Predictive Low-Motion Interaction

• Predictive low-motion interaction is a technique that uses real-time forecasting and probabilistic models to minimize unnecessary motion in human, robotic, and mixed-initiative systems.
• It combines methods like LSTM-based motion prediction, control barrier functions, and model predictive control to optimize safety and efficiency.
• Empirical results show significant reductions in safety violations and physical movement, enhancing both performance and accessibility across diverse applications.

Predictive low-motion interaction encompasses computational, robotic, and user interface techniques designed to minimize unnecessary motion—whether by humans, robots, or mixed-initiative systems—through the application of real-time prediction, probabilistic modeling, and control synthesis. The central goal is to make interactions fluid and efficient by anticipating the future state of agents and leveraging this foresight to reduce costly or risky movement. This article presents an integrated overview of predictive low-motion interaction across collaborative robotics, egocentric human-object forecasting, human–computer interface design, and robot manipulation, including modeling frameworks, control architectures, optimization, and empirical findings.

1. Principles of Predictive Low-Motion Interaction

Predictive low-motion interaction is predicated on the use of computational models that forecast future states (trajectories, targets, contact points) of agents in a shared environment. These models inform control or interaction strategies that minimize physical motion subject to task constraints. Core principles include:

• State prediction via probabilistic or dynamic forecasting: Incorporating epistemic uncertainty into predictions, e.g., hand trajectories or manipulator poses.
• Formal safety and decision-theoretic integration: Embedding predicted agent states into explicit safety-constrained optimization or interaction paradigms.
• Mixed-initiative and preview-based interaction: Integrating AI support for target selection and preview, while maintaining human agency in acceptance/discard decisions.
• Low-dimensional goal/task modeling: Reducing task representations to essential variables (e.g., palm center in $ℝ^3$, pixel coordinates in $ℝ^4$, or ranked GUI targets).

This approach prevents conservative fallback behavior (e.g., unnecessary braking or excessive hesitation) by dynamically tailoring safety, acceptance, and control margins to real-time prediction uncertainty (Busellato et al., 28 Aug 2025, Berengueres, 13 Nov 2025, Liu et al., 2022, Izadinia et al., 2021, Klar et al., 2022).

2. Forecasting and Uncertainty Quantification

Human and robot motion forecasting modules underpin predictive low-motion interaction systems. These modules generate future state estimates, along with quantifiable uncertainty, to inform downstream control and interface logic.

Probabilistic Human Motion Forecasting (UA-PCBF)

• Input: Sliding window of previous $T_{in}$ palm positions, $P_{in} = \{p_{t-T_{in}+1},...,p_t\} \subset ℝ^3$.
• Architecture:
  • LSTM encoder: $LSTM_{enc}(P_{in}) \to (h_{enc}, c_{enc})$
  • Autoregressive LSTM decoder for $k=1..T_{out}$:

  $$o_k, (h_{dec_k}, c_{dec_k}) = LSTM_{dec}(x_{dec_{k-1}}, (h_{dec_{k-1}},c_{dec_{k-1}}))$$ - Probabilistic output: $[\mu_k, \log \sigma_k^2] = W_o o_k + b_o$ ($\mu_k \in ℝ^3$, $\log \sigma_k^2 \in ℝ^3$)

• Loss: Weighted sum of Gaussian NLL and MSE over $T_{out}$ steps: $$L_{NLL} = \frac{1}{2}\sum_k [\log \sigma_k^2 + \|p_{true_k}-\mu_k\|^2/\sigma_k^2]$$, $L_{MSE} = \sum_k\|\mu_k-p_{true_k}\|^2$,

$L = \rho L_{NLL} + \omega L_{MSE}$

• Uncertainty: Step-wise output variance $\sigma_k^2$ forms diagonal covariance $\Sigma_k$, used for safety margin inflation (Busellato et al., 28 Aug 2025).

Egocentric Hand-Object Interaction Prediction (OCT)

• Input: Sequence of key video frames $V = \{f_1,...,f_T\}$; embedded hand, object, global context features.

• Normalization: Bounding box centers, type embeddings, temporal (sinusoidal) embeddings.

• Network:

  • Encoder stacks self-attention blocks over hand/object/global tokens.
  • Decoder auto-regressively predicts $F$ future steps, cross-attending to the current query and encoded last-frame tokens.
  • Conditional variational autoencoders (C-VAEs) model both hand motions and contact points, allowing sampling of $20$ future candidate trajectories and hotspots.
• Loss: Combined trajectory reconstruction and KL divergence (for hand and object C-VAE heads).
• Sensitivity: Capture low-speed movements, with C-VAEs outperforming deterministic MLP or bivariate Gaussian outputs (ADE down to $0.12$), and ablations showing importance of trajectory conditioning and global context tokens (Liu et al., 2022).

