Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. Reinforcement learning (RL), building on Bellman’s optimality equation, naturally optimizes for a single goal, yet can be made goal-directed by augmenting the state with the goal. Instead, we propose a new RL framework, derived from a dynamic programming equation for the all pairs shortest path (APSP) problem, which naturally solves goal-directed queries. We show that this approach has computational benefits for both standard and approximate dynamic programming. Interestingly, our formulation prescribes a novel protocol for computing a trajectory: instead of predicting the next state given its predecessor, as in standard RL, a goal-conditioned trajectory is constructed by first predicting an intermediate state between start and goal, partitioning the trajectory into two. Then, recursively, predicting intermediate points on each sub-segment, until a complete trajectory is obtained. We call this trajectory structure a sub-goal tree. Building on it, we additionally extend the policy gradient methodology to recursively predict sub-goals, resulting in novel goal-based algorithms. Finally, we apply our method to neural motion planning, where we demonstrate significant improvements compared to standard RL on navigating a 7-DoF robot arm between obstacles.

Tasks in mobile manipulation planning often require thousands of individual motions to complete. Such tasks require reasoning about complex goals as well as the feasibility of movements in configuration space. In discrete representations, planning complexity is exponential in the length of the plan. In mobile manipulation, parameters for an action often draw from a continuous space, so we must also cope with an infinite branching factor. Task and motion planning (TAMP) methods integrate logical search over high-level actions with geometric reasoning to address this challenge. We present an algorithm that searches the space of possible task and motion plans and uses statistical machine learning to guide the search process. Our contributions are as follows: 1) we present a complete algorithm for TAMP; 2) we present a randomized local search algorithm for plan refinement that is easily formulated as a Markov decision process (MDP); 3) we apply reinforcement learning (RL) to learn a policy for this MDP; 4) we learn from expert demonstrations to efficiently search the space of high-level task plans, given options that address different (potential) infeasibilities; and 5) we run experiments to evaluate our system in a variety of simulated domains. We show significant improvements in performance over prior work.

The execution of long-horizon tasks under uncertainty is a fundamental challenge in robotics. Recent approaches have made headway on these tasks with an integration of task and motion planning. In this paper, we present Interfaced Belief Space Planning (IBSP): a modular approach to task and motion planning in belief space. We use a task-independent interface layer to combine an off-the-shelf classical planner with motion planning and inference. We determinize the problem under the maximum likelihood observation assumption to obtain a deterministic representation where successful plans generate goal-directed observations. We leverage properties of maximum likelihood observation determinizations to obtain a simple representation of (optimistic) belief space dynamics that is well-suited to planning. Our interface is implemented with standard belief state queries, requiring only the ability to sample, compute unnormalized likelihoods, and compute maximum likelihood states. Our contribution is a novel algorithm for task and motion planning in belief space that has minimal dependence on the details of the inference engine used. IBSP can work with a broad class of black box state estimators, with zero changes to the algorithm. We validate our approach in simulated tasks for the PR2 that account for continuous state, different types of initial state distributions, and negative observations.