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Factor graph is a graph representing the factorization of a probability distribution function, and has been utilized in many autonomous machine computing tasks, such as localization, tracking, planning and control etc. We are developing an architecture with the goal of using factor graph as a common abstraction for most, if not, all autonomous machine computing tasks. If successful, the architecture would provide a very simple interface of mapping autonomous machine functions to the underlying compute hardware. As a first step of such an attempt, this paper presents our most recent work of developing a factor graph accelerator for LiDAR-Inertial Odometry (LIO), an essential task in many autonomous machines, such as autonomous vehicles and mobile robots. By modeling LIO as a factor graph, the proposed accelerator not only supports multi-sensor fusion such as LiDAR, inertial measurement unit (IMU), GPS, etc., but solves the global optimization problem of robot navigation in batch or incremental modes. Our evaluation demonstrates that the proposed design significantly improves the real-time performance and energy efficiency of autonomous machine navigation systems. The initial success suggests the potential of generalizing the factor graph architecture as a common abstraction for autonomous machine computing, including tracking, planning, and control etc.