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1,133
Learning movement primitives
- International Symposium on Robotics Research (ISRR2003
, 2004
"... Abstract. This paper discusses a comprehensive framework for modular motor control based on a recently developed theory of dynamic movement primitives (DMP). DMPs are a formulation of movement primitives with autonomous nonlinear differential equations, whose time evolution creates smooth kinematic ..."
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Cited by 102 (14 self)
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Abstract. This paper discusses a comprehensive framework for modular motor control based on a recently developed theory of dynamic movement primitives (DMP). DMPs are a formulation of movement primitives with autonomous nonlinear differential equations, whose time evolution creates smooth kinematic control policies. Model-based control theory is used to convert the outputs of these policies into motor commands. By means of coupling terms, on-line modifications can be incorporated into the time evolution of the differential equations, thus providing a rather flexible and reactive framework for motor planning and execution. The linear parameterization of DMPs lends itself naturally to supervised learning from demonstration. Moreover, the temporal, scale, and translation invariance of the differential equations with respect to these parameters provides a useful means for movement recognition. A novel reinforcement learning technique based on natural stochastic policy gradients allows a general approach of improving DMPs by trial and error learning with respect to almost arbitrary optimization criteria. We demonstrate the different ingredients of the DMP approach in various examples, involving skill learning from demonstration on the humanoid robot DB, and learning biped walking from demonstration in simulation, including self-improvement of the movement patterns towards energy efficiency through resonance tuning. 1
The Stochastic Motion Roadmap: A sampling framework for planning with Markov motion uncertainty
- in Robotics: Science and Systems III (Proc. RSS 2007
, 2008
"... Abstract — We present a new motion planning framework that explicitly considers uncertainty in robot motion to maximize the probability of avoiding collisions and successfully reaching a goal. In many motion planning applications ranging from maneuvering vehicles over unfamiliar terrain to steering ..."
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Cited by 96 (20 self)
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Abstract — We present a new motion planning framework that explicitly considers uncertainty in robot motion to maximize the probability of avoiding collisions and successfully reaching a goal. In many motion planning applications ranging from maneuvering vehicles over unfamiliar terrain to steering flexible medical needles through human tissue, the response of a robot to commanded actions cannot be precisely predicted. We propose to build a roadmap by sampling collision-free states in the configuration space and then locally sampling motions at each state to estimate state transition probabilities for each possible action. Given a query specifying initial and goal configurations, we use the roadmap to formulate a Markov Decision Process (MDP), which we solve using Infinite Horizon Dynamic Programming in polynomial time to compute stochastically optimal plans. The Stochastic Motion Roadmap (SMR) thus combines a sampling-based roadmap representation of the configuration space, as in PRM’s, with the well-established theory of MDP’s. Generating both states and transition probabilities by sampling is far more flexible than previous Markov motion planning approaches based on problem-specific or grid-based discretizations. We demonstrate the SMR framework by applying it to nonholonomic steerable needles, a new class of medical needles that follow curved paths through soft tissue, and confirm that SMR’s generate motion plans with significantly higher probabilities of success compared to traditional shortest-path plans. I.
Proto-value functions: A laplacian framework for learning representation and control in markov decision processes
- Journal of Machine Learning Research
, 2006
"... This paper introduces a novel spectral framework for solving Markov decision processes (MDPs) by jointly learning representations and optimal policies. The major components of the framework described in this paper include: (i) A general scheme for constructing representations or basis functions by d ..."
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Cited by 92 (10 self)
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This paper introduces a novel spectral framework for solving Markov decision processes (MDPs) by jointly learning representations and optimal policies. The major components of the framework described in this paper include: (i) A general scheme for constructing representations or basis functions by diagonalizing symmetric diffusion operators (ii) A specific instantiation of this approach where global basis functions called proto-value functions (PVFs) are formed using the eigenvectors of the graph Laplacian on an undirected graph formed from state transitions induced by the MDP (iii) A three-phased procedure called representation policy iteration comprising of a sample collection phase, a representation learning phase that constructs basis functions from samples, and a final parameter estimation phase that determines an (approximately) optimal policy within the (linear) subspace spanned by the (current) basis functions. (iv) A specific instantiation of the RPI framework using least-squares policy iteration (LSPI) as the parameter estimation method (v) Several strategies for scaling the proposed approach to large discrete and continuous state spaces, including the Nyström extension for out-of-sample interpolation of eigenfunctions, and the use of Kronecker sum factorization to construct compact eigenfunctions in product spaces such as factored MDPs (vi) Finally, a series of illustrative discrete and continuous control tasks, which both illustrate the concepts and provide a benchmark for evaluating the proposed approach. Many challenges remain to be addressed in scaling the proposed framework to large MDPs, and several elaboration of the proposed framework are briefly summarized at the end.
The Open Motion Planning Library
, 2012
"... We describe the Open Motion Planning Library (OMPL), a new library for sampling-based motion planning, which contains implementations of many state-of-the-art planning algorithms. The library is designed in a way that allows the user to easily solve a variety of complex motion planning problems with ..."
