Trot-Walk in Quadruped Robotics

• Trot-Walk is a dynamic, diagonal-synchronized trot gait used for rapid traversal while enabling proprioceptive terrain sensing in quadruped robots.
• It operates at about 2 Hz with short stance durations and employs joint-torque estimation to infer ground reaction forces during dynamic impacts.
• Experiments show Trot-Walk offers faster traversal at the cost of increased measurement variance and lower proprioceptive fidelity compared to slower gaits.

“Trot-Walk” denotes the locomotion-oriented trot gait used in the experiments of “Effect of Gait Design on Proprioceptive Sensing of Terrain Properties in a Quadrupedal Robot,” where the authors refer to the standard dynamic trot on the Ghost Robotics Spirit 40 quadruped simply as “Trot-Walk” or \trotloco (Fulcher et al., 26 Sep 2025). In that usage, it is not a separate canonical quadruped gait but a specific implementation of a trot for rapid traversal while performing proprioceptive terrain sensing. Its defining features are diagonal synchronization, laboratory operation at about $f=2\,\mathrm{Hz}$, short stance durations typical of a trot, and a sensing pipeline based on joint-torque estimation and inferred toe forces. The gait is studied primarily as a contrast to the slower, sensing-oriented Crawl N’ Sense gait, thereby exposing the trade-off between locomotion speed and terrain-measurement fidelity (Fulcher et al., 26 Sep 2025).

1. Terminological scope and gait identity

In the cited terrain-sensing experiments, the locomotion-oriented trot gait is referred to simply as “Trot-Walk” (Fulcher et al., 26 Sep 2025). The footfall sequence is that of a two-beat trot: the front-left (FL) and rear-right (RR) legs form one diagonal pair, while the front-right (FR) and rear-left (RL) legs form the other; within each diagonal pair, the two legs are exactly in phase, and the two diagonal pairs alternate with a half-cycle offset $(\Delta \phi = 0.5\ \text{cycle})$ (Fulcher et al., 26 Sep 2025).

This designation can be misread as implying a hybrid between walk and trot. The phase structure described in the experiments does not support that reading. In quadruped gait theory, walk is associated with quarter-cycle offsets across the four feet, whereas trot is associated with diagonal synchronization and antiphase between the diagonals. Tero et al. describe walk as a phase sequence with roughly $90^\circ$ separations and trot as the diagonal pair in-phase solution $(\theta_0=\theta_3,\ \theta_1=\theta_2)$ with a $180^\circ$ phase shift between the two pairs (Tero et al., 2013). This suggests that “Trot-Walk” is best understood as a naming convention internal to the sensing study, not as a distinct intermediate gait class.

The practical role of the gait in that study is equally specific. It is the locomotion-oriented condition against which a quasi-static sensing gait is evaluated. The contrast is therefore not between two stylistic variants of the same task, but between two different operating regimes: one optimized for traversal and one optimized for force–depth measurement (Fulcher et al., 26 Sep 2025).

2. Timing, trajectory generation, and low-level actuation

The gait can be parameterized by a normalized leg phase,

$\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$

with $\phi_{FL0}=\phi_{RR0}=0$ and $\phi_{FR0}=\phi_{RL0}=0.5$ (Fulcher et al., 26 Sep 2025). If $T=1/f$ is the stride period and $\beta$ is the duty factor, the contact schedule is written as

$(\Delta \phi = 0.5\ \text{cycle})$0

In the laboratory trials, the nominal stride frequency was set to about $(\Delta \phi = 0.5\ \text{cycle})$1, corresponding to one full gait cycle in $(\Delta \phi = 0.5\ \text{cycle})$2, although the robot could be driven between $(\Delta \phi = 0.5\ \text{cycle})$3 and $(\Delta \phi = 0.5\ \text{cycle})$4 via joystick (Fulcher et al., 26 Sep 2025). The resulting swing-stance duty factors were on the order of $(\Delta \phi = 0.5\ \text{cycle})$5–$(\Delta \phi = 0.5\ \text{cycle})$6, which the study identifies as typical of a trot (Fulcher et al., 26 Sep 2025).

