Inverse optimal control with time-varying objectives: application to human jumping movement analysis.

Analysis of complex human movements can provide valuable insights for movement rehabilitation, sports training, humanoid robot design and control, and human-robot interaction. To accomplish complex movement, the central nervous system must coordinate the musculo-skeletal system to achieve task and internal (e.g., effort minimisation) objectives. This paper proposes an inverse optimal control approach for analysing complex human movement that does not assume that the control objective(s) remains constant throughout the movement. The movement trajectory is assumed to be optimal with respect to a cost function composed of the sum of weighted basis cost functions, which may be time varying. The weights of the cost function are recovered using a sliding window. To illustrate the proposed approach, a dataset consisting of standing broad jump to targets at three different distances is collected. The method can be used to extract control objectives that influence task success, identify different motion strategies/styles, as well as to observe how control strategy changes during the motor learning process. Kinematic analysis confirms that the identified control objectives, including centre-of-mass takeoff vector and foot placement upon landing are important to ensure that a given participant lands on the target. The dataset, including nearly 800 jump trajectories from 22 participants is also provided.

Estimation and Observability Analysis of Human Motion on Lie Groups.

This article proposes a framework for human-pose estimation from the wearable sensors that rely on a Lie group representation to model the geometry of the human movement. 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 develop the equations for employing the extended Kalman filter on Lie groups (LG-EKF) to explicitly account for the non-Euclidean geometry of the state space. We present the observability analysis of an arbitrarily long kinematic chain of SO(3) elements based on a differential geometric approach, representing a generalization of kinematic chains of a human body. The observability is investigated for the system using marker position measurements. The proposed algorithm is compared with two competing approaches: 1) the extended Kalman filter (EKF) and 2) unscented KF (UKF) based on the Euler angle parametrization, in both simulations and extensive real-world experiments. The results show that the proposed approach achieves significant improvements over the Euler angle-based filters. It provides more accurate pose estimates, is not sensitive to gimbal lock, and more consistently estimates the covariances.