Extended Operational Space Kinematics, Dynamics, and Control of Redundant Non-Serial Compound Robotic Manipulators

An extended operational space kinematics and dynamics formulation is presented for control of redundant non-serial compound robotic manipulators. A broad spectrum of high load capacity non-serial manipulators used in earth moving, material handling, and construction applications is addressed. Departing from conventional approaches that rely on Jacobian pseudoinverses and local null-space projections, a globally valid, differential geometry-based, multi-valued inverse kinematic mapping is defined at the configuration level, with explicit self-motion parameterization of manipulator redundancy. The formulation yields coupled second-order ordinary differential equations of manipulator dynamics on the product space of task variables and self-motion coordinates. This enables direct integration of system dynamics with control strategies, such as model predictive control or feedback design, while maintaining task constraint compliance. The methods presented are validated through simulation and control of a multi-degree of redundancy non-serial compound material loader manipulator, demonstrating advantages in generality, numerical accuracy, and trajectory smoothness.