The Cartesian foot trajectory is described as piecewise stance and swing motion. For $(\Delta \phi = 0.5\ \text{cycle})$7,

$(\Delta \phi = 0.5\ \text{cycle})$8

and for $(\Delta \phi = 0.5\ \text{cycle})$9,

$90^\circ$0

$90^\circ$1

In practice, these trajectories are sent to the robot’s onboard microcontroller at $90^\circ$2, and low-level joint PD controllers track them (Fulcher et al., 26 Sep 2025).

The laboratory operating point emphasizes dynamic traversal. Ground penetration speeds in the Trot-Walk gait typically exceed $90^\circ$3 at touchdown, step length is adjusted on the fly by an operator, and in the laboratory trials the robot covered $90^\circ$4 per step at $90^\circ$5, yielding forward speeds of $90^\circ$6 (Fulcher et al., 26 Sep 2025). Actuator commands are standard position–torque setpoints, with a desired joint trajectory plus a small feedforward or implicit feedthrough of estimated gravity compensation. The low gear ratios—$90^\circ$7 on hip/abductor and $90^\circ$8 on knee—permit accurate motor-torque estimation from current sensors (Fulcher et al., 26 Sep 2025).

3. Proprioceptive sensing architecture during dynamic trot

The terrain-sensing interpretation of Trot-Walk depends on a proprioceptive pipeline built on actuator current sensing. Each of the three leg joints carries a high-bandwidth current sensor; through the motor constant $90^\circ$9, this is converted into an estimate of joint torque. By combining all three joint torques with the instantaneous Jacobian, the robot estimates ground reaction forces at the toe (Fulcher et al., 26 Sep 2025).

A momentum-observer-style filter runs at $(\theta_0=\theta_3,\ \theta_1=\theta_2)$0 on the microcontroller to remove much of the inertial and gravitational torque contributions, attempting to leave only external contact torques (Fulcher et al., 26 Sep 2025). In post-processing, a 4th-order Savitzky–Golay filter with a window of about $(\theta_0=\theta_3,\ \theta_1=\theta_2)$1 is applied to the recorded ground-reaction-force time series. The purpose is to smooth out high-frequency impact noise while preserving the overall force profile from touchdown through stance (Fulcher et al., 26 Sep 2025).

Dynamic trot creates an observability problem absent in slower multi-contact sensing gaits. Because only two feet are on the ground at any instant in a trot, the simple three-point plane fit used by Crawl N’ Sense is no longer possible (Fulcher et al., 26 Sep 2025). The sensing study therefore uses a regression-based extension of the plane estimator, carrying forward the previous step’s plane estimate via body-pose-based kinematics and then refitting using at least three estimated contact points across successive instants. This permits inference of penetration depth even on deformable ground, though with lower confidence than the quasi-static crawl gait (Fulcher et al., 26 Sep 2025).

The overall sensing regime is therefore strongly shaped by locomotion dynamics. Trot-Walk samples the substrate under short stance intervals, elevated touchdown speeds, and limited support geometry. This suggests that the quality of the inferred force–depth relationship depends not only on sensor calibration, but also on phase timing, impact transients, and the geometric underdetermination of the contact frame.

4. Experimental performance on deformable terrain

The experiments quantify Trot-Walk against static penetrometer measurements and against Crawl N’ Sense on two tasks: estimation of penetration resistance in homogeneous sand and detection of brittle surface-crust rupture (Fulcher et al., 26 Sep 2025).

