Research ArticleSPACE ROBOTS

Material remodeling and unconventional gaits facilitate locomotion of a robophysical rover over granular terrain

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Science Robotics  13 May 2020:
Vol. 5, Issue 42, eaba3499
DOI: 10.1126/scirobotics.aba3499
  • Fig. 1 Prototype rovers with legged gait capabilities.

    (A) NASA’s RP15 prototype. (B) The Mini Rover resting on a bed of loosely packed poppy seeds on an incline of θbed ≈ 20. (C) Four top-view rendered snapshots of the Mini Rover executing a quadrupedal gait: an RS gait with no modulation. In the RS gait, all wheels except the one colored in red sweep toward the rear of the rover for 2.7 s. The sweep direction for each wheel in each snapshot is shown with the black arrows. Once the sweep is complete, the wheel begins the reset phase, where the wheel is colored in red. The Mini Rover lifts the resetting wheel with its four-bar linkage and rotates it 90° toward the front of the rover in 0.9 s. The reset direction for each wheel is shown in red arrows.

  • Fig. 2 Robustness and performance of the rotary sequence gait.

    (A) Horizontal displacement over time of the Mini Rover at rest for 5 s using wheel spin only on a 0 slope of loose poppy seeds for 30 s and then executing the RS gait described in Fig. 1C for 60 s. Data shown are means ± SD for seven runs. The time interval shaded yellow from 0 to 35 s is the “wheel spin phase,” and shaded orange from 35 to 95 s is the “RS gait” phase. The Mini Rover reaches the end of the test bed near the 80-s mark. (B) Mean ± SD velocities going uphill of the RS gait shown in (Fig. 1C) for different granular slope angles, varying the θbed in (Fig. 1B), with seven trials for each bed angle. (C) Mean ± SD average velocity over seven trials each in the steady state of the RS gait on a θbed = 15 poppy slope, with various subsystems of the gait disabled.

  • Fig. 3 Isolation studies of single-wheel force response.

    (A) Side view and top view schematics of the single-wheel gantry test bed. The Cartesian coordinate system {x, y, z} describes the world frame aligned with the test bed, whereas a local Wheel coordinate system {F, F, FN}, which rotates about z by θsweep, defines the force responses parallel, perpendicular, and normal to the wheel at each sampled θsweep. The wheel coordinate system rotates over time as the appendage executes its gait. (B) Top-down sketch of the sweeping wheel path input into the system in (A) at different θbed values. The shaded rectangle is a projection of the top-down view of a single wheel for scale.

  • Fig. 4 Single-wheel force response in stationary versus moving frames.

    (A) For vx = 0 mm/s and θbed = 0, force components for a stationary RS gait sweep rearward with wheel spin off versus wheels spinning at 2.1 rad/s. RFT calculation of the resistive forces for this trajectory gives flat force response curves with respect to θsweep, because of cylindrical symmetry about the z axis. (B) For θbed = 0, varying vx in the gantry system (Fig. 2A) varies the drawbar force curves with respect to sweep angles. Experiments in solid lines, mean ± SD across 20 sweeps in the steady state, and wheel spinning at 2.1 rad/s. Inset: 3D RFT simulation diagram for vx = 11 mm/s.

  • Fig. 5 Propulsive forces in the Mini Rover’s RS gait.

    (A) Drawbar forces exerted over time by the Mini Rover using the RS gait with four sweeping legs up a bed of loosely packed poppy seeds at θbed = [0,8,15] (inset shows experiment setup). Data shown are means ± SD over seven trials for each value of θbed. (B) Mini Rover saturated drawbar forces with the RS gait (top) experimental (solid) versus RFT-based calculation (dashed) over time for two gaits cycles of the RS gait, summed over all four locomoting appendages. Bottom: Mean saturated drawbar pull with respect to θbed for experiment (error bars) versus RFT calculation (dashed). (C) Drawbar forces exerted over time by the Mini Rover using the RS gait with three sweeping legs (with rear left leg sweeping disabled) up a bed of loosely packed poppy seeds at θbed = [0,8,15]. Data shown are means ± SD over seven trials for each value of θbed. (D) Mean ± SD velocities going uphill of the RS gait with four sweeping wheels versus selectively disabled sweeping wheels for different granular slope angles, varying the θbed with seven trials performed for each bed angle.

  • Fig. 6 Propulsive forces of RP15 and Mini Rover in wet granular media.

    (A) Drawbar forces exerted over time by RP15 during tests in a bed of moist sand at JSC (diagram shows experiment setup). Blue data points show one trial of RP15 executing a wheel spin motion for 120 s, and black data show the means ± SD for three trials of RP15 executing an RS gait for 170 s. (B) Drawbar force versus time for three moist sand RS gait drawbar trials of the Mini Rover. Each different colored line represents a different trial. The Mini Rover generates increasing drawbar force with the RS gait even with one appendage sweeping mechanism disabled and in a much more cohesive substrate than the dry GM trials with three active wheels. Inset: Mini Rover in a bed of moist sand exerting drawbar forces with the RS gait in a bed of moist sand (top view). Qualitatively, the grouser-sand interaction appears to closely mirror the RP15 experiments (e.g., the grousers became smooth as the wheels spin and sand aggregates between the grousers.)