3. Control Synthesis and Optimization Frameworks

Control Barrier Functions for Safe HRI

A control-affine robotic system:

$\dot{x} = f(x) + g(x)u,\quad x\in ℝ^n, u\in ℝ^m$

defines a safe set $C = \{ x: h(x) \geq 0 \}$ with control barrier function $h(x)$. A controller maintains $C$'s forward invariance if:

$$\dot{h}(x,u) = \nabla h(x) \cdot [f(x) + g(x)u] \geq -\alpha(h(x))$$

with $\alpha$ a class–K function. Solved as a QP:

$$u^* = \arg\min_u \|u-u_{nom}\|^2 \ \text{s.t. } \nabla h\cdot g(x)u \geq -\nabla h\cdot f(x) - \alpha(h(x))$$

Predictive CBFs (PCBF): simulate nominal $u_{nom}$ over horizon $[t, t+T_{out}]$, evaluate barrier $h_p(\tau) = h(p(\tau)) - m(\tau-t)$, enforcing constraints by forward sampling.

UA-PCBFs: project forecasted hand uncertainty onto robot-hand axis to inflate safety margin dynamically, enforcing

$$h_{ua}(\tau, x) = d_{min} + \bar{\sigma}(\tau, x) - d(\tau, x)$$

with $$\bar{\sigma} = \min\{\gamma\,\sigma_{proj}(\tau), d_{min}\}, \bar{\sigma}(0)=0$$; $\gamma$ tunes inflation strength. Real-time control QP with slack penalties is solved at 1–2 ms latency, 1 kHz rates (Busellato et al., 28 Aug 2025).

Model Predictive Control of Human Movement

Discrete-time joint-muscle dynamics:

$x_k = [q_k; \dot{q}_k; a_k; \bar{a}_k; p_k; e_k]$

where $q_k$ are joint angles, $a_k$ muscle activations. Dynamics iteratively propagate via second-order muscle models:

$$a_i(k+1) = a_i(k) + \Delta t\, \bar{a}_i(k) \ \bar{a}_i(k+1) = \bar{a}_i(k) + \Delta t\, ( \alpha\, a_i(k) + \beta\,u_i(k) )$$

with excit. constant $t_e$, activ. constant $t_a$, actuator gain $g_i$. MPC solves, over a horizon $N$:

$$J_N(x_0, u(\cdot)) = \sum_{k=0}^{N-1} \ell(x_k, u_k)$$

Subject to state/input constraints; preferred “JAC” cost is:

$$\ell(x_k, u_k) = \|p_k - p^*\|_2 + r_1\|u_k\|_2^2 + r_2\|\ddot{q}_k\|_2^2$$

After solving, MPC applies $u_0^*$ and shifts the horizon. CFAT estimates realistic joint-torque limits $g_i$ via fitting observed joint trajectories (Klar et al., 2022).

Riemannian Motion Predictive Control

Nonprehensile setting: robot must administer low-motion pushes in $SE(2)$ (planar pose), using Riemannian metric $G(q)$ and geodesic distances $d_G(p,p')$ to combine attractor and avoidance fields in RMPflow. At each cycle:

1. Capture depth → 3D detection → physics scene (Bullet).
2. Sample $K$ policy weight sets, simulate horizon $H$ rollouts.
3. Reward: $$r_t(s_t,u_t) = [d_{o_c,l_g}^{t-1} - d_{o_c,l_g}^{t}] - \sum_{i\neq c} \|p_i^t - p_i^{t-1}\|$$.
4. Select best trajectory to execute by maximizing cumulative predicted reward.

Robust to occlusion and clutter, with update rates $\sim15$ Hz (Izadinia et al., 2021).

4. Application Paradigms in Collaborative Robotics and HCI

Safer, Fluid Human–Robot Interaction (UA-PCBF)

UA-PCBFs support collaborative robots sharing workspace with humans by fusing probabilistic hand motion forecasts (mean + variance) with dynamic control barrier functions. Key outcomes include:

• Nearly $100\times$ reduction in safety violations versus baseline reactive CBF.
• No increase in completion time or path length; modest reductions in some measures.
• Real-time CPBF-QP with uncertainty-adaptive margins and slack variables for minimally invasive, provably safe, low-motion collaboration (Busellato et al., 28 Aug 2025).

Egocentric Joint Interaction Forecasting

The Object-Centric Transformer (OCT) predicts not only hand trajectories but also fine-grained object contact hotspots from egocentric video. Quantitative benchmarks show:

• ADE/FDE for hand trajectory forecasting $=0.12/0.11$ on Epic-Kitchens-100, exceeding Divided-Transformer and LSTM baselines.
• Hotspot map SIM/AUC-J/NSS $=0.19/0.69/0.72$, also leading all baselines.
• Sensitivity to slow, subtle hand movement; ablations confirm utility of stochasticity, trajectory-conditioning, and context attendance (Liu et al., 2022).