For homogeneous sand with three compaction levels, ground truth from a static penetrometer was $(\theta_0=\theta_3,\ \theta_1=\theta_2)$2 for medium compaction, $(\theta_0=\theta_3,\ \theta_1=\theta_2)$3 for low compaction, and $(\theta_0=\theta_3,\ \theta_1=\theta_2)$4 for high compaction (Fulcher et al., 26 Sep 2025). Trot-Walk estimates, aggregated over four trials and two forelegs, were approximately $(\theta_0=\theta_3,\ \theta_1=\theta_2)$5 for medium compaction, $(\theta_0=\theta_3,\ \theta_1=\theta_2)$6 for low compaction, and $(\theta_0=\theta_3,\ \theta_1=\theta_2)$7 for high compaction, with a measurement coefficient of variation of $(\theta_0=\theta_3,\ \theta_1=\theta_2)$8–$(\theta_0=\theta_3,\ \theta_1=\theta_2)$9 (Fulcher et al., 26 Sep 2025). The study therefore reports that the robot can measure a consistent difference in strength between low- and high-resistance substrates, but that the locomotion-oriented trot gait contains larger magnitude and variance in measurements (Fulcher et al., 26 Sep 2025).

For sand with brittle crust, rupture detection was defined by a force drop greater than $180^\circ$0 in the filtered time series during a step (Fulcher et al., 26 Sep 2025). The Trot-Walk confusion matrix over three trials and the forelegs yielded sensitivity $180^\circ$1 and specificity $180^\circ$2, with $180^\circ$3 false positives in $180^\circ$4 non-rupture steps (Fulcher et al., 26 Sep 2025). The study summarizes this succinctly: Trot-Walk nearly always declared a rupture, even on uniform sand or rigid boards (Fulcher et al., 26 Sep 2025).

A compact comparison with Crawl N’ Sense is useful because the paper is organized around that contrast.

Aspect	Trot-Walk	Crawl N’ Sense
Penetration speed	$180^\circ$5	$180^\circ$6
Magnitude accuracy	Overestimates by $180^\circ$7–$180^\circ$8	Matches static penetrometer within $180^\circ$9–$\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$0
Measurement variation	CV $\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$1–$\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$2	CV $\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$3–$\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$4
Rupture detection	Sensitivity $\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$5, specificity $\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$6	Specificity $\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$7, sensitivity $\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$8

The interpretation given in the study is mechanical rather than purely statistical. Crawl N’ Sense performs a dedicated slow penetration with stable tripod support and gathers about $\phi_i(t) = (f t + \phi_{i0}) \bmod 1,$9 data points per step in the quasi-static regime, whereas Trot-Walk’s dynamic impacts, short stance of about $\phi_{FL0}=\phi_{RR0}=0$0–$\phi_{FL0}=\phi_{RR0}=0$1, and only two-foot support introduce inertial artifacts and unmodeled leg dynamics (Fulcher et al., 26 Sep 2025). These appear as higher-frequency noise in ground-reaction estimates and much larger variance in fitted penetration resistance.

5. Relation to broader quadruped gait research

The specific Trot-Walk implementation belongs to a larger quadruped literature in which walk and trot are treated as distinct phase-locked coordination modes, and in which gait transitions are analyzed through resonance, viability, energy efficiency, and stability. In the coupled-oscillator model of Tero et al., walk appears at low $\phi_{FL0}=\phi_{RR0}=0$2 as a stable phase sequence with roughly $\phi_{FL0}=\phi_{RR0}=0$3 separations, whereas trot emerges when the leg-driving frequency comes into resonance with the spine-twist mode $\phi_{FL0}=\phi_{RR0}=0$4, yielding the diagonal-pair in-phase arrangement with a $\phi_{FL0}=\phi_{RR0}=0$5 phase shift between the pairs; with horse-like parameters, the numerically observed walk→trot transition occurs at $\phi_{FL0}=\phi_{RR0}=0$6 (Tero et al., 2013).

