Abstract
We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path.Enforcing this condition directly in form of a servo constraint leads to differential-algebraic equations (DAEs) of arbitrarily high index. Typically, the model equations are of index 5, which already poses high regularity conditions. If we relax the servo constraints and consider the system from an optimal control point of view, the strong regularity conditions vanish, and the solution can be obtained by standard techniques.By means of the well-known n-car example and an overhead crane, the theoretical and expected numerical difficulties of the direct DAE and the alternative modeling approach are illustrated. We show how the formulation of the problem in an optimal control context works and address the solvability of the optimal control system. We discuss that the problematic DAE behavior is still inherent in the optimal control system and show how its evidences depend on the regularization parameters of the optimization.
Highlights
We consider mechanical systems with servo constraints; see, e.g., [7, 8, 19], for which a part of the motion is specified
In the direct modeling approach, the inputs are regarded as variables, whereas the desired output is formulated as a constraint. This constraint makes the model equations a system of differential-algebraic equations (DAE) even though the dynamics of the system may be given in the form of an ODE
We show that for Example 2 with ν = 0 and R0 = 0, the DAE approach of Configuration 1 is equivalent to the optimal control formulation in Configuration 3, provided that Q > 0
Summary
We consider mechanical systems with servo constraints; see, e.g., [7, 8, 19], for which a part of the motion is specified. Heiland that makes an end effector follow a prescribed trajectory Often, these configurations are called inverse dynamics problems or, since the number of degrees of freedom exceeds the number of controls, underactuated mechanical systems. In the direct modeling approach, the inputs are regarded as variables, whereas the desired output is formulated as a constraint. This constraint makes the model equations a system of differential-algebraic equations (DAE) even though the dynamics of the system may be given in the form of an ODE. We analyze the optimal control approach and investigate methods for the solution of the resulting equation systems. This includes the DAE case and the optimal control approach for which
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
