  The challenge of preparing a system in a designated state spans diverse
facets of quantum mechanics. To complete this task of steering quantum states,
one can employ quantum control through a sequence of generalized measurements
which direct the system towards the target state. In an active version of this
protocol, the obtained measurement readouts are used to adjust the protocol
on-the-go. This enables a sped-up performance relative to the passive version
of the protocol, where no active adjustments are included. In this work, we
consider such active measurement-driven steering as applied to the challenging
case of many-body quantum systems. For helpful decision-making strategies, we
offer Hilbert-space-orientation techniques, comparable to those used in
navigation. The first one is to tie the active-decision protocol to the greedy
accumulation of the cost function, such as the target state fidelity. We show
the potential of a significant speedup, employing this greedy approach to a
broad family of Matrix Product State targets. For system sizes considered here,
an average value of the speedup factor $f$ across this family settles about
$20$, for some targets even reaching a few thousands. We also identify a
subclass of Matrix Product State targets, for which the value of $f$ increases
with system size. In addition to the greedy approach, the second wayfinding
technique is to map out the available measurement actions onto a Quantum State
Machine. A decision-making protocol can be based on such a representation,
using semiclassical heuristics. This State Machine-based approach can be
applied to a more restricted set of targets, sometimes offering advantages over
the cost function-based method. We give an example of a W-state preparation
which is accelerated with this method by $f\simeq3.5$, outperforming the greedy
protocol for this target.
