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Evaluation of rotation formalisms in three dimensions using a Lissajous knot

An evaluation of three dimensional rotation formalisms using a Lissajous knot is given. The optimal parameterization of SO(3) is determined so that robotics attitude system can become more effective. Given a robot's local translational velocity and local angular velocity, numerical integrations along a robot's trajectory using rotation formalisms are performed. Comparing the resulting trajectory with a robot's true trajectory, this paper considers numerical error, integration time and steps as parameterization methods' evaluation criteria.