---
title: Trot-Walk in Quadruped Robotics
url: https://www.emergentmind.com/topics/trot-walk
type: topic
---

# Trot-Walk in Quadruped Robotics

“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` [2509.22065]. 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 [2509.22065].

## 1. Terminological scope and gait identity

In the cited terrain-sensing experiments, the locomotion-oriented trot gait is referred to simply as “Trot-Walk” [2509.22065]. 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 \((\Delta \phi = 0.5\ \text{cycle})\) [2509.22065].

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 [1310.7568]. 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 [2509.22065].

## 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 \(\phi_{FR0}=\phi_{RL0}=0.5\) [2509.22065]. If \(T=1/f\) is the stride period and \(\beta\) is the duty factor, the contact schedule is written as
\[
\text{stance: } \phi_i \in [0,\beta], \qquad
\text{swing: } \phi_i \in (\beta,1).
\]
In the laboratory trials, the nominal stride frequency was set to about \(f=2\,\mathrm{Hz}\), corresponding to one full gait cycle in \(0.5\,\mathrm{s}\), although the robot could be driven between \(1\) and \(4\,\mathrm{Hz}\) via joystick [2509.22065]. The resulting swing-stance duty factors were on the order of \(0.3\)–\(0.4\), which the study identifies as typical of a trot [2509.22065].

The Cartesian foot trajectory is described as piecewise stance and swing motion. For \(0 \le \phi \le \beta\),
\[
x_i(\phi)=x_{\text{touchdown}} + (\phi/\beta)\,(x_{\text{liftoff}}-x_{\text{touchdown}}), \qquad
z_i(\phi)=z_{\text{touchdown}},
\]
and for \(\beta < \phi < 1\),
\[
x_i(\phi)=x_{\text{liftoff}} + ((\phi-\beta)/(1-\beta))\,(x_{\text{touchdown}}-x_{\text{liftoff}}),
\]
\[
z_i(\phi)=z_{\text{touchdown}} + h_{\text{swing}}\sin\!\bigl(\pi(\phi-\beta)/(1-\beta)\bigr).
\]
In practice, these trajectories are sent to the robot’s onboard microcontroller at \(1\,\mathrm{kHz}\), and low-level joint PD controllers track them [2509.22065].

The laboratory operating point emphasizes dynamic traversal. Ground penetration speeds in the Trot-Walk gait typically exceed \(50\,\mathrm{cm/s}\) at touchdown, step length is adjusted on the fly by an operator, and in the laboratory trials the robot covered \(\sim 0.1\,\mathrm{m}\) per step at \(\sim 2\,\mathrm{Hz}\), yielding forward speeds of \(\sim 0.2\,\mathrm{m/s}\) [2509.22065]. 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—\(6{:}1\) on hip/abductor and \(12{:}1\) on knee—permit accurate motor-torque estimation from current sensors [2509.22065].

## 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 \(K_m\), 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 [2509.22065].

A momentum-observer-style filter runs at \(1\,\mathrm{kHz}\) on the microcontroller to remove much of the inertial and gravitational torque contributions, attempting to leave only external contact torques [2509.22065]. In post-processing, a 4th-order Savitzky–Golay filter with a window of about \(60\,\mathrm{ms}\) 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 [2509.22065].

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 [2509.22065]. 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 [2509.22065].

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 [2509.22065].

For homogeneous sand with three compaction levels, ground truth from a static penetrometer was \(6.8 \pm 1.3\,\mathrm{N/cm}\) for medium compaction, \(3.4 \pm 1.3\,\mathrm{N/cm}\) for low compaction, and \(21.3 \pm 4.0\,\mathrm{N/cm}\) for high compaction [2509.22065]. Trot-Walk estimates, aggregated over four trials and two forelegs, were approximately \(14.6 \pm 5.2\,\mathrm{N/cm}\) for medium compaction, \(7.1 \pm 2.8\,\mathrm{N/cm}\) for low compaction, and \(36.8 \pm 9.4\,\mathrm{N/cm}\) for high compaction, with a measurement coefficient of variation of \(35\)–\(45\%\) [2509.22065]. 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 [2509.22065].

