ResearchInterpolating solid orientations with circular blending quaternion curves
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Cited by (63)
A tolerance constrained G<sup>2</sup> continuous path smoothing and interpolation method for industrial SCARA robots
2020, Robotics and Computer-Integrated ManufacturingCitation Excerpt :For six-axis articulated robots, the robot end-effector orientation can be represented by rotation matrix, Euler angles, quaternion, and axis-angle vector [32]. Robotic orientation path can be smoothed by circular quaternion curve [33], quaternion Hermite curve [34], Bezier curve in SO(3) [35], or quaternion B-splines [36]. Refs. [37, 38] proposed using local Frenet frame of position path to represent rotation path.
Real-time feedrate scheduling for five-axis machining by simultaneously planning linear and angular trajectories
2018, International Journal of Machine Tools and ManufactureSmooth orientation interpolation using parametric quintic-polynomial-based quaternion spline curve
2018, Journal of Computational and Applied MathematicsA class of generalized B-spline quaternion curves
2015, Applied Mathematics and ComputationCitation Excerpt :Similarly, the B-spline quaternion curve by Nielson and Heiland [8] also fails to have C2-continuity (see [2] for more details). There are also many other methods to construct quaternion curves in S3, but most of the curves are C1-continuous [1,9,10]. Due to the discontinuity in the second derivatives, big jumps may occur in the angular acceleration at some curve joints, which leads to undesirable effects in generating naturally looking rotations.
Bézier curves and C<sup>2</sup> interpolation in Riemannian manifolds
2007, Journal of Approximation TheoryA tolerance constrained robot path circular interpolation method for industrial SCARA robots
2021, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture