RAAD 2026

Classical methodologies in mathematical physics and robotics suffer from several fundamental limitations. First, accessibility is restricted because ideas, concepts, methods, and results are fragmented across multiple mathematical formalisms. Mastery of only a subset of these systems prevents effective access to knowledge expressed in others. Second, redundancy arises from the repeated representation of the same information in different mathematical languages, leading to reduced efficiency. Third, there is insufficient integration and articulation among these formalisms, resulting in inconsistencies, lack of unification, limited generalization, and weak interoperability. Geometric Algebra was developed in response to these challenges, and, in light of advances in modern scientific theory, it provides a powerful and compact framework for unifying and optimizing the expression of fundamental concepts and their consequences.
This keynote lecture will center on three complementary geometric frameworks: signed distance fields, geometric algebra, and Riemannian geometry, which together offer expressive and computationally efficient representations for learning, planning, control, and optimization in robotics. Signed distance fields enable implicit shape representation through distance functions, which can be encoded and learned using various modeling and data-driven approaches. Geometric algebra provides a unified treatment of geometric primitives and transformations, including 6D poses, planes, lines, circles, and spheres, allowing constraints and interactions in robotic systems to be expressed in a compact and consistent manner. Riemannian geometry extends models and algorithms originally formulated in Euclidean spaces to curved manifolds, enabling principled handling of structured objects such as spheres, matrices, and subspaces, as well as more general smooth manifolds equipped with a Riemannian metric for distance measurement.
The lecture will clarify the distinctions, complementarities, and interconnections among these three geometric paradigms and demonstrate how they jointly contribute to key robotic applications, with particular emphasis on navigation, path planning, and manipulation. From a dynamics and control perspective, both Euler–Lagrange formulations and Hamiltonian mechanics on phase space will be expressed within the geometric algebra framework. The control architecture is centered on a quadratic programming formulation that integrates motion objectives expressed as geometric constraints on joint accelerations with physical limitations arising from unilateral contacts and force-constrained grasping.
Furthermore, modern learning techniques, including neural networks, convolutional neural networks, and physics-informed neural networks, will be incorporated into the control loop using geometric algebra as a unifying representational backbone. The lecture will also present the application of Quantum Fuzzy Control strategies to robotic manipulators. Practical demonstrations will include modeling and control of robotic arms for grasping and manipulation tasks, as well as applications to quadrotors and humanoid robots.