Sequential Action Control for models of underactuated underwater vehicles in a planar ideal fluid

The International Journal of Robotics Research

2018

Self Cite

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actionsthe second-order needle variations of optimal control-as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Lastly, the underactuated dynamic underwater vehicle model demonstrates convergence even in the presence of a velocity field.

Section: Simulation Resultsmentioning

confidence: 99%

“…where normalΛ ≜ h T ρ ρ T h and α d ∈ normalℝ − expresses the desired value of the mode insertion gradient term (see, for example, Mamakoukas et al, 2016). Typically, α d = γ J o , where J o is the cost function (3) computed using default dynamics f 1 .…”

Section: Control Synthesismentioning

confidence: 99%

Feedback synthesis for underactuated systems using sequential second-order needle variations

Mamakoukas

MacIver

The International Journal of Robotics Research

2018

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“…In view of this observation, our previous work in [3]- [7] presented Sequential Action Control (SAC), a receding horizon approach for control of nonlinear systems, that exploits elements from hybrid systems theory [8], [9]. In contrast with the aforementioned MPC methods, the openloop solution in SAC optimizes the needle variation [10] of the cost resulting in a single, constant magnitude action which does not optimize, but rather improves the cost function value relative to applying only a nominal control signal.…”

Section: Introductionmentioning

confidence: 85%

Iterative Sequential Action Control for Stable, Model-Based Control of Nonlinear Systems

Tzorakoleftherakis

IEEE Trans. Automat. Contr.

2019

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This paper presents iterative Sequential Action Control (iSAC), a receding horizon approach for control of nonlinear systems. The iSAC method has a closed-form open-loop solution, which is iteratively updated between time steps by introducing constant control values applied for short duration. Application of a contractive constraint on the cost is shown to lead to closedloop asymptotic stability under mild assumptions. The effect of asymptotically decaying disturbances on system trajectories is also examined. To demonstrate the applicability of iSAC, we employ a variety of systems and conditions, including a 13dimensional quaternion-based quadrotor and NASA's TRACE spacecraft. Each system is tested in different scenarios, ranging from feasible and infeasible trajectory tracking, to setpoint stabilization, with or without the presence of external disturbances. Finally, limitations of this work are discussed.

“…where the effective mass and moment of inertia of the rigid body are given by M = diag(6.04, 17.31, 8.39) g and J = diag(1.57, 27.78, 54.11)g·cm 2 , respectively. This example is inspired by work in [45], [50] and the parameters used for the effective mass and moment of inertia of a rigid body correspond to measurements of a fish. The control inputs are F 2 = T 3 = 0 and F 3 ≥ 0.…”

Section: Underactuated Dynamic 3d Fishmentioning

confidence: 99%

Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

Mamakoukas

MacIver

Robotics: Science and Systems XIII

2017

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Abstract-This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions-the needle variations of optimal control-as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.