Sumeet Singh
Sumeet Singh is a Ph.D. candidate in Aeronautics and Astronautics. He received a B.Eng. in Mechanical Engineering and a Diploma of Music (Performance) from University of Melbourne in 2012, and a M.Sc. in Aeronautics and Astronautics from Stanford University in 2015. Prior to joining Stanford, Sumeet worked in the Berkeley Micromechanical Analysis and Design lab at University of California Berkeley in 2011 and the Aeromechanics Branch at NASA Ames in 2013.
Sumeet’s current research interests are twofold: 1) Robust motion planning for constrained nonlinear systems, and 2) Risk-sensitive Model Predictive Control (MPC). Within the first topic, Sumeet is investigating the design of nonlinear control algorithms for online generation of robust motion plans with guaranteed margins of safety for constrained robotic systems in cluttered environments. The second topic focuses on the development and analysis of stochastic MPC algorithms for robust and risk-sensitive decision making problems.
Awards:
- Qualcomm Innovation Fellowship (2018)
- Stanford Graduate Fellowship - Office of Technology Licensing Fellow
Currently at Google Brain
ASL Publications
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S. Singh, B. Landry, A. Majumdar, J.-J. E. Slotine, and M. Pavone, “Robust Feedback Motion Planning via Contraction Theory,” Int. Journal of Robotics Research, vol. 42, no. 9, pp. 655–688, 2023.
Abstract:
@article{SinghLandryEtAl2019, author = {Singh, S. and Landry, B. and Majumdar, A. and Slotine, J-J. E. and Pavone, M.}, title = {Robust Feedback Motion Planning via Contraction Theory}, journal = {{Int. Journal of Robotics Research}}, volume = {42}, number = {9}, pages = {655--688}, year = {2023}, keywords = {pub}, owner = {ssingh19}, timestamp = {2019-09-11}, url = {https://journals.sagepub.com/doi/pdf/10.1177/02783649231186165} } -
S. Singh, S. M. Richards, V. Sindhwani, J.-J. E. Slotine, and M. Pavone, “Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization,” Int. Journal of Robotics Research, vol. 40, no. 10–11, pp. 1123–1150, 2021.
Abstract: We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of stabilizability, a constraint which guarantees the existence of robust tracking controllers for arbitrary open-loop trajectories generated with the learned system. Leveraging tools from contraction theory and statistical learning in reproducing kernel Hilbert spaces, we formulate stabilizable dynamics learning as a functional optimization with a convex objective and bi-convex functional constraints. Under a mild structural assumption and relaxation of the functional constraints to sampling-based constraints, we derive the optimal solution with a modified representer theorem. Finally, we utilize random matrix feature approximations to reduce the dimensionality of the search parameters and formulate an iterative convex optimization algorithm that jointly fits the dynamics functions and searches for a certificate of stabilizability. We validate the proposed algorithm in simulation for a planar quadrotor, and on a quadrotor hardware testbed emulating planar dynamics. We verify, both in simulation and on hardware, significantly improved trajectory generation and tracking performance with the control-theoretic regularized model over models learned using traditional regression techniques, especially when learning from small supervised datasets. The results support the conjecture that the use of stabilizability constraints as a form of regularization can help prune the hypothesis space in a manner that is tailored to the downstream task of trajectory generation and feedback control. This produces models that are not only dramatically better conditioned, but also data efficient.
@article{SinghRichardsEtAl2020, author = {Singh, S. and Richards, S. M. and Sindhwani, V. and Slotine, J-J. E. and Pavone, M.}, title = {Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization}, journal = {{Int. Journal of Robotics Research}}, volume = {40}, number = {10--11}, pages = {1123-1150}, year = {2021}, url = {/wp-content/papercite-data/pdf/Singh.Richards.ea.IJRR20.pdf}, owner = {ssingh19}, timestamp = {2020-03-25} } -
S. Singh, “Robust Control, Planning, and Inference for Safe Robot Autonomy,” PhD thesis, Stanford University, Dept. of Aeronautics and Astronautics, Stanford, California, 2019.
