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Register a new userLearning Sampling Distributions Using Local 3D Workspace Decompositions for Motion Planning in High Dimensions
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Added by
Constantinos Chamzas
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Earlier work has shown that reusing experience from prior motion planning problems can improve the efficiency of similar, future motion planning queries. However, for robots with many degrees-of-freedom, these methods exhibit poor generalization across different environments and often require large datasets that are impractical to gather. We present SPARK and FLAME , two experience-based frameworks for sampling-based planning applicable to complex manipulators in 3 D environments. Both combine samplers associated with features from a workspace decomposition into a global biased sampling distribution. SPARK decomposes the environment based on exact geometry while FLAME is more general, and uses an octree-based decomposition obtained from sensor data. We demonstrate the effectiveness of SPARK and FLAME on a Fetch robot tasked with challenging pick-and-place manipulation problems. Our approaches can be trained incrementally and significantly improve performance with only a handful of examples, generalizing better over diverse tasks and environments as compared to prior approaches.
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A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or deterministically to uniformly cover the state space. Yet, the motion of many robotic systems is often restricted to small regions of the state space, due to, for example, differential constraints or collision-avoidance constraints. To accelerate the planning process, it is thus desirable to devise non-uniform sampling strategies that favor sampling in those regions where an optimal solution might lie. This paper proposes a methodology for non-uniform sampling, whereby a sampling distribution is learned from demonstrations, and then used to bias sampling. The sampling distribution is computed through a conditional variational autoencoder, allowing sample generation from the latent space conditioned on the specific planning problem. This methodology is general, can be used in combination with any sampling-based planner, and can effectively exploit the underlying structure of a planning problem while maintaining the theoretical guarantees of sampling-based approaches. Specifically, on several planning problems, the proposed methodology is shown to effectively learn representations for the relevant regions of the state space, resulting in an order of magnitude improvement in terms of success rate and convergence to the optimal cost.
Sampling-based motion planners have experienced much success due to their ability to efficiently and evenly explore the state space. However, for many tasks, it may be more efficient to not uniformly explore the state space, especially when there is prior information about its structure. Previous methods have attempted to modify the sampling distribution using hand selected heuristics that can work well for specific environments but not universally. In this paper, a policy- search based method is presented as an adaptive way to learn implicit sampling distributions for different environments. It utilizes information from past searches in similar environments to generate better distributions in novel environments, thus reducing overall computational cost. Our method can be incor- porated with a variety of sampling-based planners to improve performance. Our approach is validated on a number of tasks, including a 7DOF robot arm, showing marked improvement in number of collision checks as well as number of nodes expanded compared with baseline methods.
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 a 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 from the recent literature. Video: https://youtu.be/iVfpX9BpBRo Code: https://git.io/JCT0g
Sampling-based motion planners rely on incremental densification to discover progressively shorter paths. After computing feasible path $xi$ between start $x_s$ and goal $x_t$, the Informed Set (IS) prunes the configuration space $mathcal{C}$ by conservatively eliminating points that cannot yield shorter paths. Densification via sampling from this Informed Set retains asymptotic optimality of sampling from the entire configuration space. For path length $c(xi)$ and Euclidean heuristic $h$, $IS = { x | x in mathcal{C}, h(x_s, x) + h(x, x_t) leq c(xi) }$. Relying on the heuristic can render the IS especially conservative in high dimensions or complex environments. Furthermore, the IS only shrinks when shorter paths are discovered. Thus, the computational effort from each iteration of densification and planning is wasted if it fails to yield a shorter path, despite improving the cost-to-come for vertices in the search tree. Our key insight is that even in such a failure, shorter paths to vertices in the search tree (rather than just the goal) can immediately improve the planners sampling strategy. Guided Incremental Local Densification (GuILD) leverages this information to sample from Local Subsets of the IS. We show that GuILD significantly outperforms uniform sampling of the Informed Set in simulated $mathbb{R}^2$, $SE(2)$ environments and manipulation tasks in $mathbb{R}^7$.
This paper presents c2g-HOF networks which learn to generate cost-to-go functions for manipulator motion planning. The c2g-HOF architecture consists of a cost-to-go function over the configuration space represented as a neural network (c2g-network) as well as a Higher Order Function (HOF) network which outputs the weights of the c2g-network for a given input workspace. Both networks are trained end-to-end in a supervised fashion using costs computed from traditional motion planners. Once trained, c2g-HOF can generate a smooth and continuous cost-to-go function directly from workspace sensor inputs (represented as a point cloud in 3D or an image in 2D). At inference time, the weights of the c2g-network are computed very efficiently and near-optimal trajectories are generated by simply following the gradient of the cost-to-go function. We compare c2g-HOF with traditional planning algorithms for various robots and planning scenarios. The experimental results indicate that planning with c2g-HOF is significantly faster than other motion planning algorithms, resulting in orders of magnitude improvement when including collision checking. Furthermore, despite being trained from sparsely sampled trajectories in configuration space, c2g-HOF generalizes to generate smoother, and often lower cost, trajectories. We demonstrate cost-to-go based planning on a 7 DoF manipulator arm where motion planning in a complex workspace requires only 0.13 seconds for the entire trajectory.
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