This paper shows how the information required to solve arbitrary single loop inverse kinematics problems can be reduced to a single scalar equation using simple algebraic considerations. Then, a set of variable substitutions allows us to express this fundamental equation into a second-order multinomial. A recurrent expression has been obtained for the control points of this multinomial when expressed in Bernstein basis. This is the key result that allows us to devise a new subdivision technique for solving inverse kinematics problems. To this end, we have actually adopted concepts and algorithms developed —and widely tested— in the context of Computer Graphics applications. Contrary to other approaches, the one presented here is clearly less involved, it does not require any algebraic symbolic manipulation to elaborate the input data, and its extension to multiple-loop kinematic chains is really straightforward. Moreover, although it can be classified within the same category as interval-based techniques, it does not require any interval arithmetic computation.
- Control Point
- Inverse Kinematic
- Bernstein Polynomial
- Inverse Kinematic Problem
- Bernstein Basis
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Bombín, C., Ros, L., Thomas, F. (2000). A Concise Bézier Clipping Technique for Solving Inverse Kinematics Problems. In: Lenarčič, J., Stanišić, M.M. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4120-8_6
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Online ISBN: 978-94-011-4120-8
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