UC San Diego

This work presents a new trajectory planning formulation that aims to maximize the probability of finding a target inside a bound domain using a robot over a specified time interval. A preliminary algorithm is developed to detect stationary targets, which is further extended to detect moving targets. Values are assigned at every grid point in the domain based on its distance from the robot; each value represents the probability of not finding the target if it is at that location. A cost function is formulated that computes the likelihood of not finding the target for any given path provided the target is inside the domain.

This cost function is minimized with a set of bound constraints on inputs to obtain an optimal path to find the target. The algorithm incorporates an adjoint-based gradient method to link the input parameters to the cost function. The cost function is nonlinear which makes it hard for most commercial off-the-shelf (COTS) optimization packages to solve it.

For faster convergence the recently developed low storage reduced Hessian box constraint optimization method (LRH-B) was used.

Results show our algorithm outperforms other optimization algorithms, and also explain how this framework is beneficial in terms of application.