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Key research themes
1. How can explicit equations of motion for constrained multibody systems be formulated and leveraged for control and simulation?
This research area focuses on developing explicit, unified formulations of the equations of motion (EOM) for constrained mechanical systems, especially multibody systems with holonomic and nonholonomic constraints, including cases with redundant constraints or singular mass matrices. Such formulations facilitate stable and efficient simulation and enable advanced control strategies that accommodate complex constraint topologies, passive joints, and changing degrees of freedom.
Key finding: Introduced a projection-based dynamics formulation for constrained multibody systems that does not require linear independence of constraint equations, allowing simulation and control in presence of redundant constraints and... Read more
Key finding: Presented a new explicit closed-form equation of motion that unifies treatment of constrained mechanical systems with holonomic and nonholonomic constraints, valid for both positive definite and positive semi-definite mass... Read more
Key finding: Extended classical D’Alembert’s principle to accommodate both ideal (doing zero work) and non-ideal constraints (doing positive or negative work) within lagrangian mechanics framework, leading to general explicit equations of... Read more
Key finding: Built upon the Udwadia-Kalaba fundamental equation, this work systematically designs analytical dynamics and servo control for constrained mechanical systems with holonomic and nonholonomic constraints, independent of... Read more
Key finding: Established a duality between constrained motion and trajectory tracking control in nonlinear mechanical systems: the imposition of constraints corresponds to control objectives, with d’Alembert’s principle yielding an... Read more
2. What are the fundamental principles and geometric frameworks describing the reactive constraint forces and determinism in general nonholonomic constrained systems?
This theme explores the geometric and analytical foundations of constrained mechanical systems, focusing on the characterization of reactive forces respecting determinism and the intrinsic geometry of the space of kinetic states. It investigates generalized notions of virtual work and principles of least constraint, aiming to unify the treatment of ideal and non-ideal constraint forces in both holonomic and nonholonomic settings with frame-independent formulations. The research employs advanced differential geometry (jet bundles, Chetaev bundles) and clarifies conditions for uniqueness and well-posedness of dynamics.
Key finding: Extended lagrangian mechanics to incorporate non-ideal constraint forces that may perform positive or negative work, broadening d’Alembert’s principle. Introduced explicit equations of motion for constrained discrete... Read more
Key finding: Presented an algebraic methodology employing polynomial matrices, finite and infinite Jordan pairs, to derive closed-form solutions for constrained linear mechanical systems including those with singular mass matrices.... Read more
3. How can constraint propagation and constraint satisfaction techniques improve model representation and computational efficiency in solving combinatorial and hybrid systems?
This research theme examines methods in constraint programming encompassing constraint satisfaction problem (CSP) formulation, propagation techniques, and search algorithms to efficiently handle combinatorial problems and verification of hybrid dynamical systems. It addresses binary and non-binary constraint conversions, domain reduction (filtering) algorithms, solving nonlinear inequality constraints, and synthesis of invariants via constraint-based verification methods. These techniques balance completeness and efficiency, enabling scalable solutions to CSPs in diverse applications.
Key finding: Analyzed fundamental constraint propagation algorithms for constraint satisfaction problems (CSPs), detailing methods to reduce variable domains by filtering inconsistent values (constraint propagation). Described translation... Read more
Key finding: Outlined the historical development and conceptual foundations of constraint programming, emphasizing representation of problems as sets of variables constrained by logical relations. Introduced the seminal scene labeling... Read more
Key finding: Presented a constraint-based methodology for discovering inductive invariants of hybrid systems expressed as Boolean combinations of polynomial inequalities. Formulated verification conditions as ∃∀ constraints, encoding... Read more
Key finding: Developed an algebraic framework applying polynomial matrices and Jordan decomposition techniques to obtain explicit time-domain solutions to constrained linear mechanical systems modeled by singular higher-order differential... Read more
Key finding: Proposed a generalized solver framework for over-constrained systems expressed as constraint hierarchies with multiple preference levels and soft constraints. Investigated comparator-based solution ranking (local and global)... Read more