Finite-state machine

Overview

A device that assists movement has to know which mode the user is in, and when the mode changes. The problem is to detect each change quickly enough for the assistance to match it 2411.12573 §1. The core idea in this paper is a small FSM with four states: Sit, Walk, Stair Ascent and Stair Descent. Level walking, standing and ramp walking are merged into Walk 2411.12573 §2.1. Each transition between states is one binary decision, and each decision uses one instantaneous characteristic feature (ICF) 2411.12573 §2.1. Gait events, namely maximum hip flexion and heel strike, are taken from separate detectors that use the thigh angle and the ground reaction force 2411.12573 §2.1.

The invariant the paper relies on is that the device runs no classifier when it decides. The authors trained several classifiers offline, then kept the two best performers, a linear SVM and a logistic regression, and replaced them with if/else thresholds on the one-dimensional ICF [arxiv:2411.12573 §2.2]. The thresholds are therefore the whole decision rule at run time.

Only one card lists this slug so far. The page describes that one variant and its personalization options, and other FSM designs are not covered yet.

Variants

Offline-trained threshold FSM

Each transition has a threshold on one ICF. The thresholds come from the offline classifiers, trained on the Reznick et al. dataset with a 90/10 split 2411.12573 §2.1 2411.12573 §2.2. Table 1 gives the values. The thresholds are shared by both exoskeletons except one, W-SD / SD-W, which differs for eWalk and autonomyo 2411.12573 tab. 1. The non-personalized version is the comparison baseline in the paper's accuracy tests 2411.12573 §4.2. Card: Locomotion Mode Transitions.

Statistics-based rescaling (SBA)

Each threshold is multiplied by the ratio between the mean plus or minus the standard deviation of the new user's ICF and the same statistic from the training data 2411.12573 §2.5.1 2411.12573 eq. 6. The card does not state which sign applies to which transition, so this step needs the paper text before it is implemented 2411.12573 §2.5.1.

Bayesian-optimization tuning (BO)

Each threshold pair for one transition pair is searched with Bayesian optimization. A Gaussian-process surrogate (RBF kernel) is fitted to the observed costs, and an acquisition function with weight 0.5 picks the next candidate 2411.12573 §2.5.2 2411.12573 eq. 8 [arxiv:2411.12573 eq. 9]. The cost is computed from labelled ground-truth transitions, so this variant is supervised 2411.12573 alg. 2. The paper runs 30 iterations and compares them with 100 evaluations of a grid search [arxiv:2411.12573 §4.3]. Card: Locomotion Mode Transitions.

When to use which

The choice depends on what the deployed device has available. The paper's results are the only evidence here, and they come from 10 subjects per exoskeleton 2411.12573 §3.

Implementation sketch

Language-agnostic outline of the common core. The card does not give the transition list per state in text, so the table is read from fig. 1 and must be checked against the paper. The direction of each comparison is also not stated on the card 2411.12573 §2.1.

# The four states  [arxiv:2411.12573 §2.1]
SIT, WALK, STAIR_ASC, STAIR_DESC = range(4)

# Feature extraction at each gait event  [arxiv:2411.12573 §2.1] [tab. 1]
def extract_icfs(gait_cycle):
    # ICF-1: thigh angle at maximum hip flexion (MHF)
    icf1 = gait_cycle.thigh_angle_at_mhf
    # ICF-2: MHF-minus-heel-strike difference, as defined in §2.1
    icf2 = gait_cycle.mhf_minus_hs
    # ICF-3: thigh angular velocity inside the thigh-angle window THR
    icf3 = gait_cycle.thigh_velocity_in_thr
    return {"ICF-1": icf1, "ICF-2": icf2, "ICF-3": icf3}

# Transition table: current state -> (target, ICF name, threshold name)
# Which transitions leave each state is read from [fig. 1]
TRANSITIONS = {
    WALK: [(SIT, "ICF-3", "W-S"), (STAIR_ASC, "ICF-1", "W-SA"),
           (STAIR_DESC, "ICF-2", "W-SD")],
    # ...reverse transitions, read from [fig. 1]
}

# One binary decision per transition, each on one ICF  [arxiv:2411.12573 §2.1]
def step(state, icfs, thresholds):
    for target, icf_name, th_name in TRANSITIONS.get(state, []):
        # Comparison direction per transition: check §2.1 before use
        if compare(icfs[icf_name], thresholds[th_name]):
            return target
    return state

# Personalize one threshold with statistics  [arxiv:2411.12573 §2.5.1] [eq. 6]
def rescale_threshold(th_train, icf_train, icf_new, sign):
    # sign is +1 or -1 per transition; the assignment is not stated on the card
    num = mean(icf_new) + sign * std(icf_new)
    den = mean(icf_train) + sign * std(icf_train)
    return th_train * num / den

Contradictions

None known across papers, since only one card lists this slug. Within the card, the subject S2 is reported differently in two places. The results say W-S was missed before tuning and detected after 2411.12573 §4.2. The discussion says W-S and S-W improved from 80% and 60% to 100% [arxiv:2411.12573 §5.3]. Both statements come from the same paper and do not match.

Papers

• Exoskeleton mode-transition paper (arXiv:2411.12573): an FSM with ICF thresholds for walk, sit and stair transitions, with statistics-based rescaling and Bayesian-optimization tuning, tested on two exoskeletons.