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Journal ArticleDOI

CHOMP: Covariant Hamiltonian optimization for motion planning

TL;DR: CHOMP (covariant Hamiltonian optimization for motion planning), a method for trajectory optimization invariant to reparametrization, uses functional gradient techniques to iteratively improve the quality of an initial trajectory, optimizing a functional that trades off between a smoothness and an obstacle avoidance component.
Abstract: In this paper, we present CHOMP (covariant Hamiltonian optimization for motion planning), a method for trajectory optimization invariant to reparametrization. CHOMP uses functional gradient techniques to iteratively improve the quality of an initial trajectory, optimizing a functional that trades off between a smoothness and an obstacle avoidance component. CHOMP can be used to locally optimize feasible trajectories, as well as to solve motion planning queries, converging to low-cost trajectories even when initialized with infeasible ones. It uses Hamiltonian Monte Carlo to alleviate the problem of convergence to high-cost local minima (and for probabilistic completeness), and is capable of respecting hard constraints along the trajectory. We present extensive experiments with CHOMP on manipulation and locomotion tasks, using seven-degree-of-freedom manipulators and a rough-terrain quadruped robot.

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Citations
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Journal ArticleDOI
TL;DR: A sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and an efficient formulation of the no-collisions constraint that directly considers continuous-time safety are presented.
Abstract: We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naA¯ve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt. We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http://rll.berkeley.edu/trajopt/ijrr.

655 citations


Cites background or methods from "CHOMP: Covariant Hamiltonian optimi..."

  • ...…that TrajOpt was computationally faster than the alternatives on the considered benchmark (around 100 − 200 ms on arm-planning problems and solves full body 18 DOF planning problems for the PR2 robot in under a second on an Intel i7 3.5 GHz CPU), and solved a larger fraction of the problems given…...

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  • ...…art, our algorithm differs fundamentally in the following two ways: 1) Distance fields versus convex-convex collision checking: CHOMP uses the Euclidean distance transform—a precomputed function on a voxel grid that specifies the distance to the nearest obstacle, or the distance out of an obstacle....

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  • ...However, CHOMP (Covariant Hamiltonian Optimization for Motion Planning) [41, 61] revived interest in trajectory optimization methods by demonstrating the effectiveness on several robotic platforms including the HERB mobile manipulation platform, the LittleDog quadruped, and the PR2 robot....

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Book
27 Mar 2018
TL;DR: Imitation learning as discussed by the authors is a generalization of reinforcement learning, where a teacher can demonstrate a desired behavior rather than attempting to manually engineer it, which is referred to as imitation learning.
Abstract: As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a teacher to demonstrate a desired behavior rather than attempt to manually engineer it. This process of learning from demonstrations, and the study of algorithms to do so, is called imitation learning. This work provides an introduction to imitation learning. It covers the underlying assumptions, approaches, and how they relate; the rich set of algorithms developed to tackle the problem; and advice on effective tools and implementation. We intend this paper to serve two audiences. First, we want to familiarize machine learning experts with the challenges of imitation learning, particularly those arising in robotics, and the interesting theoretical and practical distinctions between it and more familiar frameworks like statistical supervised learning theory and reinforcement learning. Second, we want to give roboticists and experts in applied artificial intelligence a broader appreciation for the frameworks and tools available for imitation learning. We pay particular attention to the intimate connection between imitation learning approaches and those of structured prediction Daume III et al. [2009]. To structure this discussion, we categorize imitation learning techniques based on the following key criteria which drive algorithmic decisions: 1) The structure of the policy space. Is the learned policy a time-index trajectory (trajectory learning), a mapping from observations to actions (so called behavioral cloning [Bain and Sammut, 1996]), or the result of a complex optimization or planning problem at each execution as is common in inverse optimal control methods [Kalman, 1964, Moylan and Anderson, 1973]. 2) The information available during training and testing. In particular, is the learning algorithm privy to the full state that the teacher possess? Is the learner able to interact with the teacher and gather corrections or more data? Does the learner have a (typically a priori) model of the system with which it interacts? Does the learner have access to the reward (cost) function that the teacher is attempting to optimize? 3) The notion of success. Different algorithmic approaches provide varying guarantees on the resulting learned behavior. These guarantees range from weaker (e.g., measuring disagreement with the agent’s decision) to stronger (e.g., providing guarantees on the performance of the learner with respect to a true cost function, either known or unknown). We organize our work by paying particular attention to distinction (1): dividing imitation learning into directly replicating desired behavior (sometimes called behavioral cloning) and learning the hidden objectives of the desired behavior from demonstrations (called inverse optimal control or inverse reinforcement learning [Russell, 1998]). In the latter case, behavior arises as the result of an optimization problem solved for each new instance that the learner faces. In addition to method analysis, we discuss the design decisions a practitioner must make when selecting an imitation learning approach. Moreover, application examples—such as robots that play table tennis [Kober and Peters, 2009], programs that play the game of Go [Silver et al., 2016], and systems that understand natural language [Wen et al., 2015]— illustrate the properties and motivations behind different forms of imitation learning. We conclude by presenting a set of open questions and point towards possible future research directions for machine learning.

