A step towards generating human-like walking gait via trajectory optimization through contact for a bipedal robot with one-sided springs on toes

Chao, Kenneth; Hur, Pilwon

doi:10.1109/iros.2017.8206361

Cited by 7 publications

(10 citation statements)

References 16 publications

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“…In the separation problems in ( 29) and (30) we have included the K 1 ∩ B n 1 and K 2 ∩ B m 1 constraint without specifying a formulation. We provide a mixed integer programming formulation for the CQLF conditions (12) in § 4.2 and for the EQLF conditions (18) in § 4.3.…”

Section: Cutting Plane Algorithmmentioning

confidence: 99%

“…To state the sufficiency conditions ( 12) required for a CQLF in the general form (25), we set n = n x , (10), and K 2 = K = Gr SOL(Dx, F ) ⊆ R nx+nc . In the separation problem for a CQLF, we are given a matrix P l xx , and we wish to verify if the conditions (12) hold for this matrix. Thus, we seek a vector w = (x, λ) ∈ B nx+nc 1 such that either w T P l xx w ≤ 0 or −w T M (P l xx )w ≤ 0 for some (x, λ) ∈ Gr SOL(Dx, F ).…”

Section: Common Quadratic Lyapunov Functionmentioning

confidence: 99%

“…Thus, we seek a vector w = (x, λ) ∈ B nx+nc 1 such that either w T P l xx w ≤ 0 or −w T M (P l xx )w ≤ 0 for some (x, λ) ∈ Gr SOL(Dx, F ). If no such vector exits, then we have verified that P l xx satisfies conditions (12), else the associated vector may be added to the appropriate set U l or V l in the master problem (27).…”

Section: Common Quadratic Lyapunov Functionmentioning

confidence: 99%

“…The modeling and study of dynamical systems with complementarity conditions has been steadily increasing, with application in electrical circuit simulation, robotics, nonsmooth mechanics, economics, bioengineering [1,5,9,10,29,30,35,36,39,40,41]. Another important recent application of interest is robotics, where complementarity is required to model the friction forces that arise in contact-based manipulation tasks [12,25,27,32,34,33].…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of Discrete-Time Linear Complementarity Systems

Raghunathan,

Linderoth

2020

Preprint

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A Discrete-Time Linear Complementarity System (DLCS) is a dynamical system in discrete time whose state evolution is governed by linear dynamics in states and algebraic variables that solve a Linear Complementarity Problem (LCP). The DLCS is the hybrid dynamical system that is the discrete-time counterpart of the well-known Linear Complementarity System (LCS). We derive sufficient conditions for Lyapunov stability of a DLCS when using a quadratic Lyapunov function that depends only on the state variables and a quadratic Lyapunov function that depends both on the state and the algebraic variables. The sufficient conditions require checking the feasibility of a copositive program over nonconvex cones. Our results only assume that the LCP is solvable and do not require the solutions to be unique. We devise a novel, exact cutting plane algorithm for the verification of stability and the computation of the Lyapunov functions. To the best of our knowledge, our algorithm is the first exact approach for stability verification of DLCS. A number of numerical examples are presented to illustrate the approach. Though our main object of study in this paper is the DLCS, the proposed algorithm can be readily applied to the stability verification of LCS. In this context, we show the equivalence between the stability of a LCS and the DLCS resulting from a time-stepping procedure applied to the LCS for all sufficiently small time steps.

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Section: Cutting Plane Algorithmmentioning

confidence: 99%

Section: Common Quadratic Lyapunov Functionmentioning

confidence: 99%

Section: Common Quadratic Lyapunov Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of Discrete-Time Linear Complementarity Systems

Raghunathan,

Linderoth

2020

Preprint

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“…Here, with a higher-order representation of the system within a finite element, contact changes are constrained to only occur at the mesh points. If this is not done, as in [17,18], complementarity is not guaranteed within the finite element (e.g. the foot could leave or strike the ground at a collocation point).…”

Section: Our Approachmentioning

confidence: 99%

Contact-Implicit Trajectory Optimization Using Orthogonal Collocation

Patel

Shield

Kazi

et al. 2019

IEEE Robot. Autom. Lett.

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In this paper we propose a method to improve the accuracy of trajectory optimization for dynamic robots with intermittent contact by using orthogonal collocation. Until recently, most trajectory optimization methods for systems with contacts employ mode-scheduling, which requires an a priori knowledge of the contact order and thus cannot produce complex or non-intuitive behaviors. Contact-implicit trajectory optimization methods offer a solution to this by allowing the optimization to make or break contacts as needed, but thus far have suffered from poor accuracy. Here, we combine methods from direct collocation using higher order orthogonal polynomials with contact-implicit optimization to generate trajectories with significantly improved accuracy. The key insight is to increase the order of the polynomial representation while maintaining the assumption that impact occurs over the duration of one finite element.

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