A Survey of Distributed Optimization Methods for Multi-Robot Systems

Halsted, Trevor; Shorinwa, Ola; Yu, Javier; Schwager, Mac

doi:10.48550/arxiv.2103.12840

Cited by 13 publications

(26 citation statements)

References 99 publications

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“…Additionally, if two agents i, j are mutual neighbors, i.e., j ∈ N i and i ∈ N j , then the constraint involving i and j will appear twice in C (i.e., as duplicate row entries). We therefore refer to (22) as the Reduced Duplicate Centralized Problem. There are two reasons we choose this problem for solving the backward pass over the original Reduced Non-Duplicate Centralized Problem (RNDCP): 1) Construction of the non-duplicate constraint matrix C requires checking if mutual neighbors exist for every agent which does not scale for large N 2) C can be easily constructed using the matrices A i used in the forward pass of Merged CADMM-OSQP To justify the usage of ( 22), we make the following assumption about the corresponding RNDCP: Assumption 3.…”

Section: Backward Passmentioning

confidence: 99%

“…In our case, we additionally rely on LICQ to ensure that the Lagrange multipliers satisfying the KKT conditions are unique [45, Section 3]. The connection between the duplicate problem (22) and the corresponding RNDCP is shown in the following lemma.…”

Section: Backward Passmentioning

confidence: 99%

“…A suitable method for deriving such algorithms is the Alternating Direction Method of Multipliers (ADMM) [9]. In particular, ADMM-based methods have been proposed [13,22,44], yielding elegant decentralized solutions for multiagent control. Furthermore, recent works employing ADMM in a stochastic setting, [37,26], have shown to be capable of successfully encompassing both the safety under uncertainty and scalability desired attributes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM

Pereira¹,

D.²,

Oswin³

et al. 2022

Preprint

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In this work, we propose a novel safe and scalable decentralized solution for multi-agent control in the presence of stochastic disturbances. Safety is mathematically encoded using stochastic control barrier functions and safe controls are computed by solving quadratic programs. Decentralization is achieved by augmenting to each agent's optimization variables, copy variables, for its neighbors. This allows us to decouple the centralized multi-agent optimization problem. However, to ensure safety, neighboring agents must agree on what is safe for both of us and this creates a need for consensus. To enable safe consensus solutions, we incorporate an ADMM-based approach. Specifically, we propose a Merged CADMM-OSQP implicit neural network layer, that solves a mini-batch of both, local quadratic programs as well as the overall consensus problem, as a single optimization problem. This layer is embedded within a Deep FBSDEs network architecture at every time step, to facilitate endto-end differentiable, safe and decentralized stochastic optimal control. The efficacy of the proposed approach is demonstrated on several challenging multi-robot tasks in simulation. By imposing requirements on safety specified by collision avoidance constraints, the safe operation of all agents is ensured during the entire training process. We also demonstrate superior scalability in terms of computational and memory savings as compared to a centralized approach.

show abstract

Section: Backward Passmentioning

confidence: 99%

Section: Backward Passmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM

Pereira¹,

D.²,

Oswin³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…More specifically, every local entity transmits multiple inverted blocks of the covariance matrix per MLE iteration. Recently, Xu et al reformulated the factorized GP training method using the exact consensus alternating direction method of multipliers (ADMM) [Boyd et al, 2011], which is appealing in centralized multi-agent settings [Halsted et al, 2021]. Consensus ADMM reduces the communication overhead of GP training, but requires high computational resources to solve a nested optimization problem at every ADMM-iteration.…”

Section: Introductionmentioning

confidence: 99%

Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning

Kontoudis¹,

Stilwell²

2022

Preprint

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In this paper, we propose decentralized and scalable algorithms for Gaussian process (GP) training and prediction in multi-agent systems. To decentralize the implementation of GP training optimization algorithms, we employ the alternating direction method of multipliers (ADMM). A closed-form solution of the decentralized proximal ADMM is provided for the case of GP hyper-parameter training with maximum likelihood estimation. Multiple aggregation techniques for GP prediction are decentralized with the use of iterative and consensus methods. In addition, we propose a covariancebased nearest neighbor selection strategy that enables a subset of agents to perform predictions. The efficacy of the proposed methods is illustrated with numerical experiments on synthetic and real data.

show abstract

“…A suitable method for deriving such algorithms is the Alternating Direction Method of Multipliers (ADMM) [9]. In particular, several ADMM-based methods such as [13,22,44], have been proposed, yielding elegant decentralized solutions for multi-agent control. Furthermore, recent works employing ADMM in a stochastic setting [37,26], have shown to be capable of successfully encompassing both the safety under uncertainty and scalability desired attributes.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM

Pereira¹,

D.²,

Oswin³

et al. 2022

Robotics: Science and Systems XVIII

View full text Add to dashboard Cite

In this work, we propose a novel safe and scalable decentralized solution for multi-agent control in the presence of stochastic disturbances. Safety is mathematically encoded using stochastic control barrier functions and safe controls are computed by solving quadratic programs. Decentralization is achieved by augmenting to each agent's optimization variables, copy variables, for its neighbors. This allows us to decouple the centralized multi-agent optimization problem. However, to ensure safety, neighboring agents must agree on what is safe for both of us, creating a need for consensus. To enable safe consensus solutions, we incorporate an ADMM-based approach. Specifically, we propose a Merged Consensus ADMM-OSQP implicit neural network layer, that solves a mini-batch of both, local quadratic programs as well as the overall consensus problem, as a single optimization problem. This layer is embedded within a Deep Forward-Backward Stochastic Differential Equations (FBSDEs) network architecture at every time step, to facilitate end-to-end differentiable, safe and decentralized stochastic optimal control. The efficacy of the proposed approach is demonstrated on several challenging multi-robot tasks in simulation. By imposing collision avoidance constraints, the safe operation of all agents is ensured during the entire training process. We also demonstrate superior scalability in terms of computational and memory savings as compared to a centralized approach.

show abstract

A Survey of Distributed Optimization Methods for Multi-Robot Systems

Cited by 13 publications

References 99 publications

Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM

Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM

Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning

Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM

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