Walking and mobility are essential aspects of our daily lives, enabling us to engage in various activities. Gait disorders and impaired mobility are widespread challenges faced by older adults and people with neurological injuries, as these conditions can significantly impact their quality of life, leading to a loss of independence and an increased risk of mortality. In response to these challenges, rehabilitation, and assistive robotics have emerged as promising alternatives to conventional gait therapy, offering potential solutions that are less labor-intensive and costly. Despite numerous advances in wearable lower-limb robotics, their current applicability remains confined to laboratory settings. To expand their utility to broader gait impairments and daily living conditions, there is a pressing need for more intelligent robot controllers. In this dissertation, these challenges are tackled from two perspectives: First, to improve the robot's understanding of human motion and intentions which is crucial for assistive robot control, a robust human locomotion estimation technique is presented, focusing on measuring trunk motion. Employing an invariant extended Kalman filtering method that takes sensor misplacement into account, improved convergence properties over the existing methods for different locomotion modes are shown. Secondly, to enhance safe and effective robot-aided gait training, this dissertation proposes to directly learn from physical therapists' demonstrations of manual gait assistance in post-stroke rehabilitation. Lower-limb kinematics of patients and assistive force applied by therapists to the patient's leg are measured using a wearable sensing system which includes a custom-made force sensing array. The collected data is then used to characterize a therapist's strategies. Preliminary analysis indicates that knee extension and weight-shifting play pivotal roles in shaping a therapist's assistance strategies, which are then incorporated into a virtual impedance model that effectively captures high-level therapist behaviors throughout a complete training session. Furthermore, to introduce safety constraints in the design of such controllers, a safety-critical learning framework is explored through theoretical analysis and simulations. A safety filter incorporating an online iterative learning component is introduced to bring robust safety guarantees for gait robotic assistance and training, addressing challenges such as stochasticity and the absence of a known prior dynamic model.

Lower-limb wearable assistive robots could alter the users gait kinematics by inputting external power, which can be interpreted as mechanical perturbation to subject normal gait. The change in kinematics may affect the dynamic stability. This work attempts to understand the effects of different physical assistance from these robots on the gait dynamic stability.

A knee exoskeleton and ankle assistive device (Robotic Shoe) are developed and used to provide walking assistance. The knee exoskeleton provides personalized knee joint assistive torque during the stance phase. The robotic shoe is a light-weighted mechanism that can store the potential energy at heel strike and release it by using an active locking mechanism at the terminal stance phase to provide push-up ankle torque and assist the toe-off. Lower-limb Kinematic time series data are collected for subjects wearing these devices in the passive and active mode. The changes of kinematics with and without these devices on lower-limb motion are first studied. Orbital stability, as one of the commonly used measure to quantify gait stability through calculating Floquet Multipliers (FM), is employed to asses the effects of these wearable devices on gait stability. It is shown that wearing the passive knee exoskeleton causes less orbitally stable gait for users, while the knee joint active assistance improves the orbital stability compared to passive mode. The robotic shoe only affects the targeted joint (right ankle) kinematics, and wearing the passive mechanism significantly increases the ankle joint FM values, which indicates less walking orbital stability. More analysis is done on a mechanically perturbed walking public data set, to show that orbital stability can quantify the effects of external mechanical perturbation on gait dynamic stability. This method can further be used as a control design tool to ensure gait stability for users of lower-limb assistive devices.