This paper proposes the use of piecewise C^n smooth curve for mobile-base motion planning and control, coined Timed-Elastic Smooth Curve (TESC) planner. Based on a Timed-Elastic Band, the problem is defined so that the trajectory lies on a spline in SE(2) with non-vanishing n-th derivatives at every point. Formulated as a multi-objective nonlinear optimization problem, it allows imposing soft constraints such as collision-avoidance, velocity, acceleration and jerk limits, and more. The planning process is realtime-capable allowing the robot to navigate in dynamic complex scenarios. The proposed method is compared against the state-of-the-art in various scenarios. Results show that trajectories generated by the TESC planner have smaller average acceleration and are more efficient in terms of total curvature and pseudo-kinetic energy while being produced with more consistency than state-of-the-art planners do.