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Operator overloading is a powerful feature of modern object-oriented programming languages; it can be used to customize the default algebraic operators to a point where the programming syntax can accommodate new algebras acting on complex objects. The present work introduces a custom T (T, ) algebra which can be used to express kinematic transformations in chains of frames that move in threedimensional space; relevant algebraic properties of T are discussed; finally the algebra is translated into a set of algorithms that can fit into the operator-overloading capabilities of the C++ language. Topics such as templates, serialization, optimizations and examples in the field mechanical simulation are discussed; moreover a novel method for run-time and compile-time validation of the syntax is exposed, so that the order of the products is checked for kinematic consistency hence showing the advantage of this approach also for educational purposes.

GROUP ALGEBRA FOR ROBOTIC APPLICATIONS BY MEANS OF OPERATOR OVERLOADING