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Continuously Shaping Projections and Operational Space Tasks

Projection operators are widely employed in multi-objective robot control. It is an open research question how to achieve continuous transitions between different idempotent projectors which is required for dynamic task priority rearrangement. We formalize projection shaping, providing a solution to deal with rank changes in a smooth fashion. Furthermore, we derive meaningful shaping operators and show that damped least squares is a special case of our general formulation. Finally, we extend the Stack-of-Tasks prioritization scheme for continuous priority rearrangement of single task dimensions. Simulation results validate our approach.