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Cited by 90 (17 self)
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We describe the Open Motion Planning Library (OMPL), a new library for sampling-based motion planning, which contains implementations of many state-of-the-art planning algorithms. The library is designed in a way that allows the user to easily solve a variety of complex motion planning problems with minimal input. OMPL facilitates the addition of new motion planning algorithms and it can be conveniently interfaced with other software components. A simple graphical user interface (GUI) built on top of the library, a number of tutorials, demos and programming assignments have been designed to teach students about sampling-based motion planning. Finally, the library is also available for use through the
LQR-Trees: Feedback motion planning via sums of squares verification
- International Journal of Robotics Research
, 2010
"... Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses rigorously computed stability regions to build a sparse tree ..."
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Cited by 68 (21 self)
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Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses rigorously computed stability regions to build a sparse tree of LQR-stabilized trajectories. The region of attraction of this nonlinear feedback policy “probabilistically covers ” the entire controllable subset of the state space, verifying that all initial conditions that are capable of reaching the goal will reach the goal. We numerically investigate the properties of this systematic nonlinear feedback design algorithm on simple nonlinear systems, prove the property of probabilistic coverage, and discuss extensions and implementation details of the basic algorithm. 1
Dynamic-Domain RRTs: Efficient Exploration by Controlling the Sampling Domain
- IN PROCEEDINGS IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 2005
"... Sampling-based planners have solved difficult problems in many applications of motion planning in recent years. In particular, techniques based on the Rapidly-exploring Random Trees (RRTs) have generated highly successful singlequery planners. Even though RRTs work well on many problems, they have w ..."
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Cited by 68 (10 self)
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Sampling-based planners have solved difficult problems in many applications of motion planning in recent years. In particular, techniques based on the Rapidly-exploring Random Trees (RRTs) have generated highly successful singlequery planners. Even though RRTs work well on many problems, they have weaknesses which cause them to explore slowly when the sampling domain is not well adapted to the problem. In this paper we characterize these issues and propose a general framework for minimizing their effect. We develop and implement a simple new planner which shows significant improvement over existing RRT-based planners. In the worst cases, the performance appears to be only slightly worse in comparison to the original RRT, and for many problems it performs orders of magnitude better.
Where’s waldo? sensor-based temporal logic motion planning
- in IEEE International Conference on Robotics and Automation, 2007
, 2007
"... Abstract — Given a robot model and a class of admissible environments, this paper provides a framework for automatically and verifiably composing controllers that satisfy high level task specifications expressed in suitable temporal logics. The desired task specifications can express complex robot b ..."
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Cited by 67 (9 self)
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Abstract — Given a robot model and a class of admissible environments, this paper provides a framework for automatically and verifiably composing controllers that satisfy high level task specifications expressed in suitable temporal logics. The desired task specifications can express complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, resulting in a novel paradigm for sensor-based temporal logic motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multi-robot specifications. Our computational approach is based on first creating discrete controllers satisfying so-called General Reactivity(1) formulas. If feasible, the discrete controller is then used in order to guide the sensor-based composition of continuous controllers resulting in a hybrid controller satisfying the high level specification, but only if the environment is admissible. Index Terms — Motion planning, temporal logics, sensorbased planning, controller synthesis, hybrid control.
Near-optimal Character Animation with Continuous Control
- ACM TRANSACTIONS ON GRAPHICS (SIGGRAPH 2007).
, 2007
"... We present a new approach to realtime character animation with interactive control. Given a corpus of motion capture data and a desired task, we automatically compute near-optimal controllers using a low-dimensional basis representation. We show that these controllers produce motion that fluidly r ..."
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Cited by 65 (9 self)
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We present a new approach to realtime character animation with interactive control. Given a corpus of motion capture data and a desired task, we automatically compute near-optimal controllers using a low-dimensional basis representation. We show that these controllers produce motion that fluidly responds to several dimensions of user control and environmental constraints in realtime. Our results indicate that very few basis functions are required to create high-fidelity character controllers which permit complex user navigation and obstacle-avoidance tasks.
Reciprocal n-body Collision Avoidance
- INTERNATIONAL SYMPOSIUM ON ROBOTICS RESEARCH
, 2009
"... In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace. In our formulation, each robot acts fully independently, and does not communicate with other robots. Based o ..."
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Cited by 65 (22 self)
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In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace. In our formulation, each robot acts fully independently, and does not communicate with other robots. Based on the definition of velocity obstacles, we derive sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program. We test our approach on several dense and complex simulation scenarios involving thousands of robots and compute collision-free actions for all of them in only a few milliseconds. To the best of our knowledge, this method is the first that can guarantee local collision-free motion for a large number of robots in a cluttered workspace.
Using interpolation to improve path planning: The Field D* algorithm
- Journal of Field Robotics
, 2006
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