Humans are capable of complex manipulation and locomotion tasks. They are able to achieve energy-efficient gait, reject disturbances, handle changing loads, and adapt to environmental constraints. Using inspiration from the human body, robotics researchers aim to develop systems with similar capabilities. Research suggests that humans minimize a task specific cost function when performing movements. In order to learn this cost function from demonstrations and incorporate it into a controller, it is first imperative to accurately estimate the expert motion. The captured motions can then be analyzed to extract the objective function the expert was minimizing.

We propose a framework for human motion estimation from wearable sensors. Human body joints are modeled by matrix Lie groups, using special orthogonal groups SO(2) and SO(3) for joint pose and special Euclidean group SE(3) for base link pose representation. To estimate the human joint pose, velocity and acceleration, we provide the equations for employing the extended Kalman Filter on Lie Groups, thus explicitly accounting for the non-Euclidean geometry of the state space. Incorporating interaction constraints with respect to the environment or within the participant allows us to track global body position without an absolute reference and ensure viable pose estimate. The algorithms are extensively validated in both simulation and real-world experiments.

Next, to learn underlying expert control strategies from the expert demonstrations we present a novel fast approximate multi-variate Gaussian Process regression. The method estimates the underlying cost function, without making assumptions on its structure. The computational efficiency of the approach allows for real time forward horizon prediction. Using a linear model predictive control framework we then reproduce the demonstrated movements on a robot. The learned cost function captures the variability in expert motion as well as the correlations between states, leading to a controller that both produces motions and reacts to disturbances in a human-like manner. The model predictive control formulation allows the controller to satisfy task and joint space constraints avoiding obstacles and self collisions, as well as torque constraints, ensuring operational feasibility. The approach is validated on the Franka Emika robot using real human motion exemplars.