Learning Stable Nonlinear Dynamical Systems With Gaussian Mixture Models

By Seyed Mohammad Khansari-Zadeh, Aude Gemma Billard. 2011

827 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Probabilistic & Bayesian Methods

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Citations in the corpus

Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning (2017, methodology): “However, the most efficient model-based algorithms have used relatively simple function approximators, such as Gaussian processes [6], [21], [22], time-varying linear models [5], [23], [24], and mixtures of Gaussians [25].”
Algorithmic Framework for Model-based Deep Reinforcement Learning with Theoretical Guarantees (2018, background): “…time-varying linear models (Levine & Koltun, 2013; Lioutikov et al., 2014; Levine & Abbeel, 2014; Yip & Camarillo, 2014), mixture of Gaussians (Khansari-Zadeh & Billard, 2011), to neural networks (Hunt et al., 1992; Nagabandi et al., 2017; Kurutach et al., 2018; Tangkaratt et al., 2014;…”
Learning Self-Correctable Policies and Value Functions from Demonstrations with Negative Sampling (2019, neutral): “We refer to [Kurutach et al., 2018, Clavera et al., 2018, Sun et al., 2018b, Chua et al., 2018, Sanchez-Gonzalez et al., 2018, Pascanu et al., 2017, Khansari-Zadeh and Billard, 2011, Luo et al., 2018] and the reference therein for recent work on model-based RL. Off-policy reinforcement learning…”
Benchmark for Skill Learning from Demonstration: Impact of User Experience, Task Complexity, and Start Configuration on Performance (2019, background): “Based on the choice of motion generation strategy, the majority of skill learning approaches can be further broadly categorized into four groups: time-invariant (stable) dynamical systems [2], [3], [13], time-dependent dynamical systems [7], [9], [10], time-dependent statistical methods [8], [14], [”
DeepMPC: Learning Deep Latent Features for Model Predictive Control (2015, background): “Thus, several recent works attempt to learn more general dynamics models such as Gaussian mixture models [7, 21] and Gaussian processes [22].”
An Algorithmic Perspective on Imitation Learning (2018, methodology): “Behavior cloning methods such as [Pomerleau, 1988, Khansari-Zadeh and Billard, 2011] also employ deterministic policies.”
Improving Multi-Step Prediction of Learned Time Series Models (2015, neutral): “…Vector Regression (Müller, Smola, and Rätsch 1997), Gaussian process regression (Wang, Hertzmann, and Blei 2005; Ko et al. 2007), Nadaraya-Watson kernel regression (Basharat and Shah 2009), Gaussian mixture models (Khansari-Zadeh and Billard 2011), and Kernel PCA (Ralaivola and D’Alche-Buc 2004).”
Neural learning of vector fields for encoding stable dynamical systems (2014, methodology): “Recent studies have emphasized that stability of a predefined target plays an important role for the generalization ability in robotics tasks [17].”
Modeling Long-horizon Tasks as Sequential Interaction Landscapes (2020, background): “Primitives can be used as building blocks that can be composed, for example by a state machine [27], to enable more advanced robot behavior.”
Learning robot motions with stable dynamical systems under diffeomorphic transformations (2015, methodology): “They became of special interest by focusing on the “what to imitate” problem [12, 13].”
Geometrical Invariance and Smoothness Maximization for Task-Space Movement Generation (2016, neutral): “3) Control Lyapunov function-based dynamic movements (CLF-DM)[50].”
Recent Advances in Robot Learning from Demonstration (2020, methodology): “Existing literature in LfD has explored a wide variety of choices for what is considered to be the state, such as end-effector position (81), velocity (70), orientation (82), force (66, 76), joint angles (75), and torques (79).”
Constraints extraction from asymmetrical bimanual tasks and their use in coordinated behavior (2018, methodology): “We further determined a continuous coupling function γ{νM ,νS} by encoding the norm of the coupled variables using a SEDS model (stable estimator of dynamical system [41]).”
Trajectory-Based Skill Learning Using Generalized Cylinders (2018, background): “Khansari-Zadeh and Billard (2011) introduced the Stable Estimator of Dynamical Systems (SEDS) approach which uses a constrained optimization technique to model a set of demonstrations as a dynamic system.”
Learning control Lyapunov function to ensure stability of dynamical system-based robot reaching motions (2014, methodology): “In our previous work, Stable Estimator of Dynamical systems (SEDS) [6], we developed for the first time a formal stability analysis and formulated explicit constraints to ensure global asymptotic stability of nonlinear autonomous DS that are modeled as a mixture of Gaussian functions.”
Imitation Learning (2017, background): “Statistical models can deal with sensor error or inaccurate demonstrations; however, incomplete demonstrations can result in suboptimal behavior [Khansari-Zadeh and Billard 2011].”
Trajectories and keyframes for kinesthetic teaching: A human-robot interaction perspective (2012, methodology): “Dynamical system approaches such as Stable Estimator of Dynamical Systems (SEDS) [13] and Dynamic Movement Primitives (DMP) [17] and mixture models (e.”
Robot Learning System Based on Adaptive Neural Control and Dynamic Movement Primitives (2019, methodology): “The SEDS presented in [3] is similar to our DMP-based model.”