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Coauthor with Kevin M. Lynch of a textbook on modern robotics, connecting rigid-body geometry with robot mechanics, motion planning and control.^[ref]

Jean Gallier is a computer scientist whose research connects mathematical foundations with computer programming and geometric applications. His earlier work includes formal verification, automated deduction and unification; his later interests include computer graphics, computer vision, robotics and the geometry of curves and surfaces.^[ref]

His Curves and Surfaces in Geometric Modeling: Theory and Algorithms by Jean Gallier develops geometric constructions with explicit mathematical foundations. For example, its account of affine maps separates the geometry of points from the linear maps acting on displacement vectors, a distinction useful when describing transformations in computer graphics.^[ref]

Homepage: www.cis.upenn.edu/~jean/

Coauthor with Frank C. Park of a textbook on modern robotics. Its treatment connects rotation matrices, rigid-body motion, planning and control through a common geometric formulation.^[ref]

Robotics studies the design, modelling and control of machines that interact with their surroundings through sensing and motion. A robot combines sensors, actuators, computation and a mechanical structure. A robot arm must relate joint motion to the position and orientation of its end effector; a mobile robot must also estimate where it is relative to its environment.^[ref]

Kinematics asks which motions a mechanism permits. Dynamics determines the forces and torques needed to produce them, while feedback control corrects deviations using measurements. A desired path is useful only when the mechanism can realize it within constraints such as motor effort, contact and obstacles. These connections make robotics a meeting point of mechanics, geometry, statistical inference and control theory.