Humans can observe a single, imperfect demonstration and immediately generalize to very different problem settings. Robots, in contrast, often require hundreds of examples and still struggle to generalize beyond the training conditions. We argue that this limitation arises from the inability to recover the latent explanations that underpin intelligent behavior, and that these explanations can take the form of structured programs consisting of high-level goals, sub-task decomposition, and execution constraints. In this work, we introduce Rational Inverse Reasoning (RIR), a framework for inferring these latent programs through a hierarchical generative model of behavior. RIR frames few-shot imitation as Bayesian program induction: a vision-language model iteratively proposes structured symbolic task hypotheses, while a planner-in-the-loop inference scheme scores each by the likelihood of the observed demonstration under that hypothesis. This loop yields a posterior over concise, executable programs. We evaluate RIR on a suite of continuous manipulation tasks designed to test one-shot and few-shot generalization across variations in object pose, count, geometry, and layout. With as little as one demonstration, RIR infers the intended task structure and generalizes to novel settings, outperforming state-of-the-art vision-language model baselines.

In complex manipulation tasks, e.g., manipulation by pivoting, the motion of the object being manipulated has to satisfy path constraints that can change during the motion. Therefore, a single grasp may not be sufficient for the entire path, and the object may need to be regrasped. Additionally, geometric data for objects from a sensor are usually available in the form of point clouds. The problem of computing grasps and regrasps from point-cloud representation of objects for complex manipulation tasks is a key problem in endowing robots with manipulation capabilities beyond pick-and-place. In this paper, we formalize the problem of grasping/regrasping for complex manipulation tasks with objects represented by (partial) point clouds and present an algorithm to solve it. We represent a complex manipulation task as a sequence of constant screw motions. Using a manipulation plan skeleton as a sequence of constant screw motions, we use a grasp metric to find graspable regions on the object for every constant screw segment. The overlap of the graspable regions for contiguous screws are then used to determine when and how many times the object needs to be regrasped. We present experimental results on point cloud data collected from RGB-D sensors to illustrate our approach.

Their approach involved modeling the problem using a set of processes, each dedicated to searching for a plan, akin to representing search nodes on an open list. Each process is characterized by a probabilistic performance profile, modeled by a random variable indicating the probability of successful termination given processing time, as well as a random variable modeling the deadline corresponding to each partial plan, which is only revealed after planning is concluded. The meta-level problem lies in finding an optimal schedule of processing time across all processes that maximizes the probability that any process delivers a plan before its deadline. A simplified version of this problem, known as "simplified allocating planning effort when actions expire," assumes discrete time intervals and has been proven to be NP-hard. However, under the condition of known deadlines, the problem becomes solvable in pseudo-polynomial time through dynamic programming. Later, this line of work was extended to consider interleaved planning and execution, where partial plans can be executed during the search [62, 63]. While this body of work bears relevance to our research, it primarily concentrates on deriving symbolic plans. In contrast, our focus lies in elaborating existing symbolic plans through motion-level reasoning to make them executable for a robot, optimizing the likelihood of meeting a pre-specified deadline.

Vision-Language Models (VLM) can generate plausible high-level plans when prompted with a goal, the context, an image of the scene, and any planning constraints. However, there is no guarantee that the predicted actions are geometrically and kinematically feasible for a particular robot embodiment. As a result, many prerequisite steps such as opening drawers to access objects are often omitted in their plans. Robot task and motion planners can generate motion trajectories that respect the geometric feasibility of actions and insert physically necessary actions, but do not scale to everyday problems that require common-sense knowledge and involve large state spaces comprised of many variables. We propose VLM-TAMP, a hierarchical planning algorithm that leverages a VLM to generate goth semantically-meaningful and horizon-reducing intermediate subgoals that guide a task and motion planner. When a subgoal or action cannot be refined, the VLM is queried again for replanning. We evaluate VLM- TAMP on kitchen tasks where a robot must accomplish cooking goals that require performing 30-50 actions in sequence and interacting with up to 21 objects. VLM-TAMP substantially outperforms baselines that rigidly and independently execute VLM-generated action sequences, both in terms of success rates (50 to 100% versus 0%) and average task completion percentage (72 to 100% versus 15 to 45%). See project site https://zt-yang.github.io/vlm-tamp-robot/ for more information.

PDDLStream solvers have recently emerged as viable solutions for Task and Motion Planning (TAMP) problems, extending PDDL to problems with continuous action spaces. Prior work has shown how PDDLStream problems can be reduced to a sequence of PDDL planning problems, which can then be solved using off-the-shelf planners. However, this approach can suffer from long runtimes. In this paper we propose LAZY, a solver for PDDLStream problems that maintains a single integrated search over action skeletons, which gets progressively more geometrically informed, as samples of possible motions are lazily drawn during motion planning. We explore how learned models of goal-directed policies and current motion sampling data can be incorporated in LAZY to adaptively guide the task planner. We show that this leads to significant speed-ups in the search for a feasible solution evaluated over unseen test environments of varying numbers of objects, goals, and initial conditions. We evaluate our TAMP approach by comparing to existing solvers for PDDLStream problems on a range of simulated 7DoF rearrangement/manipulation problems.

