The clinical usage of powered exoskeletons for the rehabilitation of patients affected by lower limb disorders has been constantly growing in the last decade. This paper presents a versatile and reliable gait pattern generator for these devices able to accommodate several gait requirements, i.e., step length, clearance, and time, and to suit a wide range of persons. In the proposed method, the human gait phases have been modeled with a set of trajectories as Bèzier curves, enabling a robotic lower-limb exoskeleton to walk in a continuous way, similarly to the physiological gait cycle. The kinematic, kinetic, and spatial requirements for each gait phase are translated into the control points of the Bèzier curves that define the trajectory for that phase. The outcome of this study has been tested on real scenarios with a group of healthy subjects wearing the TWIN lower-limb exoskeleton. They were asked to walk at different speeds, generally defined as slow, medium, and fast. The results are shown in terms of joint positions, velocities, and body-mass-normalized torques. The maximum hip and knee joint torque was observed in the support phase. While, at higher speeds the maximum hip torque was provided in the swing phase due to the mechanical properties and limits of the device. In terms of speed, all the subjects reached 0.44 m/s, which is the minimum required community ambulation.