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The mathematical model of 6-DoF dynamics is used in different applications. In general, software-based solutions are utilized to implement the 6-DoF dynamic model. This paper introduces the FPGA-based implementation of the 6-DoF dynamics accelerator. The proposed hardware-based approach ensures the accuracy of the nonlinear model without compromising computational speed. The model-based approach and high-level synthesis have been employed in the design and implementation stages. Regarding design strategy, standard processor architecture, and resource-sharing methods have been applied to achieve FPGA resource efficiency. Seven datapath and finite state machines have been designed for seven different subsystems. The design resulted in hardware blocks that can execute all non-linear model equations 396 times in 1 ms using fixed/floating-point hybrid case and 434 times using pure fixed-point case. The model equations, which took an average of $\mathbf {0.4986}$ s to simulate in the Simulink environment, have been run on an FPGA in $\mathbf {7.1924}~\mu \text{s}$ . For seven design cases, numerical errors, resource utilization, and timing metrics are tabulated and presented to the reader.

Estimating the 6-DoF (Degree of Freedom) object pose from a single RGB image is one of the challenging tasks in the field of computer vision. Before the pose which is defined as the translation and rotation parameters can be derived by the traditional PnP algorithm, 2D image projections of a set of 3D object keypoints must be accurately detected. In this paper, we present techniques for defining 3D object surface keypoints and predicting their corresponding 2D counterparts via deep-learning network architectures. The main technique to designate 3D object keypoints is to employ quadratic fitting scheme for calculating the principal surface curvatures as the weights and then select from all surface points the ones mostly distributive with larger curvatures to describe the object shape as possible. However, the 2D projected keypoints are not directly regressed from the network, but encoded as the unit vector fields pointing to them, so that the voting scheme to recover back those 2D keypoints can be performed. Moreover, an effective loss function with the regularization term is adopted in training ResNet for predicting image projections of object keypoints by focusing on small-scale errors. Experimental results show that our proposed technique outperforms state-of-the-art approaches in both “2D projection” and “3D transformation” metrics.