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Register a new userTraversing Environments Using Possibility Graphs with Multiple Action Types
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Michael Grey
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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Locomotion for legged robots poses considerable challenges when confronted by obstacles and adverse environments. Footstep planners are typically only designed for one mode of locomotion, but traversing unfavorable environments may require several forms of locomotion to be sequenced together, such as walking, crawling, and jumping. Multi-modal motion planners can be used to address some of these problems, but existing implementations tend to be time-consuming and are limited to quasi-static actions. This paper presents a motion planning method to traverse complex environments using multiple categories of continuous actions. To this end, this paper formulates and exploits the Possibility Graph---which uses high-level approximations of constraint manifolds to rapidly explore the possibility of actions---to utilize lower-level single-action motion planners more effectively. We show that the Possibility Graph can quickly find routes through several different challenging environments which require various combinations of actions in order to traverse.
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We present a theoretical analysis of a recent whole body motion planning method, the Randomized Possibility Graph, which uses a high-level decomposition of the feasibility constraint manifold in order to rapidly find routes that may lead to a solution. These routes are then examined by lower-level planners to determine feasibility. In this paper, we show that this approach is probabilistically complete for bipedal robots performing quasi-static walking in semi-unstructured environments. Furthermore, we show that the decomposition into higher and lower level planners allows for a considerably higher rate of convergence in the probability of finding a solution when one exists. We illustrate this improved convergence with a series of simulated scenarios.
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This paper is a study of 2D manipulation without sensing and planning, by exploring the effects of unplanned randomized action sequences on 2D object pose uncertainty. Our approach follows the work of Erdmann and Masons sensorless reorienting of an object into a completely determined pose, regardless of its initial pose. While Erdmann and Mason proposed a method using Newtonian mechanics, this paper shows that under some circumstances, a long enough sequence of random actions will also converge toward a determined final pose of the object. This is verified through several simulation and real robot experiments where randomized action sequences are shown to reduce entropy of the object pose distribution. The effects of varying object shapes, action sequences, and surface friction are also explored.
We present a novel method for safely navigating a robot in unknown and uneven outdoor terrains. Our approach trains a novel Deep Reinforcement Learning (DRL)-based network with channel and spatial attention modules using a novel reward function to compute an attention map of the environment. The attention map identifies regions in the environments elevation map with high elevation gradients where the robot could have reduced stability or even flip over. We transform this attention map into a 2D navigation cost-map, which encodes the planarity (level of flatness) of the terrain. Using the cost-map, we formulate a novel method for computing local least-cost waypoints leading to the robots goal and integrate our approach with DWA-RL, a state-of-the-art navigation method. Our approach guarantees safe, locally least-cost paths and dynamically feasible robot velocities in highly uneven terrains. Our hybrid approach also leads to a low sim-to-real gap, which arises while training DRL networks. We observe an improvement in terms of success rate, the cumulative elevation gradient of the robots trajectory, and the safety of the robots velocity. We evaluate our method on a real Husky robot in highly uneven real-world terrains and demonstrate its benefits.
Computing the dominant Fourier coefficients of a vector is a common task in many fields, such as signal processing, learning theory, and computational complexity. In the Sparse Fast Fourier Transform (Sparse FFT) problem, one is given oracle access to a $d$-dimensional vector $x$ of size $N$, and is asked to compute the best $k$-term approximation of its Discrete Fourier Transform, quickly and using few samples of the input vector $x$. While the sample complexity of this problem is quite well understood, all previous approaches either suffer from an exponential dependence of runtime on the dimension $d$ or can only tolerate a trivial amount of noise. This is in sharp contrast with the classical FFT algorithm of Cooley and Tukey, which is stable and completely insensitive to the dimension of the input vector: its runtime is $O(Nlog N)$ in any dimension $d$. In this work, we introduce a new high-dimensional Sparse FFT toolkit and use it to obtain new algorithms, both on the exact, as well as in the case of bounded $ell_2$ noise. This toolkit includes i) a new strategy for exploring a pruned FFT computation tree that reduces the cost of filtering, ii) new structural properties of adaptive aliasing filters recently introduced by Kapralov, Velingker and ZandiehSODA19, and iii) a novel lazy estimation argument, suited to reducing the cost of estimation in FFT tree-traversal approaches. Our robust algorithm can be viewed as a highly optimized sparse, stable extension of the Cooley-Tukey FFT algorithm. Finally, we explain the barriers we have faced by proving a conditional quadratic lower bound on the running time of the well-studied non-equispaced Fourier transform problem. This resolves a natural and frequently asked question in computational Fourier transforms. Lastly, we provide a preliminary experimental evaluation comparing the runtime of our algorithm to FFTW and SFFT 2.0.
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