554 citations

Proceedings ArticleDOI
23 Jun 2013
TL;DR: A novel approach for incorporating collision avoidance into trajectory optimization as a method of solving robotic motion planning problems, solving a suite of 7-degree-of-freedom arm-planning problems and 18-DOF full-body planning problems and benchmarked the algorithm against several other motion planning algorithms.
Abstract: We present a novel approach for incorporating collision avoidance into trajectory optimization as a method of solving robotic motion planning problems. At the core of our approach are (i) A sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary. (ii) An efficient formulation of the no-collisions constraint that directly considers continuous-time safety and enables the algorithm to reliably solve motion planning problems, including problems involving thin and complex obstacles. We benchmarked our algorithm against several other motion planning algorithms, solving a suite of 7-degree-of-freedom (DOF) arm-planning problems and 18-DOF full-body planning problems. We compared against sampling-based planners from OMPL, and we also compared to CHOMP, a leading approach for trajectory optimization. Our algorithm was faster than the alternatives, solved more problems, and yielded higher quality paths. Experimental evaluation on the following additional problem types also confirmed the speed and effectiveness of our approach: (i) Planning foot placements with 34 degrees of freedom (28 joints + 6 DOF pose) of the Atlas humanoid robot as it maintains static stability and has to negotiate environmental constraints. (ii) Industrial box picking. (iii) Real-world motion planning for the PR2 that requires considering all degrees of freedom at the same time.

471 citations


Cites background from "CHOMP: Covariant Hamiltonian optimi..."

  • ...This version is not yet publicly available at the time of publication, but it was made available to us by the authors [28]....

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Journal ArticleDOI
TL;DR: In the context of robotics and automation, learning from demonstration (LfD) is the paradigm in which robots acquire new skills by learning to imitate an expert.
Abstract: In the context of robotics and automation, learning from demonstration (LfD) is the paradigm in which robots acquire new skills by learning to imitate an expert. The choice of LfD over other robot ...

354 citations


Cites methods from "CHOMP: Covariant Hamiltonian optimi..."

  • ...Methods that utilize motion planning (5, 6) aim to overcome some of the burdens of traditional robot programming by eliminating the need to specify the entire sequence of low-level actions, such as trajectories....

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Proceedings ArticleDOI
01 Jan 2017
TL;DR: This work proposes a method to incrementally build ESDFs from Truncated Signed Distance Fields (TSDFs), a common implicit surface representation used in computer graphics and vision, and shows that it can build TSDFs faster than Octomaps, and that it is more accurate than occupancy maps.
Abstract: Micro Aerial Vehicles (MAVs) that operate in unstructured, unexplored environments require fast and flexible local planning, which can replan when new parts of the map are explored. Trajectory optimization methods fulfill these needs, but require obstacle distance information, which can be given by Euclidean Signed Distance Fields (ESDFs). We propose a method to incrementally build ESDFs from Truncated Signed Distance Fields (TSDFs), a common implicit surface representation used in computer graphics and vision. TSDFs are fast to build and smooth out sensor noise over many observations, and are designed to produce surface meshes. We show that we can build TSDFs faster than Octomaps, and that it is more accurate to build ESDFs out of TSDFs than occupancy maps. Our complete system, called voxblox, is available as open source and runs in real-time on a single CPU core. We validate our approach on-board an MAV, by using our system with a trajectory optimization local planner, entirely on-board and in real-time.