Abstract: Integrating autonomous robots into safety-critical settings requires reasoning about uncertainty at all levels of the autonomy stack. This thesis presents novel algorithmic tools for imbuing robustness within two hierarchically complementary areas, namely: motion planning and decision-making. In Part I of the thesis, by harnessing the theories of contraction and semi-infinite convex optimization and the computational tool of sum-of-squares programming, we present a unified framework for robust real-time motion planning for complex underactuated nonlinear systems. Broadly, the approach entails pairing open-loop motion planning algorithms that neglect uncertainty and are optimized for generating trajectories for simple kinodynamic models in real-time, with robust nonlinear trajectory-tracking feedback controllers. We demonstrate how to systematically synthesize these controllers and integrate them within planning to generate and execute certifiably safe trajectories that are robust to the closed-loop effects of disturbances and planning with simplified models. In Part II of the thesis, we demonstrate how to embed the control-theoretic advancements developed in Part I as constraints within a novel semi-supervised algorithm for learning dynamical systems from user demonstrations. The constraints act as a form of context-driven hypothesis pruning to yield learned models that jointly balance regression performance and stabilizability, ultimately resulting in generated trajectories for the robot that are conditioned for feedback control. Experimental results on a quadrotor testbed illustrate the efficacy of the proposed algorithms in Parts I and II of the thesis, and clear connections between theory and hardware. Finally, in Part III of the thesis, we describe a framework for lifting notions of robustness from lowlevel motion planning to higher-level sequential decision-making using the theory of risk measures. Leveraging a class of risk measures with favorable axiomatic foundations, we demonstrate how to formulate decision-making algorithms with tunable robustness properties. In particular, we focus on a novel application of this framework to inverse reinforcement learning where we learn predictive motion models for humans in safety-critical scenarios, and illustrate their effectiveness within a commercial driving simulator featuring humans in-the-loop. The contributions within this thesis constitute an important step towards endowing modern robotic systems with the ability to systematically and hierarchically reason about safety and efficiency in the face of uncertainty, which is crucial for safety-critical applications
@phdthesis{Singh2019, author = {Singh, S.}, title = {Robust Control, Planning, and Inference for Safe Robot Autonomy}, school = {{Stanford University, Dept. of Aeronautics and Astronautics}}, year = {2019}, address = {Stanford, California}, month = aug, url = {https://stacks.stanford.edu/file/druid:pr731qc2534/Singh-PhD-augmented.pdf}, owner = {bylard}, timestamp = {2021-12-06} } -
J. Lorenzetti, B. Landry, S. Singh, and M. Pavone, “Reduced Order Model Predictive Control For Setpoint Tracking,” in European Control Conference, Naples, Italy, 2019.
Abstract: Despite the success of model predictive control (MPC), its application to high-dimensional systems, such as flexible structures and coupled fluid/rigid-body systems, remains a largely open challenge due to excessive computational complexity. A promising solution approach is to leverage reduced order models for designing the model predictive controller. In this paper we present a reduced order MPC scheme that enables setpoint tracking while robustly guaranteeing constraint satisfaction for linear, discrete, time-invariant systems. Setpoint tracking is enabled by designing the MPC cost function to account for the steady-state error between the full and reduced order models. Robust constraint satisfaction is accomplished by solving (offline) a set of linear programs to provide bounds on the errors due to bounded disturbances, state estimation, and model approximation. The approach is validated on a synthetic system as well as a high-dimensional linear model of a flexible rod, obtained using finite element methods.
@inproceedings{LorenzettiLandryEtAl2019, author = {Lorenzetti, J. and Landry, B. and Singh, S. and Pavone, M.}, title = {Reduced Order Model Predictive Control For Setpoint Tracking}, booktitle = {{European Control Conference}}, year = {2019}, address = {Naples, Italy}, month = jun, url = {https://arxiv.org/pdf/1811.06590.pdf}, owner = {jlorenze}, timestamp = {2019-04-26} } -
S. Singh, V. Sindhwani, J.-J. E. Slotine, and M. Pavone, “Learning Stabilizable Dynamical Systems via Control Contraction Metrics,” in Workshop on Algorithmic Foundations of Robotics, Merida, Mexico, 2018.
