Guiding Long-Horizon Task and Motion Planning with Vision Language Models

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.

Embodied Uncertainty-Aware Object Segmentation

We introduce uncertainty-aware object instance segmentation (UncOS) and demonstrate its usefulness for embodied interactive segmentation. To deal with uncertainty in robot perception, we propose a method for generating a hypothesis distribution of object segmentation. We obtain a set of region-factored segmentation hypotheses together with confidence estimates by making multiple queries of large pre-trained models. This process can produce segmentation results that achieve state-of-the-art performance on unseen object segmentation problems. The output can also serve as input to a belief-driven process for selecting robot actions to perturb the scene to reduce ambiguity. We demonstrate the effectiveness of this method in real-robot experiments. Website: https://sites.google.com/view/embodied-uncertain-seg

Towards Practical Finite Sample Bounds for Motion Planning in TAMP

When using sampling-based motion planners, such as PRMs, in configuration spaces, it is difficult to determine how many samples are required for the PRM to find a solution consistently. This is relevant in Task and Motion Planning (TAMP), where many motion planning problems must be solved in sequence. We attempt to solve this problem by proving an upper bound on the number of samples that are sufficient, with high probability, to find a solution by drawing on prior work in deterministic sampling and sample complexity theory. We also introduce a numerical algorithm to compute a tighter number of samples based on the proof of the sample complexity theorem we apply to derive our bound. Our experiments show that our numerical bounding algorithm is tight within two orders of magnitude on planar planning problems and becomes looser as the problem's dimensionality increases. When deployed as a heuristic to schedule samples in a TAMP planner, we also observe planning time improvements in planar problems. While our experiments show much work remains to tighten our bounds, the ideas presented in this paper are a step towards a practical sample bound.

GCS*: Forward Heuristic Search on Implicit Graphs of Convex Sets

We consider large-scale, implicit-search-based solutions to the Shortest Path Problems on Graphs of Convex Sets (GCS). We propose GCS*, a forward heuristic search algorithm that generalizes A* search to the GCS setting, where a continuous-valued decision is made at each graph vertex, and constraints across graph edges couple these decisions, influencing costs and feasibility. Such mixed discrete-continuous planning is needed in many domains, including motion planning around obstacles and planning through contact. This setting provides a unique challenge for best-first search algorithms: the cost and feasibility of a path depend on continuous-valued points chosen along the entire path. We show that by pruning paths that are cost-dominated over their entire terminal vertex, GCS* can search efficiently while still guaranteeing cost optimality and completeness. To find satisficing solutions quickly, we also present a complete but suboptimal variation, pruning instead reachability-dominated paths. We implement these checks using polyhedral-containment or sampling-based methods. The sampling-based implementation is probabilistically complete and asymptotically cost optimal, and performs effectively even with minimal samples in practice. We demonstrate GCS* on planar pushing tasks where the combinatorial explosion of contact modes renders prior methods intractable and show it performs favorably compared to the state-of-the-art. Project website: https://shaoyuan.cc/research/gcs-star/

Scaling Exponents Across Parameterizations and Optimizers

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

Trust the PRoC3S: Solving Long-Horizon Robotics Problems with LLMs and Constraint Satisfaction

Recent developments in pretrained large language models (LLMs) applied to robotics have demonstrated their capacity for sequencing a set of discrete skills to achieve open-ended goals in simple robotic tasks. In this paper, we examine the topic of LLM planning for a set of continuously parameterized skills whose execution must avoid violations of a set of kinematic, geometric, and physical constraints. We prompt the LLM to output code for a function with open parameters, which, together with environmental constraints, can be viewed as a Continuous Constraint Satisfaction Problem (CCSP). This CCSP can be solved through sampling or optimization to find a skill sequence and continuous parameter settings that achieve the goal while avoiding constraint violations. Additionally, we consider cases where the LLM proposes unsatisfiable CCSPs, such as those that are kinematically infeasible, dynamically unstable, or lead to collisions, and re-prompt the LLM to form a new CCSP accordingly. Experiments across three different simulated 3D domains demonstrate that our proposed strategy, PRoC3S, is capable of solving a wide range of complex manipulation tasks with realistic constraints on continuous parameters much more efficiently and effectively than existing baselines.

