Recent progress in contact-rich robotic manipulation has been striking, yet most deployed systems remain confined to simple, scripted routines. One of the key barriers is the lack of motion planning algorithms that can provide verifiable guarantees for safety, efficiency and reliability. To address this, a family of algorithms called Constant-Time Motion Planning (CTMP) was introduced, which leverages a preprocessing phase to enable collision-free motion queries in a fixed, user-specified time budget (e.g., 10 milliseconds). However, existing CTMP methods do not explicitly incorporate the manipulation behaviors essential for object handling. To bridge this gap, we introduce the \textit{Behavioral Constant-Time Motion Planner} (B-CTMP), an algorithm that extends CTMP to solve a broad class of two-step manipulation tasks: (1) a collision-free motion to a behavior initiation state, followed by (2) execution of a manipulation behavior (such as grasping or insertion) to reach the goal. By precomputing compact data structures, B-CTMP guarantees constant-time query in mere milliseconds while ensuring completeness and successful task execution over a specified set of states. We evaluate B-CTMP on two canonical manipulation tasks, shelf picking and plug insertion, in simulation and on a real robot. Our results show that B-CTMP unifies collision-free planning and object manipulation within a single constant-time framework, providing provable guarantees of speed and success for manipulation in semi-structured environments.

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