Abstract: 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 learnt system can be accompanied by a robust controller capable of stabilizing any trajectory that the system can generate. By leveraging tools from contraction theory, statistical learning, and convex optimization, we provide a general and tractable algorithm to learn stabilizable dynamics, which can be applied to complex underactuated systems. We validate the proposed algorithm on a simulated planar quadrotor system and observe that the control-theoretic regularized dynamics model is able to consistently generate and accurately track reference trajectories whereas the model learnt using standard regression techniques, e.g., ridge-regression (RR) does extremely poorly on both tasks. Furthermore, in aggressive flight regimes with high velocity and bank angle, the tracking controller fails to stabilize the trajectory generated by the ridge-regularized model whereas no instabilities were observed using the control-theoretic learned model, even with 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.
@inproceedings{SinghSindhwaniEtAl2018, author = {Singh, S. and Sindhwani, V. and Slotine, J.-J. E. and Pavone, M.}, title = {Learning Stabilizable Dynamical Systems via Control Contraction Metrics}, booktitle = {{Workshop on Algorithmic Foundations of Robotics}}, year = {2018}, address = {Merida, Mexico}, month = oct, url = {https://arxiv.org/abs/1808.00113}, owner = {ssingh19}, timestamp = {2019-07-27} } -
S. Singh, M. Chen, S. L. Herbert, C. J. Tomlin, and M. Pavone, “Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approach,” in Workshop on Algorithmic Foundations of Robotics, Merida, Mexico, 2018.
Abstract: In the pursuit of real-time motion planning, a commonly adopted practice is to compute a trajectory by running a planning algorithm on a simplified, low-dimensional dynamical model, and then employ a feedback tracking controller that tracks such a trajectory by accounting for the full, high-dimensional system dynamics. While this strategy of planning with model mismatch generally yields fast computation times, there are no guarantees of dynamic feasibility, which hampers application to safety-critical systems. Building upon recent work that addressed this problem through the lens of Hamilton-Jacobi (HJ) reachability, we devise an algorithmic framework whereby one computes, offline, for a pair of "planner" (i.e., low-dimensional) and "tracking" (i.e., high-dimensional) models, a feedback tracking controller and associated tracking bound. This bound is then used as a safety margin when generating motion plans via the low-dimensional model. Specifically, we harness the computational tool of sum-of-squares (SOS) programming to design a bilinear optimization algorithm for the computation of the feedback tracking controller and associated tracking bound. The algorithm is demonstrated via numerical experiments, with an emphasis on investigating the trade-off between the increased computational scalability afforded by SOS and its intrinsic conservativeness. Collectively, our results enable scaling the appealing strategy of planning with model mismatch to systems that are beyond the reach of HJ analysis, while maintaining safety guarantees.
@inproceedings{SinghChenEtAl2018, author = {Singh, S. and Chen, M. and Herbert, S. L. and Tomlin, C. J. and Pavone, M.}, title = {Robust Tracking with Model Mismatch for Fast and Safe Planning: an {SOS} Optimization Approach}, booktitle = {{Workshop on Algorithmic Foundations of Robotics}}, year = {2018}, address = {Merida, Mexico}, month = oct, url = {https://arxiv.org/abs/1808.00649}, owner = {ssingh19}, timestamp = {2019-07-27} } -
Z. Wang, S. Singh, M. Pavone, and M. Schwager, “Cooperative Object Transport in 3D with Multiple Quadrotors using No Peer Communication,” in Proc. IEEE Conf. on Robotics and Automation, Brisbane, Australia, 2018.
