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Register a new userMotion Planning Transformers: One Model to Plan Them All
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Jacob John Johnson
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Transformers have become the powerhouse of natural language processing and recently found use in computer vision tasks. Their effective use of attention can be used in other contexts as well, and in this paper, we propose a transformer-based approach for efficiently solving the complex motion planning problems. Traditional neural network-based motion planning uses convolutional networks to encode the planning space, but these methods are limited to fixed map sizes, which is often not realistic in the real-world. Our approach first identifies regions on the map using transformers to provide attention to map areas likely to include the best path, and then applies local planners to generate the final collision-free path. We validate our method on a variety of randomly generated environments with different map sizes, demonstrating reduction in planning complexity and achieving comparable accuracy to traditional planners.
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In this paper we propose a novel end-to-end learnable network that performs joint perception, prediction and motion planning for self-driving vehicles and produces interpretable intermediate representations. Unlike existing neural motion planners, our motion planning costs are consistent with our perception and prediction estimates. This is achieved by a novel differentiable semantic occupancy representation that is explicitly used as cost by the motion planning process. Our network is learned end-to-end from human demonstrations. The experiments in a large-scale manual-driving dataset and closed-loop simulation show that the proposed model significantly outperforms state-of-the-art planners in imitating the human behaviors while producing much safer trajectories.
Neural network quantization methods often involve simulating the quantization process during training, making the trained model highly dependent on the target bit-width and precise way quantization is performed. Robust quantization offers an alternative approach with improved tolerance to different classes of data-types and quantization policies. It opens up new exciting applications where the quantization process is not static and can vary to meet different circumstances and implementations. To address this issue, we propose a method that provides intrinsic robustness to the model against a broad range of quantization processes. Our method is motivated by theoretical arguments and enables us to store a single generic model capable of operating at various bit-widths and quantization policies. We validate our methods effectiveness on different ImageNet models.
The analytical solution of the three--dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the very same system of equations, each of them with particular initial conditions. We compare with the common two--dimensional approximations in textbooks. A previously unnoticed pattern in the three--dimensional Foucault pendulum attractor is presented.
One Monad to Prove Them All is a modern fairy tale about curiosity and perseverance, two important properties of a successful PhD student. We follow the PhD student Mona on her adventure of proving properties about Haskell programs in the proof assistant Coq. On the one hand, as a PhD student in computer science Mona observes an increasing demand for correct software products. In particular, because of the large amount of existing software, verifying existing software products becomes more important. Verifying programs in the functional programming language Haskell is no exception. On the other hand, Mona is delighted to see that communities in the area of theorem proving are becoming popular. Thus, Mona sets out to learn more about the interactive theorem prover Coq and verifying Haskell programs in Coq. To prove properties about a Haskell function in Coq, Mona has to translate the function into Coq code. As Coq programs have to be total and Haskell programs are often not, Mona has to model partiality explicitly in Coq. In her quest for a solution Mona finds an ancient manuscript that explains how properties about Haskell functions can be proven in the proof assistant Agda by translating Haskell programs into monadic Agda programs. By instantiating the monadic program with a concrete monad instance the proof can be performed in either a total or a partial setting. Mona discovers that the proposed transformation does not work in Coq due to a restriction in the termination checker. In fact the transformation does not work in Agda anymore as well, as the termination checker in Agda has been improved. We follow Mona on an educational journey through the land of functional programming where she learns about concepts like free monads and containers as well as basics and restrictions of proof assistants like Coq. These concepts are well-known individually, but their interplay gives rise to a solution for Monas problem based on the originally proposed monadic tranformation that has not been presented before. When Mona starts to test her approach by proving a statement about simple Haskell functions, she realizes that her approach has an additional advantage over the original idea in Agda. Monas final solution not only works for a specific monad instance but even allows her to prove monad-generic properties. Instead of proving properties over and over again for specific monad instances she is able to prove properties that hold for all monads representable by a container-based instance of the free monad. In order to strengthen her confidence in the practicability of her approach, Mona evaluates her approach in a case study that compares two implementations for queues. In order to share the results with other functional programmers the fairy tale is available as a literate Coq file. If you are a citizen of the land of functional programming or are at least familiar with its customs, had a journey that involved reasoning about functional programs of your own, or are just a curious soul looking for the next story about monads and proofs, then this tale is for you.
Kinodynamic Motion Planning (KMP) is to find a robot motion subject to concurrent kinematics and dynamics constraints. To date, quite a few methods solve KMP problems and those that exist struggle to find near-optimal solutions and exhibit high computational complexity as the planning space dimensionality increases. To address these challenges, we present a scalable, imitation learning-based, Model-Predictive Motion Planning Networks framework that quickly finds near-optimal path solutions with worst-case theoretical guarantees under kinodynamic constraints for practical underactuated systems. Our framework introduces two algorithms built on a neural generator, discriminator, and a parallelizable Model Predictive Controller (MPC). The generator outputs various informed states towards the given target, and the discriminator selects the best possible subset from them for the extension. The MPC locally connects the selected informed states while satisfying the given constraints leading to feasible, near-optimal solutions. We evaluate our algorithms on a range of cluttered, kinodynamically constrained, and underactuated planning problems with results indicating significant improvements in computation times, path qualities, and success rates over existing methods.
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