Kashish Dhal

Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Mechanical Engineering


Mechanical and Aerospace Engineering

First Advisor

Kamesh Subbarao

Second Advisor

Animesh Chakravarthy


This dissertation presents a collision cone/rendezvous cone-based approach for reactive motion planning in three-dimensional dynamic environments. Collision avoidance is fundamental to robot motion planning. In dynamic environments, the path and velocities of obstacles are not known a-priori, and hence it is a common practice to use reactive planners. Reactive planners should be computationally inexpensive because they need to act fast to avoid potential collisions. To reduce the computational load, a majority of motion planning algorithms model the shapes of the robots and obstacles as a circle/sphere. However, when the objects are elongated more in one direction than another, the spherical shape approximation becomes over conservative. When multiple robots are operating in close proximity in an environment cluttered with obstacles, this reduces the available free space in which the robot trajectory can lie. In such cases, one can use ellipsoidal shape approximations. However, for non-convex objects, even ellipsoidal approximations become over-conservative and in such cases, a combination of non-convex quadric surfaces or a n-faced polyhedron provides better shape approximation. In conjunction with providing tighter shape approximations, the computational load has to be kept low. Collision cone approach is a motion planning method which computes the set of robot velocity headings that guarantees collision avoidance with another moving vehicle. This dissertation develops methods to compute the collision cone analytically for a large class of object shapes. Analytical expressions of guidance laws are derived to perform collision avoidance or rendezvous in three-dimensional environments for a range of applications. Guidance and control laws are developed for a robotic fish to perform maneuvers through a moving orifice and for a UAS to track single/multiple moving ground targets. Cooperative and non-cooperative collision avoidance and rendezvous laws are demonstrated for objects with heterogeneous shapes that may change with time, in three-dimensional dynamic environments. These laws are subsequently made robust to sensor measurement noise by incorporating them in an LMI framework.


Collision avoidance, Motion planning, Path planning, Autonomous vehicles


Aerospace Engineering | Engineering | Mechanical Engineering


Degree granted by The University of Texas at Arlington