316 citations


Cites background from "CHOMP: Covariant Hamiltonian optimi..."

  • ...One existing work that combines ESDFs and TSDFs is that of Wagner et al., who use KinectFusion combined with CHOMP for planning for an armed robot [15], [16]....

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  • ...For example, trajectory optimization-based planners, such as CHOMP [7], require distances to obstacles and collision gradient information over the entire workspace of the robot....

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References
More filters
Book
21 Oct 1957
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Abstract: From the Publisher: An introduction to the mathematical theory of multistage decision processes, this text takes a functional equation approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, strategies behind multistage games, and Markovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls a rich lode of applications and research topics. 1957 edition. 37 figures.

14,187 citations

Journal ArticleDOI
TL;DR: The multidimensional binary search tree (or k-d tree) as a data structure for storage of information to be retrieved by associative searches is developed and it is shown to be quite efficient in its storage requirements.
Abstract: This paper develops the multidimensional binary search tree (or k-d tree, where k is the dimensionality of the search space) as a data structure for storage of information to be retrieved by associative searches. The k-d tree is defined and examples are given. It is shown to be quite efficient in its storage requirements. A significant advantage of this structure is that a single data structure can handle many types of queries very efficiently. Various utility algorithms are developed; their proven average running times in an n record file are: insertion, O(log n); deletion of the root, O(n(k-1)/k); deletion of a random node, O(log n); and optimization (guarantees logarithmic performance of searches), O(n log n). Search algorithms are given for partial match queries with t keys specified [proven maximum running time of O(n(k-t)/k)] and for nearest neighbor queries [empirically observed average running time of O(log n).] These performances far surpass the best currently known algorithms for these tasks. An algorithm is presented to handle any general intersection query. The main focus of this paper is theoretical. It is felt, however, that k-d trees could be quite useful in many applications, and examples of potential uses are given.

7,159 citations


"CHOMP: Covariant Hamiltonian optimi..." refers methods in this paper

  • ...Then the distance field computation is reduced to a minimization across a set of distance field primitives pre-computed for each object in O: D( x) = min O∈O ( TFWFO )−1 x (20) Hierarchical representations, such as the k-d tree (Bentley, 1975), may be utilized to speed up this computation....

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  • ...Hierarchical representations, such as the k-d tree (Bentley, 1975), may be utilized to speed up this computation....

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Journal ArticleDOI
TL;DR: This paper reformulated the manipulator con trol problem as direct control of manipulator motion in operational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and geometric transformation.
Abstract: This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, tradi tionally considered a high level planning problem, can be effectively distributed between different levels of control, al lowing real-time robot operations in a complex environment. This method has been extended to moving obstacles by using a time-varying artificial patential field. We have applied this obstacle avoidance scheme to robot arm mechanisms and have used a new approach to the general problem of real-time manipulator control. We reformulated the manipulator con trol problem as direct control of manipulator motion in oper ational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and kine matic transformation. Outside the obstacles' regions of influ ence, we caused the end effector to move in a straight line with an...

6,515 citations

MonographDOI
01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

6,340 citations


"CHOMP: Covariant Hamiltonian optimi..." refers result in this paper

  • ...As our results illustrate, CHOMP demonstrates attractive computational efficiency and convergence even in cluttered obstacle environments....

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Journal ArticleDOI
01 Aug 1996
TL;DR: Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).
Abstract: A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collision-free configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).

4,977 citations