Structure-preserving discrete-time optimal maneuvers of a wheeled inverted pendulum

Phogat, Karmvir Singh; Banavar, Ravi N.; Chatterjee, Debasish

doi:10.1016/j.ifacol.2018.06.042

Cited by 5 publications

(5 citation statements)

References 17 publications

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“…Moreover, the system is subject to non-holonomic constrains which are due to the pure rolling of the vehicle. [34][35][36][37] The WIP can find applications in the transportation of humans and products, while significant use of it is related with warehouse management. Thanks to its capacity for dexterous maneuvering and the simplicity in its production, the use of WIP in industrial-type applications is rapidly deploying.…”

Section: Dynamic Model Of the Wipmentioning

confidence: 99%

Nonlinear Optimal Control for the Wheeled Inverted Pendulum System

Rigatos

Busawon²,

Pomares³

et al. 2019

Robotica

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SummaryThe article proposes a nonlinear optimal control method for the model of the wheeled inverted pendulum (WIP). This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. First, the dynamic model of the WIP undergoes approximate linearization around a temporary operating point which is recomputed at each time step of the control method. The linearization procedure makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. For the linearized model of the wheeled pendulum, an optimal (H-infinity) feedback controller is developed. The controller’s gain is computed through the repetitive solution of an algebraic Riccati equation at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, by using the H-infinity Kalman Filter as a robust state estimator, the implementation of a state estimation-based control scheme becomes also possible.

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Section: Dynamic Model Of the Wipmentioning

confidence: 99%

Nonlinear Optimal Control for the Wheeled Inverted Pendulum System

Rigatos

Busawon²,

Pomares³

et al. 2019

Robotica

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“…As convincingly argued in [MW01], the discrete-time dynamics (2.2) should be derived following the ideas of discrete mechanics to ensure greater numerical fidelity and accuracy; this particular technique ensures that the discretization does not violate the underlying manifold structure under time-discretization and also preserves important system invariants for conservative systems; consequently, it leads to greater accuracy than otherwise. Discrete mechanics is steadily becoming a popular tool to discretize the dynamics of physical systems; for instance, we refer the reader to [KMS10] for examples of discretized dynamics of non-holonomic systems with symmetry, [PCB18a] for examples of discretized spacecraft attitude dynamics, [PBC18] for examples of discretized wheeled inverted pendula 3, [NB18] for examples of discretized dynamics of interconnected mechanical systems, and [NS10] for examples of discretized dynamics of rigid bodies evolving on the Lie group SE(3). Hamiltonian is maximized over the entire admissible control action set at the optimal value of the control action.…”

Section: §1 Imentioning

confidence: 99%

On optimal multiplexing of an ensemble of discrete-time constrained control systems on matrix Lie groups

Maheshwari¹,

Sukumar²,

Chatterjee³

2019

Preprint

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http://www.sc.iitb.ac.in/~chatterjee A . We study a constrained optimal control problem for an ensemble of control systems. Each sub-system (or plant) evolves on a matrix Lie group, and must satisfy given state and control action constraints pointwise in time. In addition, certain multiplexing requirement is imposed: the controller must be shared between the plants in the sense that at any time instant the control signal may be sent to only one plant. We provide first-order necessary conditions for optimality in the form of suitable Pontryagin maximum principle in this problem. Two numerical experiments are presented: first, for a system of two satellites; second, for a system of two underwater vehicles performing energy optimal maneuvers under the preceding family of constraints.

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“…In order to do trajectory planning in discrete-time, we apply tools from discrete mechanics to derive a discrete-time variational integrator 2 and define an optimal control problem in discrete-time to synthesize an optimal trajectory. 2 A few modeling inaccuracies reported in [22] are being rectified in this submission.…”

Section: Trajectory Planning Of the Wipmentioning

confidence: 99%

“…During constrained motion planning scenarios, it is essential to consider voltage and current restrictions at the trajectory design stage which necessitates the modeling of the motor dynamics. A constrained path planning of WIP using variational techniques, in [22], discusses WIP modeling without current dynamics, in which the motor torque is considered as the input, and the system does not account for motor current and voltage restrictions in trajectory planning. In this article we address this issue by deriving a model of the WIP with motor dynamics in both continuous and discrete-time for constrained path planning.…”

Section: Introductionmentioning

confidence: 99%

“…In this article we address this issue by deriving a model of the WIP with motor dynamics in both continuous and discrete-time for constrained path planning. Moreover, we conduct experiments to demonstrate efficacy of the proposed scheme unlike [22]. In contrast to our technique, constrained motion planning problems in the stochastic framework is studied extensively in [23], [24] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

Albert¹,

Phogat²,

Anhalt³

et al. 2018

Preprint

Self Cite

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The Wheeled Inverted Pendulum (WIP) is an underactuated, nonholonomic mechatronic system, and has been popularized commercially as the Segway. Designing a control law for motion planning, that incorporates the state and control constraints, while respecting the configuration manifold, is a challenging problem. In this article we derive a discrete-time model of the WIP system using discrete mechanics and generate optimal trajectories for the WIP system by solving a discretetime constrained optimal control problem. Further, we describe a nonlinear continuous-time model with parameters for designing a closed loop LQ-controller. A dual control architecture is implemented in which the designed optimal trajectory is then provided as a reference to the robot with the optimal control trajectory as a feedforward control action, and an LQ-controller in the feedback mode is employed to mitigate noise and disturbances for ensuing stable motion of the WIP system. While performing experiments on the WIP system involving aggressive maneuvers with fairly sharp turns, we found a high degree of congruence in the designed optimal trajectories and the path traced by the robot while tracking these trajectories. This corroborates the validity of the nonlinear model and the control scheme. Finally, these experiments demonstrate the highly nonlinear nature of the WIP system and robustness of the control scheme.

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Structure-preserving discrete-time optimal maneuvers of a wheeled inverted pendulum

Cited by 5 publications

References 17 publications

Nonlinear Optimal Control for the Wheeled Inverted Pendulum System

Nonlinear Optimal Control for the Wheeled Inverted Pendulum System

On optimal multiplexing of an ensemble of discrete-time constrained control systems on matrix Lie groups

Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

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