CoAd: Constant-Time Planning for Continuous Goal Manipulation with Compressed Library and Online Adaptation

Recent progress in contact-rich robotic manipulation has been striking, yet most deployed systems remain confined to simple, scripted routines. One of the barriers is the lack of motion planning algorithms that can provide verifiable guarantees for safety, efficiency and reliability. Constant-Time Motion Planning (CTMP) is a recent step toward such guarantees for collision-free motion in a priori known environments:: a preprocessing phase enables queries to be answered within a fixed, user-specified time budget (e.g., 10 milliseconds). However, CTMP certifies only reachability---a binary predicate---and ignores the manipulation behavior that completes the task, which is increasingly stochastic (e.g., a learned skill) and whose success no single offline rollout can establish, let alone certify. We introduce the Behavioral Constant-Time Motion Planner (B-CTMP), which extends CTMP to two-step manipulation tasks in semi-structured environments: a collision-free motion to a behavior initiation state, followed by execution of a behavior such as grasping or insertion. B-CTMP departs from prior CTMP in two ways: neighborhoods are constructed in object-pose space rather than robot configuration space, and coverage is established by statistical certification rather than a reachability check. A plan is cached only if repeated rollouts lower-bound its success rate above a user-specified threshold, and we prove these bounds hold simultaneously across the entire cache at a prescribed confidence level. For deterministic behaviors a single rollout suffices, recovering the binary check of prior CTMP as a special case. We evaluate B-CTMP on three manipulation tasks---shelf picking, plug insertion, and wheel replacement---in simulation and on real robots. B-CTMP's certified plans succeed consistently where baselines fail during behavior execution, and it rejects infeasible object poses in constant time.

Planning long-horizon manipulation motions using a set of predefined skills is a central challenge in robotics; solving it efficiently could enable general-purpose robots to tackle novel tasks by flexibly composing generic skills. Solutions to this problem lie in an infinitely vast space of parameterized skill sequences -- a space where common incremental methods struggle to find sequences that have non-obvious intermediate steps. Some approaches reason over lower-dimensional, symbolic spaces, which are more tractable to explore but may be brittle and are laborious to construct. In this work, we introduce MOSAIC, a skill-centric, multi-directional planning approach that targets these challenges by reasoning about which skills to employ and where they are most likely to succeed, by utilizing physics simulation to estimate skill execution outcomes. Specifically, MOSAIC employs two complementary skill families: Generators, which identify ``islands of competence'' where skills are demonstrably effective, and Connectors, which link these skill-trajectories by solving boundary value problems. By focusing planning efforts on regions of high competence, MOSAIC efficiently discovers physically-grounded solutions. We demonstrate its efficacy on complex long-horizon problems in both simulation and the real world, using a diverse set of skills including generative diffusion models, motion planning algorithms, and manipulation-specific models. Visit skill-mosaic.github.io for demonstrations and examples.

Behavior Trees (BTs) offer a powerful paradigm for designing modular and reactive robot controllers. BT planning, an emerging field, provides theoretical guarantees for the automated generation of reliable BTs. However, BT planning typically assumes that a well-designed BT system is already grounded -- comprising high-level action models and low-level control policies -- which often requires extensive expert knowledge and manual effort. In this paper, we formalize the BT Grounding problem: the automated construction of a complete and consistent BT system. We analyze its complexity and introduce CABTO (Context-Aware Behavior Tree grOunding), the first framework to efficiently solve this challenge. CABTO leverages pre-trained Large Models (LMs) to heuristically search the space of action models and control policies, guided by contextual feedback from BT planners and environmental observations. Experiments spanning seven task sets across three distinct robotic manipulation scenarios demonstrate CABTO's effectiveness and efficiency in generating complete and consistent behavior tree systems.