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Conventional scanning probe microscopy (SPM)-based nanomanipulations always have to face scanner accuracy problems such as hysteresis, nonlinearity, and thermal drift. Although some scanners consist of internal position sensors, the sensitivity is not high enough to monitor high-resolution nanomanipulations. Additionally, once the scan size decreases to a nanolevel such as less than 100 nm, the noise brought by sensors is large enough to affect the performance of the closed-loop motion control system. In this paper, a non-vector space control strategy based on compressive feedback is proposed in order to improve the accuracy of SPM-based nanomanipulations. In this approach, local images (or compressive data) are used as both the reference input and feedback for a non-vector space closed-loop controller which considers the local image (or compressive data) as a set. The controller is designed in non-vector space, and it requires no prior information on features or landmarks which are widely used in traditional visual servoing. In this paper, the atomic force microscopy is used as an example of SPM to implement the non-vector space control strategy for nanomanipulations. The motivation of designing such a non-vector space controller is to solve the accuracy problem in nanomanipulation. Without this technique, the SPM-based nanomanipulations, such as nanomeasurement and nanosurgery, are difficult to conduct, with accuracy controlled under several nanometers. In order to illustrate the contributions and potential applications of this non-vector controller, at the end of this paper, an application of carbon nanotube local electrical property characterization based on a non-vector space motion control is shown to clearly verify the concept. Compared with other research in the local electrical property characterization, the non-vector space controller can ensure that the measurement accuracy (position error) is controlled within a few nanometers, which also ensures the re- iability of measurement results. Additionally, this non-vector space control method can be implemented into any kind of SPM to realize a real-time control for nanomanipulation such as nanofabrication and nanoassembly.