Stochastic Optimal Control for Modeling Reaching Movements in the Presence of Obstacles: Theory and Simulation
This work addresses the need for computational models to predict human motion in applications like robot-assisted surgery and teleoperation, though it is incremental as it builds on existing optimal control methods with specific adaptations for obstacle avoidance.
The authors tackled the problem of modeling human reaching movements around obstacles by developing a stochastic optimal control framework with probabilistic collision avoidance constraints, which they reformulated into a parametric quadratic programming problem to capture human variability and demonstrated through simulations the trade-offs between avoidance strategies, control cost, and collision probability.
In many human-in-the-loop robotic applications such as robot-assisted surgery and remote teleoperation, predicting the intended motion of the human operator may be useful for successful implementation of shared control, guidance virtual fixtures, and predictive control. Developing computational models of human movements is a critical foundation for such motion prediction frameworks. With this motivation, we present a computational framework for modeling reaching movements in the presence of obstacles. We propose a stochastic optimal control framework that consists of probabilistic collision avoidance constraints and a cost function that trades-off between effort and end-state variance in the presence of a signal-dependent noise. First, we present a series of reformulations to convert the original non-linear and non-convex optimal control into a parametric quadratic programming problem. We show that the parameters can be tuned to model various collision avoidance strategies, thereby capturing the quintessential variability associated with human motion. Then, we present a simulation study that demonstrates the complex interaction between avoidance strategies, control cost, and the probability of collision avoidance. The proposed framework can benefit a variety of applications that require teleoperation in cluttered spaces, including robot-assisted surgery. In addition, it can also be viewed as a new optimizer which produces smooth and probabilistically-safe trajectories under signal dependent noise.