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125
Robot Trajectory Optimization using Approximate Inference
"... The general stochastic optimal control (SOC) problem in robotics scenarios is often too complex to be solved exactly and in near real time. A classical approximate solution is to first compute an optimal (deterministic) trajectory and then solve a local linearquadraticgaussian (LQG) perturbation m ..."
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Cited by 69 (16 self)
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The general stochastic optimal control (SOC) problem in robotics scenarios is often too complex to be solved exactly and in near real time. A classical approximate solution is to first compute an optimal (deterministic) trajectory and then solve a local linearquadraticgaussian (LQG) perturbation model to handle the system stochasticity. We present a new algorithm for this approach which improves upon previous algorithms like iLQG. We consider a probabilistic model for which the maximum likelihood (ML) trajectory coincides with the optimal trajectory and which, in the LQG case, reproduces the classical SOC solution. The algorithm then utilizes approximate inference methods (similar to expectation propagation) that efficiently generalize to nonLQG systems. We demonstrate the algorithm on a simulated 39DoF humanoid robot. 1.
Synthesis and stabilization of complex behaviors through online trajectory optimization. IROS
, 2012
"... Abstract — We present an online trajectory optimization method and software platform applicable to complex humanoid robots performing challenging tasks such as getting up from an arbitrary pose on the ground and recovering from large disturbances using dexterous acrobatic maneuvers. The resulting be ..."
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Cited by 37 (9 self)
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Abstract — We present an online trajectory optimization method and software platform applicable to complex humanoid robots performing challenging tasks such as getting up from an arbitrary pose on the ground and recovering from large disturbances using dexterous acrobatic maneuvers. The resulting behaviors, illustrated in the attached movie, are computed only 7 x slower than real time, on a standard PC. The movie also shows results on the acrobot problem, planar swimming and onelegged hopping. These simpler problems can already be solved in real time, without precomputing anything. I.
X (2005) From task parameters to motor synergies: a hierarchical framework for approximatelyoptimal feedback control of redundant manipulators. J Robot Syst 22:691–710
"... We present a hierarchical framework for approximately optimal control of redundant manipulators. The plant is augmented with a lowlevel feedback controller, designed to yield inputoutput behavior that captures the taskrelevant aspects of plant dynamics but has reduced dimensionality. This makes i ..."
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Cited by 25 (5 self)
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We present a hierarchical framework for approximately optimal control of redundant manipulators. The plant is augmented with a lowlevel feedback controller, designed to yield inputoutput behavior that captures the taskrelevant aspects of plant dynamics but has reduced dimensionality. This makes it possible to reformulate the optimal control problem in terms of the augmented dynamics, and optimize a highlevel feedback controller without running into the curse of dimensionality. The resulting control hierarchy compares favorably to existing methods in robotics. Furthermore, we demonstrate a number of similarities to �nonhierarchical � optimal feedback control. Besides its engineering applications, the new framework addresses a key unresolved problem in the neural control of movement. It has long been hypothesized that coordination involves selective control of task parameters via muscle synergies, but the link between these parameters and the synergies capable of controlling them has remained elusive. Our framework provides this missing link. © 2005 Wiley Periodicals, Inc. *To whom all correspondence should be addressed.
icLQG: combining local and global optimization for control in information space
 IEEE Int. Conf. on Robotics and Automation
, 2009
"... AbstractWhen a mobile robot does not have perfect knowledge of its position, conventional controllers can experience failures such as collisions because the uncertainty of the position is not considered in choosing control actions. In this paper, we show how global planning and local feedback cont ..."
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Cited by 23 (0 self)
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AbstractWhen a mobile robot does not have perfect knowledge of its position, conventional controllers can experience failures such as collisions because the uncertainty of the position is not considered in choosing control actions. In this paper, we show how global planning and local feedback control can be combined to generate control laws in the space of distributions over position, that is, in information space. We give a novel algorithm for computing "informationconstrained" linear quadratic Gaussian (icLQG) policies for controlling a robot with imperfect state information. The icLQG algorithm uses the belief roadmap algorithm to efficiently search for a trajectory that approximates the globallyoptimal motion plan in information space, and then iteratively computes a feedback control law to locally optimize the global approximation. The icLQG algorithm is not only robust to imperfect state information but also scalable to highdimensional systems and environments. In addition, icLQG is capable of answering multiple queries efficiently. We demonstrate performance results for controlling a vehicle on the plane and a helicopter in three dimensions.
CHOMP: Covariant Hamiltonian Optimization for Motion Planning
"... Popular highdimensional motion planning algorithms seem to pay an overly high price in terms of trajectory quality for their performance. In domains sparsely populated by obstacles, the heuristics used by samplingbased planners to navigate narrow passages can be needlessly complex; furthermore, ad ..."
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Cited by 21 (5 self)
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Popular highdimensional motion planning algorithms seem to pay an overly high price in terms of trajectory quality for their performance. In domains sparsely populated by obstacles, the heuristics used by samplingbased planners to navigate narrow passages can be needlessly complex; furthermore, additional postprocessing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique converges over a wider range of input paths and is able to optimize higher order dynamics of trajectories than previous path optimization strategies. As a result, CHOMP can be used as a standalone motion planner in many realworld planning queries. The effectiveness of our proposed method is demonstrated in manipulation planning for a 6DOF robotic arm as well as in trajectory generation for a walking quadruped robot. 1
Graphical models inference in optimal control of stochastic multiagent systems
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2008
"... In this article we consider the issue of optimal control in collaborative multiagent systems with stochastic dynamics. The agents have a joint task in which they have to reach a number of target states. The dynamics of the agents contains additive control and additive noise, and the autonomous part ..."
