Constrained Differential Dynamic Programming Revisited

Aoyama, Yuichiro; Boutselis, George I.; Patel, Akash; Theodorou, Evangelos A.

doi:10.48550/arxiv.2005.00985

Cited by 12 publications

(22 citation statements)

References 15 publications

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“…The first category converts the constrained problems to unconstrained ones via penalty [19] while the other deals with the constraints explicitly by identifying the active ones [20]. To avoid the combinatorial problem regarding the active constraints, a constrained version of Bellman's principle of optimality has been introduced in [7], [21], which augments the control input with dual variables. However, these DDP algorithms have only been applied to a short-duration (e.g.…”

Section: B Ddp Algorithmsmentioning

confidence: 99%

“…2 ∼ 3s, 200 ∼ 300 steps of sampling period 0.01s) quadrotor planning problem and takes quite long time for simple constraints (≥ 5s, see Table 7 in [21]). In this paper, we shall exploit the differential flatness of quadrotors and the linear complexity property of DDP algorithm to generate long-duration smooth trajectories efficiently.…”

Section: B Ddp Algorithmsmentioning

confidence: 99%

“…which iteratively computes the control input and next state. Algorithm 2 summarizes the above iteration and this gives the analytical solution to the unconstrained fixed-time polynomial trajectory generation problem (21). It should be noted that Algorithm 2 can be regarded as a simplified version of Algorithm 1 with exact one iteration.…”

Section: B Fixed Time Allocation and No Constraintmentioning

confidence: 99%

See 2 more Smart Citations

DIRECT: A Differential Dynamic Programming Based Framework for Trajectory Generation

Cao¹,

Cao²,

Yuan³

et al. 2021

Preprint

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This paper introduces a differential dynamic programming (DDP) based framework for polynomial trajectory generation for differentially flat systems. In particular, instead of using a linear equation with increasing size to represent multiple polynomial segments as in literature, we take a new perspective from state-space representation such that the linear equation reduces to a finite horizon control system with a fixed state dimension and the required continuity conditions for consecutive polynomials are automatically satisfied. Consequently, the constrained trajectory generation problem (both with and without time optimization) can be converted to a discrete-time finite-horizon optimal control problem with inequality constraints, which can be approached by a recently developed interior-point DDP (IPDDP) algorithm. Furthermore, for unconstrained trajectory generation with preallocated time, we show that this problem is indeed a linear-quadratic tracking (LQT) problem (DDP algorithm with exact one iteration). All these algorithms enjoy linear complexity with respect to the number of segments. Both numerical comparisons with stateof-the-art methods and physical experiments are presented to verify and validate the effectiveness of our theoretical findings. The implementation code will be open-sourced 1 .

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Section: B Ddp Algorithmsmentioning

confidence: 99%

Section: B Ddp Algorithmsmentioning

confidence: 99%

Section: B Fixed Time Allocation and No Constraintmentioning

confidence: 99%

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DIRECT: A Differential Dynamic Programming Based Framework for Trajectory Generation

Cao¹,

Cao²,

Yuan³

et al. 2021

Preprint

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show abstract

“…The first example is taken from [17], featuring a 2D car (n=4, m=2) moving within the obstacle-ridden environment shown in Figure 2. The objective is to drive to the goal position (3,3) with final velocity 0 and orientation aligned with the horizontal axis in N =40 steps, while avoiding the obstacles.…”

Section: A Motion Planning For a Carmentioning

confidence: 99%

“…While CL involves differentiating through the KKT conditions of one-step horizon QPs, this computation must happen serially in the backward pass. In contrast, CL γ computes the required Jacobians across all time-steps in parallel using an efficient adjoint recursion associated with problem (17).…”

Section: A Motion Planning For a Carmentioning

confidence: 99%

Optimizing Trajectories with Closed-Loop Dynamic SQP

Singh¹,

Slotine²,

Sindhwani³

2021

Preprint

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Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the state-of-the-art approach when faced with additional constraints (e.g., control bounds, obstacle avoidance). However, a naïve implementation of NLP algorithms, e.g., shooting-based sequential quadratic programming (SQP), may suffer from slow convergence -caused from natural instabilities of the underlying system manifesting as poor numerical stability within the optimization. Re-interpreting the DDP closed-loop rollout policy as a sensitivity-based correction to a second-order search direction, we demonstrate how to compute analogous closedloop policies (i.e., feedback gains) for constrained problems. Our key theoretical result introduces a novel dynamic programmingbased constraint-set recursion that augments the canonical "cost-to-go" backward pass. On the algorithmic front, we develop a hybrid-SQP algorithm incorporating DDP-style closedloop rollouts, enabled via efficient parallelized computation of the feedback gains. Finally, we validate our theoretical and algorithmic contributions on a set of increasingly challenging benchmarks, demonstrating significant improvements in convergence speed over standard open-loop SQP.

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Receding Horizon Differential Dynamic Programming Under Parametric Uncertainty

Aoyama

Theodorou

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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Constrained Differential Dynamic Programming Revisited

Cited by 12 publications

References 15 publications

DIRECT: A Differential Dynamic Programming Based Framework for Trajectory Generation

DIRECT: A Differential Dynamic Programming Based Framework for Trajectory Generation

Optimizing Trajectories with Closed-Loop Dynamic SQP

Receding Horizon Differential Dynamic Programming Under Parametric Uncertainty

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