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We present principles and possible design concepts for a tractor atom interferometer (TAI) based on three-dimensional confinement and transport of ultracold atoms. The confinement reduces device size and wave-packet dispersion, enables arbitrary holding times, and facilitates control to create complex trajectories that allow for optimization to enable fast splitting and recombination, to suppress detrimental nonadiabatic excitation, and to cancel unwanted sensitivity. Thus, the design allows for further advancement of compact, high-sensitivity, quantum sensing technology. In particular, we focus on the implementation of quantum-enhanced accelerometers and gyroscopes. We discuss TAI protocols for both spin-dependent and scalar trapping potentials. Using optimal control theory, we demonstrate the splitting of the wave function on a time scale two orders of magnitude shorter than a previous proposal using adiabatic dynamics, thus maximizing the time spent at full separation, where the interferometric phase is accumulated. The performance estimates for TAI give a promising perspective for atom-interferometry-based sensing, significantly exceeding the sensitivities of current state-of-the-art devices.