Robot Impedance Control and Passivity Analysis with Inner Torque and Velocity Feedback Loops

Impedance control is a well-established technique to control interaction forces in robotics. However, real implementations of impedance control with an inner loop may suffer from several limitations. Although common practice in designing nested control systems is to maximize the bandwidth of the inner loop to improve tracking performance, it may not be the most suitable approach when a certain range of impedance parameters has to be rendered. In particular, it turns out that the viable range of stable stiffness and damping values can be strongly affected by the bandwidth of the inner control loops (e.g. a torque loop) as well as by the filtering and sampling frequency. This paper provides an extensive analysis on how these aspects influence the stability region of impedance parameters as well as the passivity of the system. This will be supported by both simulations and experimental data. Moreover, a methodology for designing joint impedance controllers based on an inner torque loop and a positive velocity feedback loop will be presented. The goal of the velocity feedback is to increase (given the constraints to preserve stability) the bandwidth of the torque loop without the need of a complex controller.Comment: 14 pages in Control Theory and Technology (2016

Dynamics for variable length multisection continuum arms

Variable length multisection continuum arms are a class of continuum robotic manipulators that generate motion by structural mechanical deformation. Unlike most continuum robots, the sections of these arms do not have (central) supporting flexible backbone, and are actuated by multiple variable length actuators. Because of the constraining nature of actuators, the continuum sections can bend and/or elongate (compress) depending on the elongation/contraction characteristics of the actuators being used. Continuum arms have a number of distinctive differences with respect to traditional rigid arms namely: smooth bending, high inherent compliance, and adaptive whole arm grasping. However, due to numerical instability and the complexity of curve parametric models, there are no spatial dynamic models for multisection continuum arms. This paper introduces novel spatial dynamics and applies these to variable length multisection continuum arms with any number of sections. An efficient recursive computational scheme for deriving the equations of motion is presented. This is applied in a general form based on structurally accurate and numerically well-posed modal kinematics that assumes circular arc deformation of continuum sections without torsion. It is shown that the proposed modal dynamics are highly scalable, producing efficient and accurate numerical results. The spatial dynamic simulation results are experimentally validated using a pneumatic muscle actuated multisection prototype continuum arm. For the first time this enables investigation of spatial dynamic effects in this class of continuum arms

Control of a compliant humanoid robot in double support phase: A geometric approach

Enhancing energy efficiency of bipedal walking is an important research problem that has been approached by design of recently developed compliant bipedal robots such as CoMan. While compliance leads to energy efficiency, it also complicates the walking control system due to further under-actuated degrees of freedom (DoF) associated with the compliant actuators. This problem becomes more challenging as the constrained motion of the robot in double support is considered. In this paper this problem is approached from a multi-variable geometric control aspect to systematically account for the compliant actuators dynamics and constrained motion of the robot in double support phase using a detailed electro-mechanical model of CoMan. It is shown that the formulation of constraint subspace is non-trivial in the case of non-rigid robots. A step-wise numerical algorithm is provided and the effectiveness of the proposed method is illustrated via simulation, using a ten DoF model of CoMan. </jats:p

Stability analysis for time delay control of nonlinear systems in discrete-time domain with a standard discretisation method

Publisher Copyright: © 2020, South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature.This paper provides stability analysis results for discretised time delay control (TDC) as implemented in a sampled data system with the standard form of zero-order hold. We first substantiate stability issues in discrete-time TDC using an example and propose sufficient stability criteria in the sense of Lyapunov. Important parameters significantly affecting the overall system stability are the sampling period, the desired trajectory and the selection of the reference model dynamics.Peer reviewe

Decentralized LQR Joint Servo Design for a Compliant Humanoid Robot via LMI Optimisation

Enhancing bipedal walking safety, robustness and efficiency has led to design of compliant humanoid robots. However, the links' interactions and coupling effects are often neglected in the design of their trajectory tracking controller. Moreover, there is not a direct decentralized approach for designing the PD-PID gains given a multivariable model of the compliant humanoid robot. This paper proposes an LMI formulation for designing decentralized PID gains in discrete time. It is shown that this method can be used to design a full state feedback for trajectory tracking which includes the compliance and links' interactions in the feedback design. Numerical simulations for a compliant compass gait and a 10 DoF humanoid models are provided to illustrate the use of this method

Global Stability Study of a Compliant Double-Inverted Pendulum Based on Hamiltonian Modeling

This paper presents a dynamical model of a compliant double-inverted pendulum that is used to approximate the physical structure of the compliant humanoid (COMAN) robot, using both the Hamiltonian and the Lagrangian approaches. A comparison between the two aims at providing insight into the various advantages and/or disadvantages associated to each approach. Through manipulation of the resulting formulae, it is shown that the Hamiltonian equations possess certain characteristics, such as the allowance of the tracking of global stability, that render this method of representation suitable for legged robotics applications. Finally, an asymptotically stabilizing control scheme is presented together with simulation results.</jats:p

Modelling human balance using switched systems with linear feedback control

We are interested in understanding the mechanisms behind and the character of the sway motion of healthy human subjects during quiet standing with eyes closed. We assume that a human body can be modelled as a single-link inverted pendulum, and the balance is achieved using liner feedback control. Using these assumptions we derive a switched model which we then investigate. Stable periodic motions (limit cycles) about an upright position are found. The existence of these limit cycles is studied as a function of system parameters. The exploration of the parameter space leads to the detection of multistability and homoclinic bifurcation