Abstract: We present a framework to enable a fleet of rigidly attached quadrotor aerial robots to transport heavy objects along a known reference trajectory without inter-robot communication or centralized coordination. Leveraging a distributed wrench controller, we provide exponential stability guarantees for the entire assembly, under a mild geometric condition. This is achieved by each quadrotor independently solving a local optimization problem to counteract the biased torque effects from each robot in the assembly. We rigorously analyze the controllability of the object, design a distributed compensation scheme to address these challenges, and show that the resulting strategy collectively guarantees full group control authority. To ensure feasibility for online implementation, we derive bounds on the net desired control wrench, characterize the output wrench space of each quadrotor, and perform subsequent trajectory optimization under these input constraints. We thoroughly validate our method in simulation with eight quadrotors transporting a heavy object in a cluttered environment subject to various sources of uncertainty, and demonstrate the algorithm’s resilience.
@inproceedings{WangSinghEtAl2018, author = {Wang, Z. and Singh, S. and Pavone, M. and Schwager, M.}, title = {Cooperative Object Transport in {3D} with Multiple Quadrotors using No Peer Communication}, booktitle = {{Proc. IEEE Conf. on Robotics and Automation}}, year = {2018}, address = {Brisbane, Australia}, month = may, url = {/wp-content/papercite-data/pdf/Wang.Singh.Pavone.ea.ICRA18.pdf}, owner = {ssingh19}, timestamp = {2018-01-16} } -
S. Singh, J. Lacotte, A. Majumdar, and M. Pavone, “Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods,” Int. Journal of Robotics Research, vol. 37, no. 13, pp. 1713–1740, 2018.
Abstract: The literature on Inverse Reinforcement Learning (IRL) typically assumes that humans take actions in order to minimize the expected value of a cost function, i.e., that humans are risk neutral. Yet, in practice, humans are often far from being risk neutral. To fill this gap, the objective of this paper is to devise a framework for risk-sensitive IRL in order to explicitly account for a human’s risk sensitivity. To this end, we propose a flexible class of models based on coherent risk measures, which allow us to capture an entire spectrum of risk preferences from risk-neutral to worst-case. We propose efficient non-parametric algorithms based on linear programming and semi-parametric algorithms based on maximum likelihood for inferring a human’s underlying risk measure and cost function for a rich class of static and dynamic decision-making settings. The resulting approach is demonstrated on a simulated driving game with ten human participants. Our method is able to infer and mimic a wide range of qualitatively different driving styles from highly risk-averse to risk-neutral in a data-efficient manner. Moreover, comparisons of the Risk-Sensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL framework more accurately captures observed participant behavior both qualitatively and quantitatively, especially in scenarios where catastrophic outcomes such as collisions can occur.
@article{SinghLacotteEtAl2018, author = {Singh, S. and Lacotte, J. and Majumdar, A. and Pavone, M.}, title = {Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods}, journal = {{Int. Journal of Robotics Research}}, volume = {37}, number = {13}, pages = {1713--1740}, year = {2018}, url = {https://arxiv.org/pdf/1711.10055.pdf}, owner = {ssingh19}, timestamp = {2019-08-21} } -
S. Singh, Y.-L. Chow, A. Majumdar, and M. Pavone, “A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms,” 2018.
Abstract: In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk-neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-time implementation. Simulation results are presented and discussed.
@unpublished{SinghChowEtAl2018, author = {Singh, S. and Chow, Y.-L. and Majumdar, A. and Pavone, M.}, title = {A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms}, note = {{Available at }\url{http://arxiv.org/abs/1703.01029}}, year = {2018}, url = {http://arxiv.org/pdf/1703.01029.pdf}, owner = {ssingh19}, timestamp = {2018-06-30} } -
S. Singh, Y.-L. Chow, A. Majumdar, and M. Pavone, “A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms,” IEEE Transactions on Automatic Control, vol. 64, no. 7, pp. 2905–2912, 2018.
Abstract: In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk-neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-time implementation. Simulation results are presented and discussed.
