PD Tracking for a Class of Underactuated Robotic Systems With Kinetic Symmetry

Kolathaya, Shishir

doi:10.1109/lcsys.2020.3005957

Cited by 10 publications

(8 citation statements)

References 12 publications

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“…Specifically, the kinematic constraints are position and velocity functions of the robot manipulator. This approach is motivated by the success of PD based QPs [11], in which the kinetic energy was used to construct CLF based constraints in QPs. It is worth mentioning that the velocity forms, despite not having the kinetic energy in the strict sense, have properties that are well associated with the same.…”

Section: Discussionmentioning

confidence: 99%

“…Hence, the QP of the form (VQP) is feasible. Therefore, we have a min-norm control law obtained similar to (11). In particular, if ψ 10 > 0, then we have that…”

Section: Proof Of This Theorem Is Not Necessary As It Is Similar Tomentioning

confidence: 99%

“…It is worth noting that this is the template Lyapunov function used to establish stability of PD controlled robotic systems [21], [14], [11]. The PD control law is of the form…”

Section: Definitionmentioning

confidence: 99%

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Energy based Control Barrier Functions for Robotic Systems

Kolathaya¹

2020

Preprint

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<div>Control barrier function (CBF) based Quadratic Programs (QPs) were introduced in early 2014 as a means to guarantee safety in affine control systems in conjunction with stability/tracking. However, due to the presence of model-based terms, they fail to provide guarantees under model perturbations. Therefore, in this paper, we propose a new class of CBFs for robotic systems that augment kinetic energy with the traditional forms. We show that with torque limits permitting, and with the kinematic models accurately known, forward invariance of safe sets generated by kinematic constraints (position and velocity) can be guaranteed. The proposed methodology is motivated by the control Lyapunov function (CLF) based QPs that use the kinetic energy function. By the property of CBF-QPs, we show that the pointwise min-norm control laws obtained are feasible and Lipschitz continuous, and can be derived analytically via the KKT conditions. In order to include stability with safety, we also augment CLF based constraints in the CBF-QPs to realize a unified control law that allows tracking with safety irrespective of the inertial parameters of the robot. We will demonstrate the robustness of this class of CBF-QPs in two robotic platforms: a 1-DOF and a 2-DOF manipulator, by scaling the masses by up to 100, and then simulating the resulting dynamics.</div>

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Section: Discussionmentioning

confidence: 99%

“…Hence, the QP of the form (VQP) is feasible. Therefore, we have a min-norm control law obtained similar to (11). In particular, if ψ 10 > 0, then we have that…”

Section: Proof Of This Theorem Is Not Necessary As It Is Similar Tomentioning

confidence: 99%

See 1 more Smart Citation

Energy based Control Barrier Functions for Robotic Systems

Kolathaya¹

2020

Preprint

Self Cite

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“…Despite its theoretical relevance, this result has limited practical use, since it provides convergence rates which are arbitrarily close to zero, and therefore a poor estimation of the empirical convergence rates evaluated by Monte-Carlo simulations or by experiments. An alternative approach [10]- [12] is to impose high lower bounds on the norms of P and D, so that the effect of (2) is dominant with respect to the left hand side of (1), i.e., the rigid body dynamics. As a result, very high gains are needed to produce meaningful convergence rates, often preventing the practical applicability of the method.…”

Section: Introductionmentioning

confidence: 99%

PD-Like Regulation of Mechanical Systems With Prescribed Bounds of Exponential Stability: The Point-to-Point Case

Calzolari

Santina

Albu‐Schäffer

2021

IEEE Control Syst. Lett.

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This letter discusses an extension of the famous PD regulator implementing point to point motions with prescribed exponential rates of convergence. This is achieved by deriving a novel global exponential stability result, dealing with mechanical systems evolving on uni-dimensional invariant manifolds of the configuration space. The construction of closed loop controllers enforcing the existence of such manifolds is then discussed. Explicit upper and lower bounds of convergence are provided, and connected to the gains of the closed loop controller. Simulations are carried out, assessing the effectiveness of the controller and the tightness of the exponential bounds.

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“…Similarly, the acrobot system is a double pendulum, but the actuated joint is the elbow, and the free joint is the shoulder [25]. Another underactuated mechanical system is the cartpendulum, studied in [26][27]. The cart-pendulum consists of a passive pendulum mounted on a cart.…”

Section: Introductionmentioning

confidence: 99%

Combined adaptive neural network and regressor‐based trajectory tracking control of flexible joint robots

Montoya–Cháirez¹,

Moreno–Valenzuela²,

Santibáñez

et al. 2021

IET Control Theory & Appl

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By relying on the input-output feedback linearization approach, a novel adaptive controller for flexible joint robots is proposed in this work. First, a model-based controller is developed to get a structure that is useful in the development of the adaptive controller. The adaptive version is developed by using two techniques. To stabilize the output function, an adaptive neural network controller is used, which approximates the non-linear function that contains the uncertainties. The desired rotor position required by the input-output feedback linearization controller is defined with the structure of a link dynamics adaptive regressor-based controller. The main reason to adopt the mentioned structure in the definition of the desired rotor link position is to guarantee its differentiability. Real-time experiment comparisons among the model-based controller, a model-based controller with desired compensation, an adaptive controller based on joint torque feedback, and an adaptive neural network-based controller are carried out. Experimental results support the theory reported in this document and the accuracy of the proposed approach.

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PD Tracking for a Class of Underactuated Robotic Systems With Kinetic Symmetry

Cited by 10 publications

References 12 publications

Energy based Control Barrier Functions for Robotic Systems

Energy based Control Barrier Functions for Robotic Systems

PD-Like Regulation of Mechanical Systems With Prescribed Bounds of Exponential Stability: The Point-to-Point Case

Combined adaptive neural network and regressor‐based trajectory tracking control of flexible joint robots

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