Zero-Click Predictive GUI Interaction (PAD Paradigm)

PAD reframes GUI interaction as a mixed-initiative, keyboard-driven, preview–accept–discard protocol:

• On holding modifier keys, system ranks and previews top predicted GUI targets via curved “chord”.
• Space cycles candidates (bounded to $k\leq6$), acceptance/discard via key-release timing ($\Delta t\approx170$ ms).
• In email-mockup: PAD eliminated all mouse clicks, saved $\approx$3 000 px of pointer travel per trial, maintained sub-minute completion times.
• In ISO 9241-9 tests: PAD@ideal distribution throughput TP$\approx$4.8 bps (trackpad: 4.2 bps), strokes/trial down to 1.08 (trackpad: 1.67), at similar error rates. Only with near-perfect prediction does PAD surpass baseline throughput; at all settings PAD halves fine-motor task load without sacrificing speed (Berengueres, 13 Nov 2025).

Simulated Biomechanical User Movements (MPC)

MuJoCo-based closed-loop MPC with second-order muscle actuation and joint-torque constraints (CFAT) simulates realistic human pointing interactions:

• JAC cost (distance + control-effort + joint acceleration) best matches recorded user trajectories (Wilcoxon $p<0.0001$).
• RMSE: cursor position $\sim$2 cm, joint angle $\sim$0.02 rad; simulation errors at or below between-user variance.
• Velocity profiles and task-performance metrics indistinguishable from real users; practical advice for horizon, cost weight, noise addition, and transfer function design provided (Klar et al., 2022).

5. Evaluation Metrics and Experimental Outcomes

Empirical evaluation employs both interaction-centric and control-centric metrics tailored to modality:

Table: Key Evaluation Metrics Across Modalities

Area	Metrics	Success Range / Highlights
HRI (UA-PCBF)	Violations/run, task time, path length	UA-PCBF $\sim$0.2/run (mock), 2.0/run (human)
Egocentric Video (OCT)	ADE, FDE, SIM, AUC-J, NSS	OCT ADE/FDE=0.12/0.11, SIM/AUC-J/NSS=0.19/0.69/0.72
GUI (PAD)	Throughput (bps), pointer travel, strokes/trial	PAD@ideal TP=4.8 bps, strokes$<$1.1/trial
Nonprehensile Manip. (RMPC)	Collision rate, recall at k%	RMPC collision: 17.9% (real), lowest among baselines

Scenarios demonstrate that predictive low-motion interaction consistently reduces unnecessary physical motion—by up to two orders of magnitude in collaborative safety violations, and by 35–60% in HCI pointing tasks—without negative impacts on speed or accuracy.

6. Limitations and Prospective Developments

While predictive low-motion paradigms yield substantial benefit, limitations remain:

• Current HCI PAD prototypes use deterministic predictions; real-world accuracies will vary, and EMG/clinical studies on RSI reduction are needed (Berengueres, 13 Nov 2025).
• Safety controller margins rely on accurate uncertainty quantification; errors in forecasted covariance may produce either excessive conservatism or latent risk (Busellato et al., 28 Aug 2025).
• Egocentric forecasting accuracy depends on annotation and model coverage; missing context tokens or suboptimal C-VAE conditioning degrade performance (Liu et al., 2022).
• Riemannian predictive control requires precise scene reconstruction and metric learning, which may bottleneck at low sensor or model fidelity (Izadinia et al., 2021).
• Biomechanical simulation necessitates individualized joint-actuation limits, with CFAT fitting and per-user scaling (Klar et al., 2022).

Ongoing research targets adaptive key-release timing, domain transfer to more complex GUIs and 3D UIs, integration with conversational agents, real-time learning from online data, and longitudinal studies with biomechanical or sensory monitoring.

7. Significance and Integration Across Domains

Predictive low-motion interaction constitutes a unifying approach for fluid human–robot collaboration, intelligent interface design, and robust robotic manipulation. Common technical threads—probabilistic state forecasting, decision-theoretic optimization, and preview-based mixed-initiative interaction—enable systems to trade cognitive effort for kinetic savings, formal safety, and improved accessibility. As demonstrated in collaborative cells (Busellato et al., 28 Aug 2025), egocentric video (Liu et al., 2022), human-computer input (Berengueres, 13 Nov 2025), and nonprehensile manipulation (Izadinia et al., 2021, Klar et al., 2022), this paradigm systematically reframes interaction design by embedding predictive models at its core, facilitating a transition from reactive motor control to anticipatory, agency-preserving workflows.