Quadratic optimization over a polyhedral cone

Tian, Ye; Jin, Qingwei; Deng, Zhibin

doi:10.3934/jimo.2016.12.269

Cited by 1 publication

(1 citation statement)

References 22 publications

(28 reference statements)

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“…Clearly, if the normal direction is not in this half-space, the normal hyper-plane Π will not properly intersect the cone (i.e. the intersection of K 6 c and Π is not an ellipsoid) [51]. We then search d as close as possible to the mean of the family of rays, while respecting this constraint.…”

Section: B Outer Approximationmentioning

confidence: 99%

Multicontact Locomotion of Legged Robots

2018

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Locomotion of legged robots on arbitrary terrain using multiple contacts is yet an open problem. To tackle it, a common approach is to rely on reduced template models (e.g. the linear inverted pendulum). However, most of existing template models are based on some restrictive hypotheses that limit their range of applications. Moreover, reduced models are generally not able to cope with the constraints of the robot complete model, such as the kinematic limits. In this paper, we propose a complete solution relying on a generic template model, based on the centroidal dynamics, able to quickly compute multi-contact locomotion trajectories for any legged robot on arbitrary terrains. The template model relies on exact dynamics and is thus not limited by arbitrary assumption. We also propose a generic procedure to handle feasibility constraints due to the robot whole body as occupancy measures, and a systematic way to approximate them using off-line learning in simulation. An efficient solver is finally obtained by introducing an original second-order approximation of the centroidal wrench cone. The effectiveness and the versatility of the approach is demonstrated in several multi-contact scenarios with two humanoid robots both in reality and in simulation.

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Section: B Outer Approximationmentioning

confidence: 99%