  • Fig. 7 Steep granular slope climbing via dynamic remodeling with an RRP gait.

    (A) Top: Two top-down snapshots showing a RRP gait with no modulation, with a time interval between each snapshot of 0.65 s. In the RRP gait, the rear wheel colored in white sweeps toward the rear of the rover up to 45°. The sweep direction for each wheel in each snapshot is shown in black arrows. Once the sweep is complete, the wheel begins the reset phase, where the wheel is colored in red. The Mini Rover lifts the resetting wheel with its four-bar linkage and rotates it 45° toward the front of the rover. Bottom: Side-view illustration of the Mini Rover climbing a hill of GM using the RRP gait. (B) Mean velocities going uphill of the RS and RRP gaits shown in Fig. 1C and (A), respectively, for different granular slope angles (θbed). Data shown are means ± SD over seven trials for each angle. There is overall less variance in the RRP gait’s mean velocity over multiple trials than the RS gait’s, because RRP exhibits a more predictable and stable speed at steep θbed. (C) Height difference color map of the GM profiles over time as the Mini Rover executes the RRP gait on a 25 granular slope, with the spatial components in the tilted bed coordinate system (x, y) shown in (A). A black line indicates the rover’s front wheel’s position over time, and a gray line indicates the rear wheel’s position over time. The rover carries the IM as a bubble of GM between these dots as it locomotes forward, maintaining a net flux of GM from the rover’s front wheels to the rear mound.

  • Fig. 8 Performance and granular transport mechanisms for the RRP gait.

    (A) Uphill displacement over time of Mini Rover using the RRP gait to climb a 28 granular incline. Turning off the wheel spinning or sweeping components of the RRP gait causes failure to climb. Data represent means ± SD for seven trials for each condition. The numbered nodes represent key events in the rover’s climbing dynamics, where the rover initiates the RRP gait at node 1, ends slide back and begins forward progress once the rear mound has formed at node 2, and ends the RRP gait at node 3. (B) Bivariate boxplot of the 2D-projected area of the IM that forms between the two wheels of the Mini Rover as it climbs with RRP (see diagram in Fig. 7C) with respect to the Mini Rover’s uphill velocity, with 13 total trials of 50 s each over three values of θbed. The solid colors are the boundary of mean trajectories over time for these two variables. At each mean trajectory point, the covariance matrix of velocity and mound area at that time stamp creates an error ellipse centered at μ (mean) with dimensions ±1σ (SD). The union of the set of error ellipses for each mean trajectory point gives the shaded regions, representing the variance between trials for each group of θbed.

  • Movie 1. Research motivation, summary of locomotion strategies, and hill climbing through terrain remodeling.

Supplementary Materials

  • robotics.sciencemag.org/cgi/content/full/5/42/eaba3499/DC1

    Fig. S1. Engineering sketches of the Mini Rover.

    Fig. S2. Diagram of rover appendage actuations.

    Fig. S3. Granular experimentation bed and gantry.

    Fig. S4. Mini Rover RS gait velocity and sinkage profiles.

    Fig. S5. Dynamic reconfiguration with the RRP gait on various slopes.

    Movie S1. RP15 climbs granular mound with the RS gait.

    Movie S2. Mini Rover using RS gait on a flat poppy seed bed.

    Movie S3. Mini Rover RS gait trial in granular experimentation bed.

    Movie S4. Single-wheel gantry trial of spin and sweep motion.

    Movie S5. Mini Rover RS gait trial measurement of drawbar force.

    Movie S6. Drawbar force measurements of RP15 prototype rover.

    Movie S7. Mini Rover RS gait drawbar force measurement in wet sand bed.

    Movie S8. Mini Rover RRP gait on sloped poppy seed bed.

    Movie S9. Comparison of Mini Rover RRP gait with wheel spin enabled versus disabled.

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. Engineering sketches of the Mini Rover.
    • Fig. S2. Diagram of rover appendage actuations.
    • Fig. S3. Granular experimentation bed and gantry.
    • Fig. S4. Mini Rover RS gait velocity and sinkage profiles.
    • Fig. S5. Dynamic reconfiguration with the RRP gait on various slopes.
    • Legends for movies S1 to S9

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). RP15 climbs granular mound with the RS gait.
    • Movie S2 (.mp4 format). Mini Rover using RS gait on a flat poppy seed bed.
    • Movie S3 (.mp4 format). Mini Rover RS gait trial in granular experimentation bed.
    • Movie S4 (.mp4 format). Single-wheel gantry trial of spin and sweep motion.
    • Movie S5 (.mp4 format). Mini Rover RS gait trial measurement of drawbar force.
    • Movie S6 (.mp4 format). Drawbar force measurements of RP15 prototype rover.
    • Movie S7 (.mp4 format). Mini Rover RS gait drawbar force measurement in wet sand bed.
    • Movie S8 (.mp4 format). Mini Rover RRP gait on sloped poppy seed bed.
    • Movie S9 (.mp4 format). Comparison of Mini Rover RRP gait with wheel spin enabled versus disabled.

    Files in this Data Supplement:

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