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[ \exists t: | q_actual(t) - \tau_planned(t) | > \sigma \cdot \textVar s \in [t-\delta,t] \left[ \frac\partial c obs\partial q(s) \right] ]
[ z^* = \arg\min_z(t) \in Z \mathcalJ[D(z(t))] \quad \texts.t. \quad \texthomotopy constraints ] hdmove2
hdmove2 achieves a 94% success rate on the narrow passage benchmark (64 DoF), compared to 12% for RRT* and 68% for CHOMP. The event-driven controller reduces average planning frequency by 63%, enabling 95 Hz control updates. [ \exists t: | q_actual(t) - \tau_planned(t) |