Differential dynamic programming with nonlinear constraints

Xie, Zhiqiang; Liu, C. Karen; Hauser, Kris

doi:10.1109/icra.2017.7989086

Cited by 93 publications

(69 citation statements)

References 13 publications

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“…To do so, they propose to handle the box constraints inside the Quadratic Programming (QP) problem that minimizes the Hamiltonian (i.e., the Q function). Following a similar approach, Xie et al [13] extend the method for arbitrary nonlinear constraints on the states and the controls. Independently, Lantoine and Russell [14] take a similar approach to handle hard constraints.…”

Section: A Motivation and Related Workmentioning

confidence: 99%

Squash-Box Feasibility Driven Differential Dynamic Programming

Marti-Saumell

Solà

Mastalli

et al. 2020

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Recently, Differential Dynamic Programming (DDP) and other similar algorithms have become the solvers of choice when performing non-linear Model Predictive Control (nMPC) with modern robotic devices. The reason is that they have a lower computational cost per iteration when compared with off-the-shelf Non-Linear Programming (NLP) solvers, which enables its online operation. However, they cannot handle constraints, and are known to have poor convergence capabilities. In this paper, we propose a method to solve the optimal control problem with control bounds through a squashing function (i.e., a sigmoid, which is bounded by construction). It has been shown that a naive use of squashing functions damage the convergence rate. To tackle this, we first propose to add a quadratic barrier that avoids the difficulty of the plateau produced by the sigmoid. Second, we add an outer loop that adapts both the sigmoid and the barrier; it makes the optimal control problem with the squashing function converge to the original control-bounded problem. To validate our method, we present simulation results for different types of platforms including a multi-rotor, a biped, a quadruped and a humanoid robot.

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Section: A Motivation and Related Workmentioning

confidence: 99%

Squash-Box Feasibility Driven Differential Dynamic Programming

Marti-Saumell

Solà

Mastalli

et al. 2020

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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“…when many constraints which have dimension exceeding the control dimension are present. As a part of the method presented in [10], a technique for satisfying linear constraints at arbitrary times in the trajectory is presented, but that method assumes that the constraint dimension does not exceed that of the control. Most recently, [11] present a method for solving problems with timevarying constraints, but still require that the relative-degree of these constraints does not exceed 1.…”

Section: Prior Workmentioning

confidence: 99%

Efficient Computation of Feedback Control for Equality-Constrained LQR

Laine

Tomlin

2019

2019 International Conference on Robotics and Automation (ICRA)

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A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed endpoint constraints. The method explicitly determines an affine relationship between the control and state variables, as in standard Riccati recursion, giving rise to feedback control policies that account for constraints. Since the linearly-constrained LQR problem arises commonly in robotic trajectory optimization, having a method that can efficiently compute these solutions is important. We demonstrate some of the useful properties and interpretations of said control policies, and we compare the computation time of our method against existing methods. arXiv:1807.00794v2 [cs.SY]

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“…One way is to reconstruct the object function containing the constraints as penalty terms [30]. The other way is to deal with the procedure itself either by solving the sub-optimal problem with state [31] or by controlling constraints [32]. However, under the iLQR framework, solving an optimal control problem with state inequality constraints and equality constraints is often computationally demanding and complicates the numerical treatment.…”

Section: Problem Reformulation Based On Ilqr Approachmentioning

confidence: 99%

Time-Energy Optimal Trajectory Planning for Variable Stiffness Actuated Robot

Chen

Kong

2019

IEEE Access

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A variable stiffness actuator is inspired by the human motor control and is the most popular actuator used to exploit the human performance and human-like motion. However, these actuators are typically highly non-linear and redundant not only in their kinematics but also in their dynamics due to their capability to modulate their stiffness and positions simultaneously. It is not trivial to generate the trajectory for a strongly non-linear and redundant dynamic system equipped with variable stiffness actuators. In this paper, a trajectory planning method for a variable stiffness actuated robot via a time-energy optimal control policy is proposed. The simulation studies demonstrate the effectiveness of the trajectory planning method through the case studies of a two degree of freedom variable stiffness actuated robot. Furthermore, the results show that the proposed method could be able to generate the motion which is similar to the human arm motion strategy.

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Differential dynamic programming with nonlinear constraints

Cited by 93 publications

References 13 publications

Squash-Box Feasibility Driven Differential Dynamic Programming

Squash-Box Feasibility Driven Differential Dynamic Programming

Efficient Computation of Feedback Control for Equality-Constrained LQR

Time-Energy Optimal Trajectory Planning for Variable Stiffness Actuated Robot

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