### Constrained Motion Planning

A Curvature-Velocity-Orientation (CVO) method was developed to incorporate aircraft dynamic constraints into the 3D motion-planning problem.  The CVO space is defined with orthogonal dimensions of translational velocity, rotational velocity, and orientation.  It is assumed that the aircraft always travels along arcs of circles during its operation.  Specifically, at each step, a circular arc tangent to the current vehicle velocity vector is defined for connecting the vehicle to the goal point or each corner point of obstacles.  The curvature of the arc, the distance to travel along the arc, and the orientation of the arc with respect to the vehicle vertical (x-z) plane are then calculated and used in mapping the goal and all obstacles from a Cartesian space into a CVO space.  A set of vehicle dynamic constraints is then applied within the CVO space.  Most of these constraints, including minimum turning radius, ranges of angular velocity, linear velocity, and acceleration, can be naturally represented as a set of inequalities (boundaries) at each time step. An optimization method is then applied within the constrained CVO space to determine a feasible navigation solution. As a major advantage of the CVO method, this solution, in the form of desired velocity, curvature, and orientation, can directly serve as the reference input to the flight control system. Therefore, the motion planning and the guidance problems are tightly integrated to reduce the information loss and the overall computational load.  Additionally, the introduction of the dynamic constraints directly into the spatial representation simplifies the optimization process, and ensures that each planned command is feasible for the aircraft to follow.

#### Recent Publication

Gu, Y., Sagoo, G. K., Seanor, B., Campa, G., Fravolini, M. L., and Napolitano, M. R., “Curvature-Velocity-Orientation Method for UAV Collision Avoidance,” 2008 AIAA Guidance, Navigation, and Control Conference, AIAA 2008-6628, Honolulu, Hawaii, August 2008.