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This paper presents a novel real-time obstacle avoidance and navigation technique called as "Free-configuration Eigenspace" (FCE). The FCE enables an autonomous robot to detect unknown obstacles and avoid collisions while simultaneously steering the robot towards the target. The methodology utilizes a two-dimensional (2D) Cartesian Eigenspace as a world model. 2D way points (in world model) are extracted by computing (through FCE model) stacked Eigenvectors of laser data at discrete time scans which manifest desired robotic trajectory. The world model is updated continuously upon obtaining discrete time laser scans sampled by on-board Light Detection and Ranging (LiDAR) sensors. The FCE technique has been implemented on Robotic Operating System and real-time robotics simulator Gazebo ® . Encouraging results are obtained and shown in this paper. The FCE has also been tested in real-time with laser scans obtained from VL6180X LiDAR sensor mounted on a custom autonomous robot. The results obtained are further compared with the state-of-the-art obstacle avoidance and path planning method called as vector field histogram (VFH). The FCE results (shown in the paper) are comparable, encouraging, and outperform VFH in path length and safe distance maintenance. [ABSTRACT FROM AUTHOR]