CHOMP: Covariant Hamiltonian optimization for motion planning

By Matthew Zucker, Nathan Ratliff Google, Anca D Dragan, Mihail Pivtoraiko, Matthew Klingensmith, Nathan D. Ratliff, Christopher M. Dellin, J. Bagnell, Siddhartha S. Srinivasa, Pittsburgh Pa and 1 more. Int. J. Robotics Res., 2013

885 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/f358d770a1c31a67a06d467827bfde9f298278ac

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Citations in the corpus

Guiding Trajectory Optimization by Demonstrated Distributions (2017, methodology): “Optimization-based methods such as Covariant Hamiltonian Optimization for Motion Planning (CHOMP) [3] andAuthor: Citation of Figure 1 is missing in text.”
Robust and Efficient Quadrotor Trajectory Generation for Fast Autonomous Flight (2019, methodology): “[10] generates discrete-time trajectories by minimizing its smoothness and collision costs using gradient descent methods.”
Real-Time Perception Meets Reactive Motion Generation (2017, methodology): “SDFs provide a way to perform fast collision checking, which has been exploited in many motion optimization works [9], [29], [30].”
Differentiable Gaussian Process Motion Planning (2019, methodology): “Thus, we use an external task loss as a regularizer that encourages smoothness and obstacle avoidance, while respecting start and goal constraints, as is often used in motion planning [24]: where F smooth corresponds to the GP prior error and F obs is the obstacle cost that are described in Eq.”
Recent Advances in Robot Learning from Demonstration (2020, methodology): “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.”
Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization (2013, background): “This version is not yet publicly available at the time of publication, but it was made available to us by the authors [28].”
Motion planning with sequential convex optimization and convex collision checking (2014, methodology): “In this work, in addition to providing a revised and extended version of our work [43], (i) we describe an extension to the algorithm described in the RSS paper to plan trajectories in SE (3) , and (ii) we provide a discussion on cases where trajectory optimization fails to ﬁnd a feasible solution.”
A unified framework for coordinated multi-arm motion planning (2018, methodology): “Similar to (Zucker et al. 2013), we simplify the representation of the robot’s structure by fitting spheres to each joint and its adjoining physical structure as shown in Figure 6.”
An Algorithmic Perspective on Imitation Learning (2018, methodology): “planning literature, the term “via-point” is used similarly to the term keyframe [Pastor et al., 2009, Paraschos et al., 2013, Zucker et al., 2013].”
Geometrically Constrained Trajectory Optimization for Multicopters (2021, methodology): “This can be alleviated by interleaving sampling-based or graph-search-based strategies into our framework, as proposed in [74]–[76].”
Spatial adaption of robot trajectories based on laplacian trajectory editing (2015, methodology): “Closely related to this approach are explicit trajectory optimization schemes as CHOMP or TrajOpt (Zucker et al. 2013; Schulman et al. 2014).”
Towards Robust Skill Generalization: Unifying Learning from Demonstration and Motion Planning (2017, background): “Similarly, Dragan et al. [15] show that trajectory adaptation to new start/goal states via dynamic movement primitives (DMPs) [16] is a result of pre-specified Hilbert norm minimization based on finite differences, thus drawing connections to CHOMP [17], a gradient-based trajectory optimizer.”
Optimization-Based Collision Avoidance (2017, neutral): “One way of dealing with obstacle avoidance is to use unconstrained optimization, in which case the objective function is augmented with “artificial potential fields” that represent the obstacles [32, 33, 34, 35, 36].”
Voxblox: Incremental 3D Euclidean Signed Distance Fields for on-board MAV planning (2016, background): “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].”
Movement primitives via optimization (2015, methodology): “We do so by proving that when updating the endpoints, the moving target tracked by the dynamical system adapts (as in Fig.1(b)) using the very same norm that we often use in trajectory optimizers like CHOMP [17] (we denote this norm by A).”
Learning position and orientation dynamics from demonstrations via contraction analysis (2018, methodology): “Other categories of LfD methods include sampling-based methods (e.g., Bowen and Alterovitz 2014), optimization-based approaches (e.g., Dragan et al. 2015; Zucker et al. 2013), geometric methods (e.g., Ahmadzadeh et al. 2017), and key-frame-based methods (e.g., Akgun et al. 2012).”
Learning preferences for manipulation tasks from online coactive feedback (2015, methodology): “Such preferences are often encoded as a cost which planners optimize [26, 50, 63].”