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.