Nonlinear constrained optimal trajectory control is an important and fundamental area of research that continues to advance in numerous fields. Many attempts have been made to present new methods that can solve for optimal trajectories more efficiently or to improve the overall performance of existing techniques. This research presents a recently developed bio-inspired method called the Virtual Motion Camouflage (VMC) method that offers a means of quickly finding, within a defined but varying search space, the optimal trajectory that is equal or close to the optimal solution. The research starts with the polynomial-based VMC method, which works within a search space that is defined by a selected and fixed polynomial type virtual prey motion. Next will be presented a means of improving the solution’s optimality by using a sequential based form of VMC, where the search space is adjusted by adjusting the polynomial prey trajectory after a solution is obtained. After the search space is adjusted, an optimization is performed in the new search space to find a solution closer to the global space optimal solution, and further adjustments are made as desired. Finally, a B-spline augmented VMC method is presented, in which a B-spline curve represents the prey motion and will allow the search space to be optimized together with the solution trajectory. It is shown that (1) the polynomial based VMC method will significantly reduce the overall problem dimension, which in practice will significantly reduce the computational cost associated with solving nonlinear constrained optimal trajectory problems; (2) the sequential VMC method will improve the solution optimality by sequentially refining certain parameters, such as the prey motion; and (3) the B-spline augmented VMC method will improve the solution iv optimality without sacrificing the CPU time much as compared with the polynomial based approach. Several simulation scenarios, including the Breakwell problem, the phantom track problem, the minimum-time mobile robot obstacle avoidance problem, and the Snell’s river problem are simulated to demonstrate the capabilities of the various forms of the VMC algorithm. The capabilities of the B-spline augmented VMC method are also shown in a hardware demonstration using a mobile robot obstacle avoidance testbed.

In the field of control systems, testbeds are a pivotal step in the validation and improvement of new algorithms for different applications. They provide a safe, controlled environment typically having a significantly lower cost of failure than the final application. Vision systems provide nonintrusive methods of measurement that can be easily implemented for various setups and applications. This work presents methods for modeling, removing distortion, calibrating, and rectifying single and two camera systems, as well as, two very different applications of vision-based control system testbeds: deflection control of shape memory polymers and trajectory planning for mobile robots. First, a testbed for the modeling and control of shape memory polymers (SMP) is designed. Red-green-blue (RGB) thresholding is used to assist in the webcam-based, 3D reconstruction of points of interest. A PID based controller is designed and shown to work with SMP samples, while state space models were identified from step input responses. Models were used to develop a linear quadratic regulator that is shown to work in simulation. Also, a simple to use graphical interface is designed for fast and simple testing of a series of samples. Second a robot testbed is designed to test new trajectory planning algorithms. A templatebased predictive search algorithm is investigated to process the images obtained through a lowcost webcam vision system, which is used to monitor the testbed environment. Also a userfriendly graphical interface is developed such that the functionalities of the webcam, robots, and optimizations are automated. The testbeds are used to demonstrate a wavefront-enhanced, Bspline augmented virtual motion camouflage algorithm for single or multiple robots to navigate through an obstacle dense and changing environment, while considering inter-vehicle conflicts, iv obstacle avoidance, nonlinear dynamics, and different constraints. In addition, it is expected that this testbed can be used to test different vehicle motion planning and control algorithms.