Trajectory planning is important in many applications involving unmanned aerial vehicles, underwater vehicles, spacecraft, and industrial manipulators. It is still a challenging task to rapidly find an optimal trajectory while taking into account dynamic and environmental constraints. In this dissertation, a unified, varying manifold based optimal trajectory planning method inspired by several predator-prey relationships is investigated to tackle this challenging problem. Biological species, such as hoverflies, ants, and bats, have developed many efficient hunting strategies. It is hypothesized that these types of predators only move along paths in a carefully selected manifold based on the prey’s motion in some of their hunting activities. Inspired by these studies, the predator-prey relationships are organized into a unified form and incorporated into the trajectory optimization formulation, which can reduce the computational cost in solving nonlinear constrained optimal trajectory planning problems. Specifically, three motion strategies are studied in this dissertation: motion camouflage, constant absolute target direction, and local pursuit. Necessary conditions based on the speed and obstacle avoidance constraints are derived. Strategies to tune initial guesses are proposed based on these necessary conditions to enhance the convergence rate and reduce the computational cost of the motion camouflage inspired strategy. The following simulations have been conducted to show the advantages of the proposed methods: a supersonic aircraft minimum-time-to-climb problem, a ground robot obstacle avoidance problem, and a micro air vehicle minimum time trajectory problem. The results show that the proposed methods can find the optimal solution with higher success rate and faster iv convergent speed as compared with some other popular methods. Among these three motion strategies, the method based on the local pursuit strategy has a relatively higher success rate when compared to the other two. In addition, the optimal trajectory planning method is embedded into a receding horizon framework with unknown parameters updated in each planning horizon using an Extended Kalman Filter