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Finding Nash equilibrial policies for two-player differential games requires solving Hamilton-Jacobi-Isaacs (HJI) PDEs. Self-supervised learning has been used to approximate solutions of such PDEs while circumventing the curse of dimensionality. However, this method fails to learn discontinuous PDE solutions due to its sampling nature, leading to poor safety performance of the resulting controllers in robotics applications when player rewards are discontinuous. This paper investigates two potential solutions to this problem: a hybrid method that leverages both supervised Nash equilibria and the HJI PDE, and a value-hardening method where a sequence of HJIs are solved with a gradually hardening reward. We compare these solutions using the resulting generalization and safety performance in two vehicle interaction simulation studies with 5D and 9D state spaces, respectively. Results show that with informative supervision (e.g., collision and near-collision demonstrations) and the low cost of self-supervised learning, the hybrid method achieves better safety performance than the supervised, self-supervised, and value hardening approaches on equal computational budget. Value hardening fails to generalize in the higher-dimensional case without informative supervision. Lastly, we show that the neural activation function needs to be continuously differentiable for learning PDEs and its choice can be case dependent. 

Abstract Sensing for wearable robots is an ongoing challenge, especially given the recent trend of soft and compliant robots. Recently, a wearable origami exoshell has been designed to sense the user’s torso motion and provide mobility assistance. The materials of the exoshell contribute to a lightweight design with compliant joints, which are ideal characteristics for a wearable device. Common sensors are not ideal for the exoshell as they compromise these design characteristics. Rotary encoders are often rigid metal devices that add considerable weight and compromise the flexibility of the joints. Inertial measurement unit sensors are affected by environments with variable electromagnetic fields and therefore not ideal for wearable applications. Hall effect sensors and gyroscopes are utilized as alternative compatible sensors, which introduce their own set of challenges: noisy measurements and drift due to sensor bias. To mitigate this, we designed the Kinematically Constrained Kalman filter for sensor fusion of gyroscopes and Hall effect sensors, with the goal of estimating the human’s torso and robot joint angles. We augmented the states to consider bias related to the torso angle in order to compensate for drift. The forward kinematics of the robot is incorporated into the Kalman filter as state constraints to address the unobservability of the torso angle and its related bias. The proposed algorithm improved the estimation performance of the torso angle and its bias, compared to the individual sensors and the standard Kalman filter, as demonstrated through bench tests and experiments with a human user. 

Soft robots have shown great potential to enable safe interactions with unknown environments due to their inherent compliance and variable stiffness. However, without knowledge of potential contacts, a soft robot could exhibit rigid behaviors in a goal-reaching task and collide into obstacles. In this paper, we introduce a Sliding Mode Augmented by Reactive Transitioning (SMART) controller to detect the contact events, adjust the robot’s desired trajectory, and reject estimated disturbances in a goal reaching task. We employ a sliding mode controller to track the desired trajectory with a nonlinear disturbance observer (NDOB) to estimate the lumped disturbance, and a switching algorithm to adjust the desired robot trajectories. The proposed controller is validated on a pneumatic-driven fabric soft robot whose dynamics is described by a new extended rigid-arm model to fit the actuator design. A stability analysis of the proposed controller is also presented. Experimental results show that, despite modeling uncertainties, the robot can detect obstacles, adjust the reference trajectories to maintain compliance, and recover to track the original desired path once the obstacle is removed. Without force sensors, the proposed model-based controller can adjust the robot’s stiffness based on the estimated disturbance to achieve goal reaching and compliant interaction with unknown obstacles. 

As humans and robots start to collaborate in close proximity, robots are tasked to perceive, comprehend, and anticipate human partners' actions, which demands a predictive model to describe how humans collaborate with each other in joint actions. Previous studies either simplify the collaborative task as an optimal control problem between two agents or do not consider the learning process of humans during repeated interaction. This idyllic representation is thus not able to model human rationality and the learning process. In this paper, a bounded-rational and game-theoretical human cooperative model is developed to describe the cooperative behaviors of the human dyad. An experiment of a joint object pushing collaborative task was conducted with 30 human subjects using haptic interfaces in a virtual environment. The proposed model uses inverse optimal control (IOC) to model the reward parameters in the collaborative task. The collected data verified the accuracy of the predicted human trajectory generated from the bounded rational model excels the one with a fully rational model. We further provide insight from the conducted experiments about the effects of leadership on the performance of human collaboration. 

This work aims to investigate the effects of knee extension assistance during squat lifting. We hypothesize that adding an external torque to the knee joint using a soft inflatable exosuit can potentially induce a reduction in the muscular effort that extends to the posterior chain muscles. A total of 8 healthy test participants are recruited and instructed to lift a weight equivalent to 10% of their bodyweight. The muscle activities of the left and right Vastus Lateralis, Biceps Femoris, Gluteus Maximus, Erector Spinae (Iliocostalis and Longissimus) and Multifidus muscle groups were studied for baseline, non-assisted, and assisted conditions. The majority of participants (6 out of 8) demonstrated consistent reduction in the muscular effort of at least one muscle group of the posterior chain. A maximum reduction of 55% in the average muscle activity of the Multifidus muscle group is observed in one participant. Different neuromuscular adaptation mechanisms were observed among subjects that ultimately led to a reduction in lower-limb or back muscles activity. The results reveal that assisting knee extension during a lifting task has significant effects on muscle activity with benefits that extend to the posterior chain muscles. This work provides early evidence that the soft inflatable knee exosuit can be used in material handling tasks to reduce muscle effort and prevent work-related injuries. 

Wearable robotics has shown to be effective for assisting in activities of daily living and restoring motor functions. The objective of this research is to develop a soft robotic exosuit for knee flexion assistance during normal walking and validate its ability to reduce the efforts of the knee flexor muscles: biceps femoris (BF) and semitendinosus (SM). The exosuit is powered by an inflatable curved fabric actuator with the capability to generate flexion torques at the knee joint. An analytical model to characterize the torque of the proposed actuator is derived and validated experimentally. It is found that the analytical torque model precisely matches the experimental results such that the highest root mean square error (RMSE) obtained is 1.237 Nm while the lowest is 0.188 Nm. In addition, the derived model outperformed a benchmark torque model such that its minimum and maximum RMSEs are approximately 90% and 70% less than the benchmark model respectively. A prototype of the knee exosuit is fabricated and tested on one healthy subject with different operating conditions to assist knee flexion during normal walking. The results show that by choosing the appropriate timing of inflation, the exosuit can reduce the electromyography activity of the BF and the SM by 32% and 23%, respectively, without impeding the knee extensor muscle or reducing the knee's range of motion.