In order to meet the demand of providing varieties of physical services in the intelligent space, this paper designed and implemented a stepping robotic system based on cellular grid map, from both hardware implementation and software algorithm aspects. In the hardware aspect, the paper designed and implemented an omni-directional wheels structure and the mobile platform, stepping robot driving system and sensing detection system. Among them, the designing of the mechanical structure of the entire stepping robot body has greatly improved the effectiveness and reliability of the hardware system. The major innovative work includes analysing and modelling the omni-directional mobile platform with six wheels in mechanics, kinematics and dynamics, the designing and implementation of optical odometer by using FPGA to parse PS/2 protocol, and the laser calibration system. In terms of software algorithms, the paper mainly focused on four contents, consisting of multi-sensor data fusion, creating of a cellular grid map, local path planning and global path planning of the stepping robot based on the map. The main innovative work in the software algorithm includes the achievement of multi-dimensional sensor data fusion algorithm by introducing Mahalanobis distance, six-direction local path planning with the solution of the Dead Angle phenomenon and the Dead Circle phenomenon, as well as extending TSP optimisation problem based on Genetic Algorithm to the state of the cellular grid map. The issues mentioned above have been realised on the simulation platform. In the field test, the precision of the stepping robotic system can reach the millimeter scale.