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Cited by 20 (1 self)
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In this article we consider the issue of optimal control in collaborative multiagent systems with stochastic dynamics. The agents have a joint task in which they have to reach a number of target states. The dynamics of the agents contains additive control and additive noise, and the autonomous part factorizes over the agents. Full observation of the global state is assumed. The goal is to minimize the accumulated joint cost, which consists of integrated instantaneous costs and a joint end cost. The joint end cost expresses the joint task of the agents. The instantaneous costs are quadratic in the control and factorize over the agents. The optimal control is given as a weighted linear combination of singleagent to singletarget controls. The singleagent to singletarget controls are expressed in terms of diffusion processes. These controls, when not closed form expressions, are formulated in terms of path integrals, which are calculated approximately by MetropolisHastings sampling. The weights in the control are interpreted as marginals of a joint distribution over agent to target assignments. The structure of the latter is represented by a graphical model, and the marginals are obtained by graphical model inference. Exact inference of the graphical model will break down in large systems, and so approximate inference methods are needed. We use naive mean field approximation and belief propagation to approximate the optimal control in systems with linear dynamics. We compare the approximate inference methods with the exact solution, and we show that they can accurately compute the optimal control. Finally, we demonstrate the control method in multiagent systems with nonlinear dynamics consisting of up to 80 agents that have to reach an equal number of target states.
Trajectory Prediction: Learning to Map Situations to Robot Trajectories
"... Trajectory planning and optimization is a fundamental problem in articulated robotics. Algorithms used typically for this problem compute optimal trajectories from scratch in a new situation. In effect, extensive data is accumulated containing situations together with the respective optimized trajec ..."
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Cited by 19 (1 self)
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Trajectory planning and optimization is a fundamental problem in articulated robotics. Algorithms used typically for this problem compute optimal trajectories from scratch in a new situation. In effect, extensive data is accumulated containing situations together with the respective optimized trajectories – but this data is in practice hardly exploited. The aim of this paper is to learn from this data. Given a new situation we want to predict a suitable trajectory which only needs minor refinement by a conventional optimizer. Our approach has two essential ingredients. First, to generalize from previous situations to new ones we need an appropriate situation descriptor – we propose a sparse feature selection approach to find such wellgeneralizing features of situations. Second, the transfer of previously optimized trajectories to a new situation should not be made in joint angle space – we propose a more efficient task space transfer of old trajectories to new situations. Experiments on a simulated humanoid reaching problem show that we can predict reasonable motion prototypes in new situations for which the refinement is much faster than an optimization from scratch. 1.
Adaptive Optimal Control for Redundantly Actuated Arms
"... Abstract. Optimal feedback control has been proposed as an attractive movement generation strategy in goal reaching tasks for anthropomorphic manipulator systems. Recent developments, such as the iterative Linear Quadratic Gaussian (iLQG) algorithm, have focused on the case of nonlinear, but still ..."
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Cited by 14 (3 self)
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Abstract. Optimal feedback control has been proposed as an attractive movement generation strategy in goal reaching tasks for anthropomorphic manipulator systems. Recent developments, such as the iterative Linear Quadratic Gaussian (iLQG) algorithm, have focused on the case of nonlinear, but still analytically available, dynamics. For realistic control systems, however, the dynamics may often be unknown, difficult to estimate, or subject to frequent systematic changes. In this paper, we combine the iLQG framework with learning the forward dynamics for a simulated arm with two limbs and six antagonistic muscles, and we demonstrate how our approach can compensate for complex dynamic perturbations in an online fashion.
Adaptive Optimal Feedback Control with Learned Internal Dynamics Models
"... Abstract. Optimal Feedback Control (OFC) has been proposed as an attractive movement generation strategy in goal reaching tasks for anthropomorphic manipulator systems. Recent developments, such as the Iterative Linear Quadratic Gaussian (ILQG) algorithm, have focused on the case of nonlinear, but ..."
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Cited by 13 (4 self)
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Abstract. Optimal Feedback Control (OFC) has been proposed as an attractive movement generation strategy in goal reaching tasks for anthropomorphic manipulator systems. Recent developments, such as the Iterative Linear Quadratic Gaussian (ILQG) algorithm, have focused on the case of nonlinear, but still analytically available, dynamics. For realistic control systems, however, the dynamics may often be unknown, difficult to estimate, or subject to frequent systematic changes. In this chapter, we combine the ILQG framework with learning the forward dynamics for simulated arms, which exhibit large redundancies, both, in kinematics and in the actuation. We demonstrate how our approach can compensate for complex dynamic perturbations in an online fashion. The specific adaptive framework introduced lends itself to a computationally more efficient implementation of the ILQG optimisation without sacrificing control accuracy – allowing the method to scale to large DoF systems. 1
Hierarchical optimal control of redundant biomechanical systems
 in 26th Annual Int. Conf. of the IEEE Engineering in Medicine and Biology Society
, 2004
"... Sensorimotor control occurs simultaneously on multiple levels. We present a general approach to designing feedback control hierarchies for redundant biomechanical systems, that approximate the (nonhierarchical) optimal control law but have much lower computational demands. The approach is applied t ..."
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Cited by 12 (3 self)
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Sensorimotor control occurs simultaneously on multiple levels. We present a general approach to designing feedback control hierarchies for redundant biomechanical systems, that approximate the (nonhierarchical) optimal control law but have much lower computational demands. The approach is applied to the task of reaching, using a detailed model of the human arm. Our hierarchy has two levels of feedback control. The high level is designed as an optimal feedback controller operating on a simplified virtual plant. The low level is responsible for transforming the dynamics of the true plant into the desired virtual dynamics. The new method may be useful not only for modelling the neural control of movement, but also for designing Functional Electric Stimulation systems that have to achieve task goals by activating muscles in real time.