To improve the safety and reliability of robotic manipulators during high-speed precision movements, this paper proposes a method for smooth and time-optimal trajectory planning incorporating kinodynamic constraints. The primary objective is to use an evolutionary algorithm to determine a trajectory by considering time and jerk within the feasible path-pseudo-velocity phase plane region. Firstly, the path parameterization theory extracted the maximum pseudo-velocity projection curve from the kinodynamic constraints. Subsequently, the feasible region in the phase plane was defined through reachability analysis of discrete linear systems. Thereafter, we constructed the trajectory function using a cubic B-spline curve, optimizing its control points with an improved carnivorous plant optimization algorithm. Finally, the effectiveness and practicality of this method were verified through simulations on a 6-DOF manipulator.