The use of CMOS Pixel Sensors (CPS) for high resolution and low material vertex detectors has been validated with the 2014 and 2015 physics runs of the STAR-PXL detector at RHIC/BNL. This opens the door to the use of CPS for inner tracking devices, with 10-100 times larger sensitive area, which require therefore a sensor design privileging power saving, response uniformity and robustness. The 350nm CMOS technology used for the STAR-PXL sensors was considered as too poorly suited to upcoming applications like the upgraded ALICE Inner Tracking System (ITS), which requires sensors with one order of magnitude improvement on readout speed and improved radiation tolerance. This triggered the exploration of a deeper sub-micron CMOS technology, Tower-Jazz 180nm, for the design of a CPS well adapted for the new ALICE-ITS running conditions. This paper reports the R & D results for the conception of a CPS well adapted for the ALICE-ITS.