For sand with brittle crust, rupture detection was defined by a force drop greater than \(5\,\mathrm{N}\) in the filtered time series during a step [2509.22065]. The Trot-Walk confusion matrix over three trials and the forelegs yielded sensitivity \(100\%\) and specificity \(12.5\%\), with \(56\) false positives in \(64\) non-rupture steps [2509.22065]. The study summarizes this succinctly: Trot-Walk nearly always declared a rupture, even on uniform sand or rigid boards [2509.22065].

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 | \(>50\,\mathrm{cm/s}\) | \(\sim 8\,\mathrm{cm/s}\) |
| Magnitude accuracy | Overestimates by \(\sim 70\)–\(110\%\) | Matches static penetrometer within \(\sim 10\)–\(20\%\) |
| Measurement variation | CV \(35\)–\(45\%\) | CV \(\sim 15\)–\(25\%\) |
| Rupture detection | Sensitivity \(100\%\), specificity \(12.5\%\) | Specificity \(\sim 96\%\), sensitivity \(\sim 63\%\) |

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 \(100\) data points per step in the quasi-static regime, whereas Trot-Walk’s dynamic impacts, short stance of about \(10\)–\(80\,\mathrm{ms}\), and only two-foot support introduce inertial artifacts and unmodeled leg dynamics [2509.22065]. 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 \(\omega\) as a stable phase sequence with roughly \(90^\circ\) separations, whereas trot emerges when the leg-driving frequency comes into resonance with the spine-twist mode \(\mu_T\), yielding the diagonal-pair in-phase arrangement with a \(180^\circ\) phase shift between the pairs; with horse-like parameters, the numerically observed walk→trot transition occurs at \(\omega \approx 1.5\) [1310.7568].

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 \(v^* \approx 1.0\,\mathrm{m/s}\), where switching reduces CoT from \(\simeq 1.3\) to \(\simeq 1.0\) and the coefficient of variation of stride duration from \(\simeq 0.25\) to \(\simeq 0.15\); the paper argues that viability is the only improved factor after gait transitions on both flat and discrete gap terrains [2306.07419]. AllGaits reaches a different post hoc conclusion: walk minimizes COT below \(\sim 0.9\,\mathrm{m/s}\), trot minimizes mean base angular velocity around \(0.6\)–\(1.2\,\mathrm{m/s}\), and pace or amble often give the lowest COT at higher speeds [2411.04787]. Shao et al. encode walk and trot directly by phase variables, using offsets \([0,\tfrac{1}{2}\pi,\pi,\tfrac{3}{2}\pi]\) for walk and \([0,\pi,\pi,0]\) for trot, and report trot→walk and walk→trot transitions in about \(1.4\)–\(1.5\,\mathrm{s}\) without explicit if–then switching logic [2201.00206].

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 [2509.22065]. Higher step frequency \(f\) and greater touchdown velocity increase inertial and impact forces, degrading the fidelity of quasi-static force-vs-depth relationships; reducing \(f\) below \(\sim 1\,\mathrm{Hz}\) or limiting touchdown speed can improve sensing at the cost of locomotion speed [2509.22065]. Increasing duty factor \(\beta\) yields more data points per ground contact and reduces peak impact impulses, thereby improving the signal-to-noise ratio in force measurements [2509.22065]. A flatter stance trajectory, with minimized vertical rebound or “bounce,” helps suppress spurious force fluctuations in dynamic trot [2509.22065]. 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 [2509.22065].

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-\(100\%\) false-alarm behavior under a simple rupture threshold [2509.22065]. Second, high sensitivity does not imply good detection performance. In the crust experiment, Trot-Walk achieved \(100\%\) sensitivity but only \(12.5\%\) specificity, so it nearly always declared a rupture whether one occurred or not [2509.22065]. 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 [2509.22065].

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 \(1\)–\(4\,\mathrm{Hz}\) 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 [2509.22065].

Source: https://www.emergentmind.com/topics/trot-walk