Robust online motion planning via contraction theory and convex optimization

Singh, Sumeet; Majumdar, Anirudha; Slotine, Jean‐Jacques E.; Pavone, Marco

doi:10.1109/icra.2017.7989693

Cited by 178 publications

(328 citation statements)

References 27 publications

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“…However, similar to the Lipschitz based approach, unless the considered tube parametrization X contains a robust positive invariant (RPI) set, the tube is growing unbounded along the prediction horizon and thus only short horizons and/or small uncertainty can be considered. In [22], [32] additive disturbances are considered and a fixed RPI set X is computed offline as an incremental Lyapunov function or using control contraction metrics.…”

Section: Setup and General Theorymentioning

confidence: 99%

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

127

133

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In this paper, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared to robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain L2 stability w.r.t. additive disturbances.As a first contribution we derive suitable monotonicity and non-increasing properties on general parameter estimation algorithms and tube/set based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this paper, we provide similar conditions for a tube based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared to state of the art approaches.

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Section: Setup and General Theorymentioning

confidence: 99%

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

127

133

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show abstract

“…Second, as a consequence of this iterative procedure, the dual metric and contraction rate pair {W (x), λ} do not possess any sort of "control-theoretic" optimality. For instance, in [32], for a known stabilizable dynamics model, both these quantities are optimized for robust control performance. In this work, these quantities are used solely as regularizers to promote stabilizability of the learned model.…”

Section: : End Whilementioning

confidence: 99%

Learning Stabilizable Dynamical Systems via Control Contraction Metrics

Singh

Sindhwani

Slotine

et al. 2019

EasyChair Preprints

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We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of stabilizability, which guarantees that the learned system can be accompanied by a robust controller capable of stabilizing any open-loop trajectory that the system may generate. By leveraging tools from contraction theory, statistical learning, and convex optimization, we provide a general and tractable semi-supervised algorithm to learn stabilizable dynamics, which can be applied to complex underactuated systems. We validated the proposed algorithm on a simulated planar quadrotor system and observed notably improved trajectory generation and tracking performance with the control-theoretic regularized model over models learned using traditional regression techniques, especially when using a small number of demonstration examples. The results presented illustrate the need to infuse standard model-based reinforcement learning algorithms with concepts drawn from nonlinear control theory for improved reliability.

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“…and c ∈ [c, c]. In order to compute the FaSTrack tracking error bound E, we must solve a Hamilton Jacobi (HJ) reachability problem for the relative dynamics defined by (1) and (2). In this case, the relative dynamics are given by:…”

Section: A Setupmentioning

confidence: 99%

Safely Probabilistically Complete Real-Time Planning and Exploration in Unknown Environments

Fridovich-Keil

Fisac

Tomlin

2019

2019 International Conference on Robotics and Automation (ICRA)

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We present a new framework for motion planning that wraps around existing kinodynamic planners and guarantees recursive feasibility when operating in a priori unknown, static environments. Our approach makes strong guarantees about overall safety and collision avoidance by utilizing a robust controller derived from reachability analysis. We ensure that motion plans never exit the safe backward reachable set of the initial state, while safely exploring the space. This preserves the safety of the initial state, and guarantees that that we will eventually find the goal if it is possible to do so while exploring safely. We implement our framework in the Robot Operating System (ROS) software environment and demonstrate it in a real-time simulation.

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Robust online motion planning via contraction theory and convex optimization

Cited by 178 publications

References 27 publications

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Learning Stabilizable Dynamical Systems via Control Contraction Metrics

Safely Probabilistically Complete Real-Time Planning and Exploration in Unknown Environments

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