Two types of constraints are employed: a constraint between consecutive nodes ((j = i + 1)) and that between non-sequential nodes (loop-closing constraints).
Using again (2.16), (2.17), it follows that the following close constraint to (2.19) for large enough : (2.25).
Fig. 2 Sample trajectory estimation result Fig. 3 Motion estimation errors using simulated data with one loop-closing constraint.
Since (varvec{H}) is symmetric, positive-definite, and sparse (i.e., the number of loop-closing constraints is small), the linear system can be efficiently solved via sparse Cholesky decomposition or the preconditioned conjugate gradient method [10, 11].
-Allowable closing time constraints which restrict closing day for each ship to a maximum allowable days, given by: {T}_g^kle {T}^k,gin G,kin S,mathrm{where} {sum}_{z=3,4}{x}_{igz}^k=1kern0.5em mathrm{and}kern0.5em iin D, (22).
However, this may render states close to constraints infeasible.
This paper presents a robust control law for a CMG-actuated space robot in presence of system uncertainties and closed-chain constraints.
The MPC-based cascade strategy yields significantly better performance than classical cascade control when operating close to constraints on the jacket flow rate.
It is closed because constraints (3) and (4) are expressed by weak inequalities and (5) by equality between terms continuous in components of a strategy.
Such estimates are known to be valid for general, closed state constraint sets, provided the functions defining the dynamic constraint are Lipschitz continuous, with respect to the time and state variables.
