Inverse optimal control to model human trajectories during locomotion

Abstract

Cobotic applications require a good knowledge of human behaviour in order to be cleverly, securely and fluidly performed. For example, to make a human and a humanoid robot perform a co-navigation or a co-manipulation task, a model of human walking trajectories is essential to make the robot follow or even anticipate the human movements. This paper aims to study the Center of Mass (CoM) path during locomotion and generate human-like trajectories with an optimal control scheme. It also proposes a metric which allows to assess this model compared to the human behaviour. CoM trajectories during locomotion of 10 healthy subjects were recorded and analysed as part of this study. Inverse optimal control was used to find the optimal cost function which best fits the model to the measurements. Then, the measurements and the generated data were compared in order to assess the performance of the presented model. Even if the experiments show a great variability in human behaviours, the model presented in this study gives an accurate approximation of the average human walking trajectories. Furthermore, this model gives an approximation of human locomotion good enough to improve cobotic tasks allowing a humanoid robot to anticipate the human behaviour.

Walking paths during collaborative carriages do not follow the simple rules observed in the locomotion of single walking subjects

“…For such analysis, we chose to compare the average trajectories with the variety of the measured trajectories. Indeed, we made the assumption that, if the average trajectories are representative of all the performed trajectories, it can be stated that all the pairs have a non-distinguishable behaviour and that a shared optimal strategy globally emerged spontaneously as already observed for individuals 22 . Thus, this data analysis tackled four main topics and aimed to answer the following questions: Differences between scenarios: Is there a scenario where the pair moves the table faster than in the others?…”

“…This metrics needed to assess if the geometric trajectories were close from one another and if the orientations of the subjects were alike. This is why, using the metrics introduced in Maroger et al 22 was suitable. Given 2 trajectories and , the following linear and angular distances , respectively and , were computed as follows: With those definitions, the smaller the distances are, the closer the compared trajectories are.…”

“…Human-like CoM trajectories can be generated using a non-holonomic system when a human is walking a straight line 18 . However, when he has to take sideways steps, a holonomic model is needed to better fit the human behaviour as it allows more degrees of freedom in the locomotion 13 , 21 , 22 . In Maroger et al 22 , a holonomic model based on an Optimal Control (IOC) problem was designed to generate human-like trajectories between a given starting and goal positions.…”

“…However, when he has to take sideways steps, a holonomic model is needed to better fit the human behaviour as it allows more degrees of freedom in the locomotion 13 , 21 , 22 . In Maroger et al 22 , a holonomic model based on an Optimal Control (IOC) problem was designed to generate human-like trajectories between a given starting and goal positions. It was optimized using a bi-level Inverse Optimal Control (IOC) scheme, first introduced in Mombaur et al 21 , to well fit average human CoM trajectories during locomotion.…”

“…Finally, an OC based model was built to simultaneously generate the CoM trajectories of both subjects during table handling tasks. This model was designed using the same method as the human locomotion model described in Maroger et al 22 . Thus, the model, introduced in this paper, was optimized to fit the average measured trajectories.…”