Recent robotics work frames the same walk–trot distinction differently. DeepTransition treats quadruped locomotion as an MDP solved by PPO with a CPG hierarchy and reports an energetically optimal transition speed on flat terrain at approximately $\phi_{FL0}=\phi_{RR0}=0$7, where switching reduces CoT from $\phi_{FL0}=\phi_{RR0}=0$8 to $\phi_{FL0}=\phi_{RR0}=0$9 and the coefficient of variation of stride duration from $\phi_{FR0}=\phi_{RL0}=0.5$0 to $\phi_{FR0}=\phi_{RL0}=0.5$1; the paper argues that viability is the only improved factor after gait transitions on both flat and discrete gap terrains (Shafiee et al., 2023). AllGaits reaches a different post hoc conclusion: walk minimizes COT below $\phi_{FR0}=\phi_{RL0}=0.5$2, trot minimizes mean base angular velocity around $\phi_{FR0}=\phi_{RL0}=0.5$3–$\phi_{FR0}=\phi_{RL0}=0.5$4, and pace or amble often give the lowest COT at higher speeds (Bellegarda et al., 2024). Shao et al. encode walk and trot directly by phase variables, using offsets $\phi_{FR0}=\phi_{RL0}=0.5$5 for walk and $\phi_{FR0}=\phi_{RL0}=0.5$6 for trot, and report trot→walk and walk→trot transitions in about $\phi_{FR0}=\phi_{RL0}=0.5$7–$\phi_{FR0}=\phi_{RL0}=0.5$8 without explicit if–then switching logic (Shao et al., 2022).

This broader literature clarifies what Trot-Walk is and is not. It is a concrete locomotion-oriented trot chosen as the sensing paper’s fast-traversal baseline, rather than a theoretically privileged gait across all objectives. A plausible implication is that its suitability depends on the evaluation criterion: rapid traversal and dynamic stability may favor a trot-like operating point, while quasi-static terrain characterization may favor slower, longer-contact alternatives.

6. Design implications and common misconceptions

The terrain-sensing study extracts several explicit gait-design guidelines for improving proprioceptive sensing during locomotion (Fulcher et al., 26 Sep 2025). Higher step frequency $\phi_{FR0}=\phi_{RL0}=0.5$9 and greater touchdown velocity increase inertial and impact forces, degrading the fidelity of quasi-static force-vs-depth relationships; reducing $T=1/f$0 below $T=1/f$1 or limiting touchdown speed can improve sensing at the cost of locomotion speed (Fulcher et al., 26 Sep 2025). Increasing duty factor $T=1/f$2 yields more data points per ground contact and reduces peak impact impulses, thereby improving the signal-to-noise ratio in force measurements (Fulcher et al., 26 Sep 2025). A flatter stance trajectory, with minimized vertical rebound or “bounce,” helps suppress spurious force fluctuations in dynamic trot (Fulcher et al., 26 Sep 2025). Because two-contact support is inherently less observable for plane fitting, incorporating additional sensors or temporarily biasing one leg to re-contact early can help recover a more accurate ground frame (Fulcher et al., 26 Sep 2025).

Several misconceptions follow directly from the data. First, Trot-Walk is not presented as an optimal gait for proprioceptive terrain sensing. The paper shows the opposite: compared with Crawl N’ Sense, it systematically overestimates penetration resistance, exhibits much larger variance, and shows near-$T=1/f$3 false-alarm behavior under a simple rupture threshold (Fulcher et al., 26 Sep 2025). Second, high sensitivity does not imply good detection performance. In the crust experiment, Trot-Walk achieved $T=1/f$4 sensitivity but only $T=1/f$5 specificity, so it nearly always declared a rupture whether one occurred or not (Fulcher et al., 26 Sep 2025). Third, the label itself should not be interpreted as a formal gait category. The implemented phase relations are those of a trot, and the term “Trot-Walk” functions as an experiment-specific name for the locomotion-oriented condition (Fulcher et al., 26 Sep 2025).

Taken together, the evidence supports a precise characterization. Trot-Walk is a dynamic diagonal-pair trot deployed on a quasi-direct-drive quadruped to study sensing during locomotion. It offers rapid coverage at $T=1/f$6–$T=1/f$7 stride rates and robust dynamic stability, but at a steep cost to proprioceptive terrain-sensing accuracy. Any attempt to make it a high-fidelity sensing gait requires slower touchdown, longer stance, and improved ground-plane observability, thereby eroding the speed advantage that motivates its use in the first place (Fulcher et al., 26 Sep 2025).