Group algebra for robotic applications by means of operator overloading

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.