The Geometry of Optimal Gaits for Inertia-Dominated Kinematic Systems

Hatton, Ross L.; Brock, Zachary; Chen, Shuoqi; Choset, Howie; Faraji, Hossein; Fu, Ruijie; Justus, Nathan; Ramasamy, Suresh

doi:10.1109/tro.2022.3164595

Cited by 12 publications

(1 citation statement)

References 22 publications

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“…Given an arbitrary limb trajectory, the corresponding trajectory of F reveals the extent to which the system is slipping or sticking. The direction of maximum slippage is given by the gradient, ∇F T and we call it the slipping direction (this is also scaled by the local value of the gradient) 3 . Correspondingly, to compute the sticking direction, we define a clockwise rotational transform, f ϵ on α:…”

Section: Stick-slip Shape Velocity Basismentioning

confidence: 99%

Classification and performance evaluation of simultaneous multithreaded architectures

Krishna¹,

Govindarajan

Proceedings Fourth International Conference on High-Performance Computing

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In this paper, we develop a geometric framework for generating non-slip quadrupedal two-beat gaits. We consider a four-bar mechanism as a surrogate model for a contact state and develop the geometric tools such as shape-change basis to aid in gait generation, local connection as the matrix-equation of motion, and stratified panels to model net locomotion in line with previous work [1]. Standard two-beat gaits in quadrupedal systems like trot divide the shape space into two equal, decoupled subspaces. The subgaits generated in each subspace space are designed independently and when combined with appropriate phasing generate a two-beat gait where the displacements add up due to the geometric nature of the system. By adding "scaling" and "sliding" control knobs to subgaits defined as flows over the shape-change basis, we continuously steer an arbitrary, planar quadrupedal system. This exhibits translational anisotropy when modulated using the scaling inputs. To characterize the steering induced by sliding inputs, we define an average path curvature function analytically and show that the steering gaits can be generated using a geometric nonslip contact modeling framework.

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Section: Stick-slip Shape Velocity Basismentioning

confidence: 99%

Classification and performance evaluation of simultaneous multithreaded architectures

Krishna¹,

Govindarajan

Proceedings Fourth International Conference on High-Performance Computing

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Optimal reorientation of planar floating snake robots with collision avoidance

Itani,

Shammas,

Abou Jaoude

2024

Robotics and Autonomous Systems

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Optimal control of robotic systems and biased Riemannian splines

Cabrera,

Hatton

2024

ESAIM: COCV

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In this paper, we study mechanical optimal control problems on a given Riemannian manifold (Q, g) in which the cost is defined by a general cometric g̃ . This investigation is motivated by our studies in robotics, in which we observed that the mathematically natural choice of cometric g̃ = g* -the dual of g- does not always capture the true cost of the motion. We then, first, discuss how to encode the system's torque-based actuators configuration into a cometric g̃ . Second, we provide and prove our main theorem, which characterizes the optimal solutions of the problem associated to general triples (Q, g, g̃ ) in terms of a 4th order differential equation. We also identify a tensor appearing in this equation as the geometric source of "biasing" of the solutions away from ordinary Riemannian splines and geodesics for (Q, g). Finally, we provide illustrative examples and practical demonstration of the biased splines as providing the true optimizers in a concrete robotics system.

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The Geometry of Optimal Gaits for Inertia-Dominated Kinematic Systems

Cited by 12 publications

References 22 publications

Classification and performance evaluation of simultaneous multithreaded architectures

Classification and performance evaluation of simultaneous multithreaded architectures

Optimal reorientation of planar floating snake robots with collision avoidance

Optimal control of robotic systems and biased Riemannian splines

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