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Challenges in Legged Locomotion

Avik De
September 30, 2019

Challenges in Legged Locomotion

This talk was made for a general audience

Avik De

September 30, 2019


  1. Vertical hopper compositions for preflexive and feedback-stabilized
    quadrupedal bounding, pacing, pronking, and trotting
    [Full and Koditschek (1999)]
    “Templates and anchors…”
    [De and Koditschek (IJRR, 2018)]
    Simple compositional controller for running gaits
    Provable coordination Robustness to
    parametric uncertainty
    Bio-inspired: animals exhibit
    similar task-level reduction

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  2. Input-decoupled anchoring
    • Can find reduced coordinates 𝑟 𝑞 s.t.
    does not appear in ሷ
    • 𝑟 𝑞 is ~ virtual leg pos
    • SLIP dynamics are exactly embedded!
    A new kind of anchoring
    Input-decoupled anchoring with actuated
    IP template behavior
    Floating torso model 𝑥 ∈ 𝑆𝐸(2)
    Invariant+attracting pitch-stable manifold (conventional anchoring/ZD)
    [Full & Kod (1999)] [Westervelt et al (2007)]

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  3. Challenges in legged locomotion: mechanics
    [Seok et. al. (2015)]
    GR Vision 60 v4
    Model S
    Vision 60
    Specific joint torque
    0.41 6.0 (15x)
    Specific peak power
    250 1,305 (5x)
    Specific energy
    40 30+ (similar)
    Control freq (Hz) 100 1,000 (10x)
    High force and power
    • The actuators (not the structure) need to support
    vehicle weight (including actuators)
    • Reciprocating swing legs need high peak power
    Specialized actuator requirements
    • High gear ratios result in high reflected actuator inertia
    • Harsh ground impact
    • High power required to swing legs
    • Control systems require very high actuator bandwidth
    for robustness/agility
    • Series-elastic limits bandwidth [Wensing (2017)]
    Efficiency fundamentally limited
    Can be seen in animals and robots

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  4. Challenges in legged locomotion: control
    • Air/water are soft, ground is hard
    • Stiff actuators that work in the factory and for
    aerial robots don’t work with legs
    • Managing interaction force requires force control
    bandwidth in the KHz range, precise detection of
    external forces, and specialized algorithms
    Impedance control
    [Posa et al (2014)]
    Air/water are predictable, whereas every single step
    for a legged robot contains unexpected contacts
    System dimension/underactuation
    Dimension Actuators
    Quadruped 36 12
    Wheeled/tracked diff
    drive (vel control)
    3 2
    Wheeled/tracked fast 6 2
    Quadrotor 12 4
    Managing contacts
    • The robot body can only be controlled via
    ground contact
    • Even state of the art trajectory optimization
    cannot navigate the millions of possible
    contact sequences in anywhere near real time
    Environment complexity
    Even a single misstep/missed contact out of
    thousands can cause total failure
    Robustness requirements

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