  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.
