Imagination-Inspired Motion Planner (I-MP)

• I-MP is a cognitive-inspired motion planning framework that uses predictive simulation and mathematical guarantees to compute convergent, adaptive spatial targets.
• It integrates environment topologization, sensor fusion, and real-time energy gradient computation to safely navigate cluttered and uncertain workspaces.
• Experimental evaluations demonstrate improved success rates, smoother trajectories, and robust adaptability compared to conventional planning methods in dynamic settings.

Imagination-Inspired Motion Planner (I-MP) refers to a class of motion planning frameworks that enable robots to enhance reliability and adaptivity in complex, unstructured environments by actively "imagining" plausible spatial outcomes before acting. This concept is rooted in principles from sensorimotor control and cognitive science, wherein the robot uses perception-action loops combined with mathematical guarantees (fixed-point theory, Hausdorff distance) to forecast and select convergent motion states, then approaches these states by computing real-time energy gradients in high-dimensional workspaces. The technique is designed specifically to handle interaction-induced uncertainties, such as unpredictable contacts, sensor noise, and dynamic physical constraints, and is realized through autonomous topologization and homogenization of environmental features, interactive closure of perception-action cycles, and continuous control adaptation.

1. Conceptual Foundations and Framework Architecture

The I-MP framework is inspired by animal intelligence, leveraging action imagination—a sensorimotor strategy that uses predictive mental simulation to anticipate action outcomes. The system comprises three main modules:

• Environment Understanding (EU): Topologizes the workspace, extracting explicit geometric properties via tactile and proximity sensing, and implicit physical properties (stiffness, damping, friction) via sensor fusion and parameter identification.
• Motion Imaginer (MI): Employs mathematical tools (fixed-point theory and Hausdorff metric) to establish a convergent set of spatial states, optimizes the selection of an imagined target state that is accessible given mission constraints and interaction parameters.
• Low-Level Controller (LC): Converts motion variations in Cartesian space into joint-level actuation commands, utilizing Jacobian transformations and continuous model-based control for safe and precise execution.

These modules interact in a closed-loop, wherein real-time environmental perception is matched with topological models, driving both anticipatory state selection and continuous motion correction.

2. Perception–Action Loop and Workspace Topologization

Central to I-MP is the closed-loop perception–action cycle:

• Sensors provide high-frequency feedback on contact and proximity, feeding the EU module.
• The workspace is topologized by partitioning it into target, robot, occupied, and free-motion domains. Explicit object geometry is extracted; implicit properties are estimated and encoded as operable vectors (e.g., $[K, D, C]^T$ for spring constant, damping, displacement).
• Environmental parameters are further homogenized into "work" metrics, linearly mapped into Cartesian space for computational efficiency.

This rich, multidimensional mapping allows the robot to reason about both physical and geometric constraints jointly, supporting the MI module in formulating plausible state destinations.

3. Mathematical Formulations and Imagined State Selection

I-MP uses rigorous mathematical tools to guarantee valid state selection and transition:

• Fixed-point theory identifies a convergence domain $X_{\mathrm{con}}$ of states, ensuring any chosen goal is physically approachable given system/evironment constraints.
• Imagined target state selection is formalized as:

$x^* = \arg\min_{x \in X_{\mathrm{con}}} d(x, s)$

where $d(\cdot, \cdot)$ is the Hausdorff distance between imagined and intended states.

• Potential fields: The planner encodes environmental energy via attractive fields $U_{+}(x)$, viscous fields $U_v(x)$ (for velocity restrictions near obstacles), and repulsive fields for inoperable objects:

$U_{\mathrm{rep}}(x) = k_0(o^* - x(t))^2$

with $o^*$ chosen to maximize the Hausdorff distance to the robot.

Least-squares parameter estimation is employed for model identification:

$J_1(0) = \sum_j [y(j) - H(j)0]^2$

and minimization conditions are set via derivatives.

4. Real-Time Energy Gradient and Control

A distinguishing feature of I-MP is real-time computation of energy gradients to drive action:

• Upon selection of $x^*$, an actuation force is computed as:

$F^* = -\nabla[U(x, x^*)]$

guiding the robot along the steepest energy descent to the imagined state, with dynamical constraints for interaction-induced safety (e.g., maintaining safe contact velocity $V_{\text{safe}}$).

• The joint-space control equation is:

$$M(q)\ddot{q} + C(q, \dot{q})\dot{q} + G(q) = \tau^* - T_{\text{ext}}$$

with torque command $\tau^* = J(q)^{-1} F^*$.

This mapping yields adaptive and robust behaviors even under evolving environmental constraints.

5. Experimental Evaluation in Real-World Clutter

Systematic experiments evaluated I-MP in both simulated and real environments:

• Motion adaptation: The planner successfully navigated cluttered tabletops, dynamically displacing operable objects and avoiding inoperable ones (based on contact model inference).
• Motion-control continuity: Velocity and joint-space trajectories remained smooth during complex contacts, avoiding catastrophic collisions.
• Reliability: Imagined displacements were empirically validated against actual robot motion, displaying minimal inconsistency and demonstrating predictive sufficiency for safe planning.
• Task scalability: In demanding scenarios (e.g., retrieving an object from a cluttered cabinet), I-MP enabled the robot to analyze object operability (e.g., distinguishing a water-filled kettle from movable packs) and execute adaptive spatial reconfiguration to achieve task goals.

6. Comparative Performance and Robustness

Quantitative benchmarking against probability-based, simulation-based, and model-based planners showed:

Method	Success Rate Improvement	Path Cost Premium
Model-based	+88.34%	+6.32%
Simulation-based	+86.82%	N/A
Probability-based	+69.51%	N/A

Stress tests and ablation studies revealed that both force and proximity sensing are required for robust operation; omitting force sensing led to frequent planning failures, while proximity-only strategies resulted in increased undesired contact forces.

7. Significance and Implications

I-MP demonstrates that action imagination, grounded in closed-loop sensorimotor control and mathematical guarantees, enables robots to adaptively and reliably plan in physically complex and uncertain environments. By integrating topological workspace mapping, convergent state selection, energy-based motion synthesis, and continuous perception feedback, I-MP bridges the gap between conventional motion planners and embodied intelligence. This approach sets a precedent for further exploration of cognitive-inspired strategies in robotics, with plausible implications for open-world adaptation, real-time task fulfiLLMent, and incremental learning via embodied experience (Wang et al., 21 Sep 2025).