@article{SinghChowEtAl2018b, author = {Singh, S. and Chow, Y.-L. and Majumdar, A. and Pavone, M.}, title = {A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms}, journal = {{IEEE Transactions on Automatic Control}}, volume = {64}, number = {7}, pages = {2905--2912}, year = {2018}, note = {{Extended version available at:} \url{http://arxiv.org/abs/1703.01029}}, url = {http://arxiv.org/pdf/1703.01029.pdf}, owner = {ssingh19}, timestamp = {2019-07-29} } -
A. Majumdar, S. Singh, A. Mandlekar, and M. Pavone, “Risk-sensitive Inverse Reinforcement Learning via Coherent Risk Models,” in Robotics: Science and Systems, Cambridge, Massachusetts, 2017.
Abstract: The literature on Inverse Reinforcement Learning (IRL) typically assumes that humans take actions in order to minimize the expected value of a cost function, i.e., that humans are risk neutral. Yet, in practice, humans are often far from being risk neutral. To fill this gap, the objective of this paper is to devise a framework for risk-sensitive IRL in order to explicitly account for an expert’s risk sensitivity. To this end, we propose a flexible class of models based on coherent risk metrics, which allow us to capture an entire spectrum of risk preferences from risk-neutral to worst-case. We propose efficient algorithms based on Linear Programming for inferring an expert’s underlying risk metric and cost function for a rich class of static and dynamic decision-making settings. The resulting approach is demonstrated on a simulated driving game with ten human participants. Our method is able to infer and mimic a wide range of qualitatively different driving styles from highly risk-averse to risk-neutral in a data-efficient manner. Moreover, comparisons of the Risk-Sensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL framework more accurately captures observed participant behavior both qualitatively and quantitatively.
@inproceedings{MajumdarSinghEtAl2017, author = {Majumdar, A. and Singh, S. and Mandlekar, A. and Pavone, M.}, title = {Risk-sensitive Inverse Reinforcement Learning via Coherent Risk Models}, booktitle = {{Robotics: Science and Systems}}, year = {2017}, address = {Cambridge, Massachusetts}, month = jul, url = {/wp-content/papercite-data/pdf/Majumdar.Singh.Mandlekar.Pavone.RSS17.pdf}, owner = {ssingh19}, timestamp = {2017-04-28} } -
S. Singh, A. Majumdar, J.-J. E. Slotine, and M. Pavone, “Robust Online Motion Planning via Contraction Theory and Convex Optimization,” in Proc. IEEE Conf. on Robotics and Automation, Singapore, 2017.
Abstract: We present a framework for online generation of robust motion plans for robotic systems with nonlinear dynamics subject to bounded disturbances, control constraints, and online state constraints such as obstacles. In an offline phase, one computes the structure of a feedback controller that can be efficiently implemented online to track any feasible nominal trajectory. The offline phase leverages contraction theory and convex optimization to characterize a fixed-size “tube” that the state is guaranteed to remain within while tracking a nominal trajectory (representing the center of the tube). In the online phase, when the robot is faced with obstacles, a motion planner uses such a tube as a robustness margin for collision checking, yielding nominal trajectories that can be safely executed (i.e., tracked without collisions under disturbances). In contrast to recent work on robust online planning using funnel libraries, our approach is not restricted to a fixed library of maneuvers computed offline and is thus particularly well-suited to applications such as UAV flight in densely cluttered environments where complex maneuvers may be required to reach a goal. We demonstrate our approach through simulations of a 6-state planar quadrotor navigating cluttered environments in the presence of a cross-wind. We also discuss applications of our approach to Tube Model Predictive Control (TMPC) and compare the merits of our method with state-of-the-art nonlinear TMPC techniques.
