In contrast, the simple point-mass spring-loaded-inverted-pendulum (SLIP) can be made to walk or run in a balanced manner with center-of-mass (COM) kinematics and ground reaction force profiles that could be mistaken for the equivalent human data. A stance limb controller is proposed that uses a planar SLIP to compute a reference trajectory for a planar anthropomorphic multibody gait model. The torso of the anthropomorphic model is made to track the computed trajectory of the SLIP using a control system. The aim of this partitioned approach to gait simulation is to endow the anthropomorphic model with the human-like gait of the simpler SLIP model. Although the SLIP model-based stance-controller allows an anthropomorphic gait model to walk in more human-like manner, it also inherits the short comings of the SLIP model. The SLIP can walk or run like a human, but only at a fixed velocity. It cannot initiate or terminate gait. Fall preventing movements, such as gait termination and compensatory stepping, are of particular relevance to kinesiologists and health care professionals. Kinesiologists have known for nearly a decade that humans restore their balance primarily by systematically altering their foot placement location. This thesis presents a human experimental validation of a planar foot placement algorithm that was originally designed to restore the balance of bipedal robots. A three-dimensional (3D) theoretical extension to the planar foot placement algorithm is also presented along with preliminary human experimental results. These models of foot placement can be used in the future to improve the capabilities of gait simulations by giving simple models human-like compensatory stepping abilities. The theoretical extension also provides some insight into how instability and balance performance can be quantified. The instability and balance performance measures have important applications for diagnosing and rehabilitating balance problems. Despite all of the progress that has been made, there is still much work to be done. Work needs to be continued to find methods that allow the anthropomorphic model to emulate the SLIP model more faithfully. Experimental work needs to be completed to realize the potential diagnostic and rehabilitation applications of the foot placement models. With continued effort, a predictive, balanced, multi-step gait simulation can be developed that will give researchers the time-saving capability of computerized hypothesis testing, and medical professionals improved diagnostic and rehabilitation methods.

This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance.

This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance.

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