Safety Embedded Differential Dynamic Programming Using Discrete Barrier States

Almubarak, Hassan; Kyle, Stachowicz,; Sadegh, Nader; Theodorou, Evangelos A.

doi:10.1109/lra.2022.3143301

Cited by 16 publications

(21 citation statements)

References 28 publications

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“…s a i,k 2 ≤ AL . After that, each agent j ∈ P i \{i} sends x j i , u j i to agent i (Line 13), so that the latter is able to perform the global updates (Line 14) using (30). Next, every agent j ∈ N i \{i} sends z j , w j to agent i, so that the latter can construct z a i , w a i (Line 15).…”

Section: Algorithmmentioning

confidence: 99%

“…are the linear and angular velocities and a i,k is the linear acceleration of vehicle i at time instant k. For all tasks, we use time step dt = 0.02s and time horizon K = 150, unless specified otherwise. Each agent's cost is of the form (54) with (30,30,0,6), R i = diag(0.5, 0.5) and Q f i = diag(100, 100, 0, 100). All cars are subject to the following box control constraints…”

Section: A Multi-vehicle Controlmentioning

confidence: 99%

“…These characteristics have established DDP as one of the most scalable nonlinear optimal control methods [21], [22] available in the literature. Several extensions for handling control and/or state constraints with DDP can be found in [23]- [30]. Game theoretic DDP-based methods for multi-agent settings have been presented in [31], [32].…”

Section: Introductionmentioning

confidence: 99%

“…For n > 0, the parts involving the dual variables in (30), will become zero with a similar argument as in [34,Section 7.2]. Therefore, the global updates are essentially taking an average of all variables (actual or copy ones) that refer to agent i.…”

mentioning

confidence: 99%

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Distributed Differential Dynamic Programming Architectures for Large-Scale Multi-Agent Control

D.¹,

Aoyama²,

Zhu³

et al. 2022

Preprint

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In this paper, we propose two novel decentralized optimization frameworks for multi-agent nonlinear optimal control problems in robotics. The aim of this work is to suggest architectures that inherit the computational efficiency and scalability of Differential Dynamic Programming (DDP) and the distributed nature of the Alternating Direction Method of Multipliers (ADMM). In this direction, two frameworks are introduced. The first one called Nested Distributed DDP (ND-DDP), is a three-level architecture which employs ADMM for enforcing a consensus between all agents, an Augmented Lagrangian layer for satisfying local constraints and DDP as each agent's optimizer. In the second approach, both consensus and local constraints are handled with ADMM, yielding a two-level architecture called Merged Distributed DDP (MD-DDP), which further reduces computational complexity. Both frameworks are fully decentralized since all computations are parallelizable among the agents and only local communication is necessary. Simulation results that scale up to thousands of vehicles and hundreds of drones verify the effectiveness of the methods. Superior scalability to large-scale systems against centralized DDP and centralized/decentralized sequential quadratic programming is also illustrated. Finally, hardware experiments on a multi-robot platform demonstrate the applicability of the proposed algorithms, while highlighting the importance of optimizing for feedback policies to increase robustness against uncertainty. A video including all results is available here https://youtu.be/tluvENcWldw.

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Section: Algorithmmentioning

confidence: 99%

Section: A Multi-vehicle Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Distributed Differential Dynamic Programming Architectures for Large-Scale Multi-Agent Control

D.¹,

Aoyama²,

Zhu³

et al. 2022

Preprint

Self Cite

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“…Through DDP, the feedback controller and optimal trajectory can be obtained simultaneously. The recent application has also considered the input saturation [30], general nonlinear constraints [31], and global solution search by random search [32]. In the work of [30], the box bounds induced from input limits are considered.…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time Differential Dynamic Programming on SO(3) With Pose Constraints

Liu

2022

IEEE Access

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The motion of many robotics systems, such as the rotation of unmanned aerial vehicles, can be modeled by SO(3). However, the difficulties in the parameterization of the SO(3) makes it hard to implement the state-of-the-art collision avoidance algorithm. In this paper, we present a new method for control on SO(3) via the combination of the nonlinear state constraints and geometric control technique. We first define the nonlinear constraints for trajectory optimization on SO(3). Then we solve the trajectory optimization problem by constrained Differential Dynamic Programming (DDP) in a Riemannian geometry framework. The first and second-order expansion of the cost function and dynamics are derived in a coordinate-free manner. The safety condition represented by nonlinear constraints is incorporated into the DDP via an active set method, where we find the active set in the backward path to obtain the optimal control policy. We validated our methods on motion planning of rigid model on SO(3) manifold where pose constraints are imposed. Our methods outperform the baseline methods in terms of convergence speed and numerical robustness to disturbance. The numerical robustness is essential when the system is initialized far from the local optimum.

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