@inproceedings{SinghMajumdarEtAl2017, author = {Singh, S. and Majumdar, A. and Slotine, J.-J. E. and Pavone, M.}, title = {Robust Online Motion Planning via Contraction Theory and Convex Optimization}, booktitle = {{Proc. IEEE Conf. on Robotics and Automation}}, year = {2017}, note = {{Extended version available at }\url{http://asl.stanford.edu/wp-content/papercite-data/pdf/Singh.Majumdar.Slotine.Pavone.ICRA17.pdf}}, address = {Singapore}, month = may, url = {/wp-content/papercite-data/pdf/Singh.Majumdar.Slotine.Pavone.ICRA17.pdf}, owner = {bylard}, timestamp = {2018-06-30} } -
S. Singh, S. D’Amico, and M. Pavone, “High-Fidelity Modeling and Control System Synthesis for a Drag-Free Microsatellite,” in Int. Symp. on Space Flight Dynamics, Munich, Germany, 2015.
Abstract: A drag-free satellite is a spacecaft composed of an internal test mass shielded by an external satellite that compensates all dominant disturbance forces encountered in the space environment such as aerodynamic drag and solar radiation pressure. By minimizing all non-gravitational disturbances on the test mass, the trajectory of the spacecraft is a near perfect geodesic. In concert with precise orbit determination techniques, drag-free satellites allow us to investigate topics in geodesy, aeronomy, and gravitational physics and conduct challenging experiments in low-disturbance environments to unprecedented accuracy. This paper addresses the development of a high-fidelity simulator and control system design for the Modular Gravitational Reference Sensor (MGRS) drag-free satellite. MGRS is a 100 kg microsatellite due to launch in 2018 into a Sun-synchronous orbit with a mean altitude of 657 km that aims to demonstrate three-axis drag-free operations with residual non-gravitational acceleration of a test mass under 10^-12 \msrootHz in the frequency range 0.01 to 1 Hz. The drag-free performance goal reflects a substantial improvement upon past drag-free missions such as TRIAD I, GPB, and GOCE, and will be accomplished at a fraction of the cost. Additionally, this mission represents a key technology demonstration within a larger research endeavour that aims to develop a multi-purpose distributed drag-free architecture based on microsatellite platforms. Our modeling framework allows us to gain a comprehensive insight into the range of expected disturbances, derive sizing constraints for a suitable micropropulsion system, and formulate a preliminary drag-free translational and attitude control system using H_∞- control techniques.
@inproceedings{SinghDAmicoEtAl2015, author = {Singh, S. and D'Amico, S.. and Pavone, M.}, title = {High-Fidelity Modeling and Control System Synthesis for a Drag-Free Microsatellite}, booktitle = {{Int. Symp. on Space Flight Dynamics}}, year = {2015}, address = {Munich, Germany}, month = oct, owner = {bylard}, timestamp = {2017-01-28}, url = {/wp-content/papercite-data/pdf/Singh.Damico.Pavone.ISSFD15.pdf} } -
S. Singh, E. Schmerling, and M. Pavone, “Decentralized Algorithms for 3D Symmetric Formations in Robotic Networks - A Contraction Theory Approach,” in Proc. IEEE Conf. on Robotics and Automation, Seattle, Washington, 2015.
Abstract: This paper presents distributed algorithms for formation control of multiple robots in three dimensions. In particular, we leverage the mathematical properties of cyclic pursuit along with results from contraction and partial contraction theory to design distributed control algorithms ensuring global convergence to symmetric formations. As a base case we consider regular polygons as desired formations and then provide extensions to Johnson solid formations. Finally, we analyze the robustness of the control algorithms under bounded additive disturbances and provide performance bounds with respect to the formation error.
@inproceedings{SinghSchmerlingEtAl2015, author = {Singh, S. and Schmerling, E. and Pavone, M.}, title = {Decentralized Algorithms for {3D} Symmetric Formations in Robotic Networks - A Contraction Theory Approach}, booktitle = {{Proc. IEEE Conf. on Robotics and Automation}}, year = {2015}, address = {Seattle, Washington}, doi = {10.1109/ICRA.2015.7139355}, month = may, owner = {bylard}, timestamp = {2017-01-28}, url = {/wp-content/papercite-data/pdf/Singh.Pavone.ICRA2015.pdf} }