27 February 2024
Electrical, hydraulic, and mechanical systems, or their combinations, are Lagrangian systems that usually exhibit complex behaviour. However, their physical nature displays special properties, such as symmetry and passivity, which have been exploited to solve many control problems, otherwise difficult to address for generic nonlinear dynamics. To cope with their high nonlinearity and large number of degrees of freedom (DOF), representations with specific structures play a crucial role in simplifying analysis, as well as control design and synthesis. For example, coordinate transformations are often used to highlight some internal structures that simplify the derivation of feedback controllers for robotic systems and prove their stability.
On this line of thought, EMERGE partners from Delft University of Technology and collaborators aim to answer the following question: Can a transformation of the generalized coordinates under which the actuators directly perform work on a subset of the configuration variables be found? The authors not only show that the answer to this question is yes but also provide necessary and sufficient conditions.
They show that there exists a class of Lagrangian dynamics, called collocated, for which a coordinate transformation decouples actuator inputs entering the equations of motion through a configuration-dependent actuation matrix. These coordinates have a physical interpretation and can be easily computed. Under mild conditions on the differentiability of the actuation matrix, a simple test allows verifying if the dynamics is collocated or not. By exploiting power invariance, they provide necessary and sufficient conditions that a change of coordinates decouples the input channels if and only if the dynamics is collocated. In addition, they use the collocated form to derive novel controllers for damped underactuated mechanical systems. To demonstrate the theoretical findings, they consider several Lagrangian systems with a focus on continuum soft robots.
Read the paper in the link below.
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