## 131. trajectory planning for maximizing the probability of finding an object inside a bound domain

__Department__: Mechanical & Aerospace Engineering

__Faculty Advisor(s)__:
Thomas R. Bewley

**Primary Student**

__Name__: Abhishek Subramanian

__Email__: absubram@ucsd.edu

__Phone__: 858-291-2282

__Grad Year__: 2017

**Student Collaborators**

Shahrouz Alimohammadi, salimoha@eng.ucsd.edu

**Abstract**

This work presents a trajectory planning formulation that specifically targets maximizing the probability of finding an object inside a bound domain using a robot. The goal is to locate the lost object within a stipulated time.
A probability distribution is defined over the domain that represents the chance of not finding the object. The value of probability at each point is assigned based on its distance from the robot. A cost function is formulated that computes the likelihood of not finding the object. This cost function is minimized with a set of constraints to obtain an optimal path to find the lost object. Bound constraints are imposed on the input control variables, i.e. the velocity and the turn rate of the robot. The algorithm incorporates an adjoint-based gradient method to link the input parameters to the cost function. This cost function is nonlinear with multiple local solutions which make it hard for most commercial off-the-shelf (COTS) optimization packages to solve it. To converge to the best local solution, the sparse sequential quadratic programming (SQP) algorithm is employed with limited-memory quasi-Newton approximations to the Hessian of Lagrangian. For faster convergence this SQP method is coupled with the recently developed reduced Hessian box constraint optimization method (RH-B). The results presented embody the efficiency of our algorithm. Since the objective function is nonconvex, different optimal paths can be obtained. The present framework can be extended to develop optimal trajectories for various unmanned vehicle applications.

**Industry Application Area(s)**

Aerospace, Defense, Security | Control Systems