Partially Observable Task and Motion Planning with Uncertainty and Risk Awareness

Integrated task and motion planning (TAMP) has proven to be a valuable approach to generalizable long-horizon robotic manipulation and navigation problems. However, the typical TAMP problem formulation assumes full observability and deterministic action effects. These assumptions limit the ability of the planner to gather information and make decisions that are risk-aware. We propose a strategy for TAMP with Uncertainty and Risk Awareness (TAMPURA) that is capable of efficiently solving long-horizon planning problems with initial-state and action outcome uncertainty, including problems that require information gathering and avoiding undesirable and irreversible outcomes. Our planner reasons under uncertainty at both the abstract task level and continuous controller level. Given a set of closed-loop goal-conditioned controllers operating in the primitive action space and a description of their preconditions and potential capabilities, we learn a high-level abstraction that can be solved efficiently and then refined to continuous actions for execution. We demonstrate our approach on several robotics problems where uncertainty is a crucial factor and show that reasoning under uncertainty in these problems outperforms previously proposed determinized planning, direct search, and reinforcement learning strategies. Lastly, we demonstrate our planner on two real-world robotics problems using recent advancements in probabilistic perception.

Practice Makes Perfect: Planning to Learn Skill Parameter Policies

One promising approach towards effective robot decision making in complex, long-horizon tasks is to sequence together parameterized skills. We consider a setting where a robot is initially equipped with (1) a library of parameterized skills, (2) an AI planner for sequencing together the skills given a goal, and (3) a very general prior distribution for selecting skill parameters. Once deployed, the robot should rapidly and autonomously learn to improve its performance by specializing its skill parameter selection policy to the particular objects, goals, and constraints in its environment. In this work, we focus on the active learning problem of choosing which skills to practice to maximize expected future task success. We propose that the robot should estimate the competence of each skill, extrapolate the competence (asking: "how much would the competence improve through practice?"), and situate the skill in the task distribution through competence-aware planning. This approach is implemented within a fully autonomous system where the robot repeatedly plans, practices, and learns without any environment resets. Through experiments in simulation, we find that our approach learns effective parameter policies more sample-efficiently than several baselines. Experiments in the real-world demonstrate our approach's ability to handle noise from perception and control and improve the robot's ability to solve two long-horizon mobile-manipulation tasks after a few hours of autonomous practice.

What Planning Problems Can A Relational Neural Network Solve?

Goal-conditioned policies are generally understood to be "feed-forward" circuits, in the form of neural networks that map from the current state and the goal specification to the next action to take. However, under what circumstances such a policy can be learned and how efficient the policy will be are not well understood. In this paper, we present a circuit complexity analysis for relational neural networks (such as graph neural networks and transformers) representing policies for planning problems, by drawing connections with serialized goal regression search (S-GRS). We show that there are three general classes of planning problems, in terms of the growth of circuit width and depth as a function of the number of objects and planning horizon, providing constructive proofs. We also illustrate the utility of this analysis for designing neural networks for policy learning.

Learning Reusable Manipulation Strategies

Humans demonstrate an impressive ability to acquire and generalize manipulation "tricks." Even from a single demonstration, such as using soup ladles to reach for distant objects, we can apply this skill to new scenarios involving different object positions, sizes, and categories (e.g., forks and hammers). Additionally, we can flexibly combine various skills to devise long-term plans. In this paper, we present a framework that enables machines to acquire such manipulation skills, referred to as "mechanisms," through a single demonstration and self-play. Our key insight lies in interpreting each demonstration as a sequence of changes in robot-object and object-object contact modes, which provides a scaffold for learning detailed samplers for continuous parameters. These learned mechanisms and samplers can be seamlessly integrated into standard task and motion planners, enabling their compositional use.