This paper aims to discuss the requirements of safe and smooth trajectory planning of transporter mobile robots to perform non-prehensile object manipulation task. In non-prehensile approach, the robot and the object must keep their grasp-less contact during manipulation task. To this end, dynamic grasp concept is employed for a box manipulation task and corresponding conditions are obtained and are represented as a bound on robot acceleration. A trajectory optimization problem is defined for general motion where dynamic grasp conditions are regarded as constraint on acceleration. The optimal trajectory planning for linear, circular and curve motions are discussed. Optimization problems for linear and circular trajectories were analytically solved by previous studies and here we focused with curve trajectory where Genetic Algorithm is employed as a solver tool. Motion simulations showed that the resulted trajectories satisfy the acceleration constraint as well as velocity boundary condition that is needed to accomplish non-prehensile box manipulation task. Manuscript profile