As robots become increasingly capable of manipulation and long-term autonomy, long-horizon task and motion planning problems are becoming increasingly important. A key challenge in such problems is that early actions in the plan may make future actions infeasible. When reaching a dead-end in the search, most existing planners use backtracking, which exhaustively reevaluates motion-level actions, often resulting in inefficient planning, especially when the search depth is large. In this paper, we propose to learn backjumping heuristics which identify the culprit action directly using supervised learning models to guide the task-level search. Based on evaluations on two different tasks, we find that our method significantly improves planning efficiency compared to backtracking and also generalizes to problems with novel numbers of objects.

Robotic planning problems in hybrid state and action spaces can be solved by integrated task and motion planners (TAMP) that handle the complex interaction between motion-level decisions and task-level plan feasibility. TAMP approaches rely on domain-specific symbolic operators to guide the task-level search, making planning efficient. In this work, we formalize and study the problem of operator learning for TAMP. Central to this study is the view that operators define a lossy abstraction of the transition model of the underlying domain. We then propose a bottom-up relational learning method for operator learning and show how the learned operators can be used for planning in a TAMP system. Experimentally, we provide results in three domains, including long-horizon robotic planning tasks. We find our approach to substantially outperform several baselines, including three graph neural network-based model-free approaches based on recent work. Video: https://youtu.be/iVfpX9BpBRo

The problem of planning for a robot that operates in environments containing a large number of objects, taking actions to move itself through the world as well as to change the state of the objects, is known as task and motion planning (TAMP). TAMP problems contain elements of discrete task planning, discrete-continuous mathematical programming, and continuous motion planning, and thus cannot be effectively addressed by any of these fields directly. In this paper, we define a class of TAMP problems and survey algorithms for solving them, characterizing the solution methods in terms of their strategies for solving the continuous-space subproblems and their techniques for integrating the discrete and continuous components of the search.

Multi-object manipulation problems in continuous state and action spaces can be solved by planners that search over sampled values for the continuous parameters of operators. The efficiency of these planners depends critically on the effectiveness of the samplers used, but effective sampling in turn depends on details of the robot, environment, and task. Our strategy is to learn functions called specializers that generate values for continuous operator parameters, given a state description and values for the discrete parameters. Rather than trying to learn a single specializer for each operator from large amounts of data on a single task, we take a modular meta-learning approach. We train on multiple tasks and learn a variety of specializers that, on a new task, can be quickly adapted using relatively little data -- thus, our system "learns quickly to plan quickly" using these specializers. We validate our approach experimentally in simulated 3D pick-and-place tasks with continuous state and action spaces.

The state of the art practice in robotics planning is to script behaviors manually, where each behavior is typically generated using trajectory optimization. However, in order for robots to be able to act robustly and adapt to novel situations, they need to plan these activity sequences autonomously. Since the conditions and effects of these behaviors are tightly coupled through time, state and control variables, many problems require that the tasks of activity planning and trajectory optimization are considered together. There are two key issues underlying effective hybrid activity and trajectory planning: the sufficiently accurate modeling of robot dynamics and the capability of planning over long horizons. Hybrid activity and trajectory planners that employ mixed integer programming within a discrete time formulation are able to accurately model complex dynamics for robot vehicles, but are often restricted to relatively short horizons. On the other hand, current hybrid activity planners that employ continuous time formulations can handle longer horizons but they only allow actions to have continuous effects with constant rate of change, and restrict the allowed state constraints to linear inequalities. This is insufficient for many robotic applications and it greatly limits the expressivity of the problems that these approaches can solve. In this work we present the ScottyActivity planner, that is able to generate practical hybrid activity and motion plans over long horizons by employing recent methods in convex optimization combined with methods for planning with relaxed plan graphs and heuristic forward search. Unlike other continuous time planners, ScottyActivity can solve a broad class of robotic planning problems by supporting convex quadratic constraints on state variables and control variables that are jointly constrained and that affect multiple state variables simultaneously. In order to support planning over long horizons, ScottyActivity does not resort to time, state or control variable discretization. While straightforward formulations of consistency checks are not convex and do not scale, we present an efficient convex formulation, in the form of a Second Order Cone Program (SOCP), that is very fast to solve. We also introduce several new realistic domains that demonstrate the capabilities and scalability of our approach, and their simplified linear versions, that we use to compare with other state of the art planners. This work demonstrates the power of integrating advanced convex optimization techniques with discrete search methods and paves the way for extensions dealing with non-convex disjoint constraints, such as obstacle avoidance.