Latest / Embodied AI 101 / Becoming the Path: Planning Motion, Shape, and Stiffness Together
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- Becoming the Path: Planning Motion, Shape, and Stiffness Together. Motion and Morphology Planning for Autonomous Manipulation in Clutter With a Shape-Shifting, Variable-Stiffness Robot • Luiza Labazanova, Liuming Qiu, J. G. Romero, L. Cheng, Thrishantha Nanayakkara, and David Navarro-Alarcon • ROMI Lab, The Hong Kong Polytechnic University, and collaborators • Advanced Intelligent Systems • 2026. Editorial note: As of August 5, 2026, the authors’ publication page lists the in-press title with “Autonomous Grasping” rather than “Autonomous Manipulation.” This episode follows the title associated with the supplied DOI; grasping is, in any case, the paper’s central manipulation operation. The Central Idea: Morphology Is an Action. Most robot planning starts with an unspoken assumption: the body is fixed. A mobile base may translate and rotate. An arm may move its joints. A gripper may open and close. But the dimensions, stiffness, and basic geometry of the platform are treated as constants around which the planner must work. That assumption becomes painful in confined environments. A mobile manipulator may have enough force and reach to handle an object, yet its base, arm, or swept volume cannot pass through the available corridor. A soft or continuum robot may conform to the same corridor, but then struggle to generate the forces or structural rigidity required to transport a useful payload. Making the rigid robot smaller sacrifices workspace and load capacity; making the soft robot stronger often sacrifices the compliance that made it attractive. Labazanova and colleagues attack this trade-off by changing the planning problem itself. Their robot does not merely decide where to move. It decides what shape to adopt, which portions of its body should be soft, and when those portions should become rigid again. The same structure acts at different times as a mobile chassis, a deformable body, and a full-body gripper. This is a particularly clear example of embodied intelligence without an end-to-end neural policy. The intelligence comes from matching a carefully designed mechanical body with a planner that treats that body’s physical state as a decision variable. Geometry, stiffness, locomotion, and manipulation are not separate modules connected at the end. They are coupled from the beginning. The work builds on the authors’ earlier Self-Reconfigurable Soft-Rigid Agent, or 2SR platform. The 2023 paper introduced the hardware, its hybrid soft-rigid kinematics, and basic demonstrations of shape formation and object handling. The new work addresses the next and more consequential question: how can such a machine autonomously choose a sequence of positions, shapes, and stiffness states that lets it traverse dense clutter and then grasp an object?. The Robot: Two Mobile Units and a Spine That Can Freeze. The 2SR robot consists of two wheeled locomotion units joined by a variable-stiffness bridge. Each locomotion unit carries power, electronics, and omnidirectional wheels. Between them are two deformable bridge segments, represented in the model by their curvatures, with a small central body section providing a reference frame. The important material is a low-melting-point alloy—Field’s metal in the original prototype—embedded inside the variable-stiffness structure. When the alloy is solid, the bridge behaves as a rigid body and preserves its current geometry. When selected sections are heated and melted, those sections become compliant enough to bend under forces generated by the locomotion units. Cooling the alloy locks the resulting shape again. This arrangement means that the robot does not need a dense array of conventional rotary joints along its spine. The wheel units themselves produce much of the deformation. If a bridge segment is softened while one unit moves relative to the rest of the body, that motion bends the segment. Once the desired curvature is reached, solidification turns the compliant arc back into a load-bearing structure. Mechanically, this is an elegant reuse of actuation. The wheel modules are not only locomotors; they are also the actuators that reshape the robot. The bridge is not only a chassis connection; it becomes the grasping surface. Variable stiffness then acts as a kind of structural memory, preserving a useful shape after the active deformation phase. The continuous configuration model is compact. Five quantities describe the planar body: the position and orientation of the central frame, plus the curvatures of the two bridge segments. On top of those continuous coordinates sits a discrete hybrid state describing which segments are rigid or compliant and which motion mode is active. The planning problem therefore involves both continuous geometry and discrete transitions. The constant-curvature representation is central. Rather than modeling every point along a soft segment as an independent degree of freedom, each segment is approximated as a circular arc. This reduces an otherwise infinite-dimensional soft-body problem to two shape variables. It also gives the planner closed-form forward kinematics for important points along the body. This simplification is not exact. The authors’ earlier thermal-image experiments found that constant curvature was a reasonable approximation at modest bends, while discrepancies grew as deformation increased. But without such a reduced model, planning jointly over locomotion and continuum shape would quickly become intractable. Why Ordinary Mobile-Robot Planning Is Not Enough. For a fixed-shape planar robot, collision checking can often be reduced to a point-robot problem. Inflate every obstacle by the robot’s footprint, then find a path for the reference point through the remaining free space. That construction no longer works when the footprint changes continuously. A passage may be inaccessible to the straight robot but accessible when the two bridge segments form an S-curve. Another corridor may require a single C-shaped bend. The collision status of the robot therefore depends on its position, orientation, two curvatures, and stiffness-dependent ability to transition between shapes. A planner could, in principle, sample directly in that full hybrid configuration space. In practice, narrow passages are already difficult for sampling-based planners when the robot is rigid. Adding shape coordinates and discrete stiffness modes makes the useful region an even smaller fraction of the search space. Samples must not only be collision-free; they must form a physically reachable sequence under the robot’s deformation mechanics. The authors had previously developed a hybrid RRT*-plus-artificial-potential-field method for less congested environments. That planner can navigate around sparse obstacles and place the robot near an object. The thesis underlying the new paper shows a failure case in which obstacles surround the target so tightly that the earlier method cannot find a route, even after extensive search. Reaching the object requires coordinated body deformation rather than a better path for a nominally rigid footprint. A naïve formulation would search over five continuous coordinates, the stiffness choices, and four associated motion modes all at once. Instead, the new planner decomposes the problem. It first reasons about the topology and clearance of the workspace, then plans paths for a small set of representative body points, and only afterward reconstructs complete robot configurations. That decomposition is the paper’s main algorithmic contribution. VAMP: Find the Corridor First, Then Fit the Body. The authors refer to their Voronoi-based adaptive morphology planning pipeline as VAMP. Its high-level philosophy is simple: do not begin by sampling arbitrary curved bodies. First identify the small number of corridors that could plausibly connect the robot to the goal. Then ask what sequence of body shapes would fit through one of those corridors. The method has four stages:. Analyze the environment using a Voronoi diagram. Plan paths for the front, middle, and rear of the robot. Fit complete robot configurations to those point paths. Select the key traverse configurations needed for execution. This is effectively a workspace-first, configuration-space-second strategy. It sacrifices some of the generality of full configuration-space search in exchange for a much more structured problem. Stage One: Turn Clutter Into a Clearance Skeleton. The first stage constructs a Voronoi diagram from the obstacle geometry. Each Voronoi region contains workspace points closest to a particular obstacle. The boundaries between two regions are points equidistant from the two nearest obstacles, while Voronoi vertices mark intersections involving three or more nearby obstacles. For navigation, the useful object is the graph formed by those boundaries and vertices. Voronoi edges follow the medial structure of free space and therefore tend to maximize local clearance. Vertices provide topological branch points at which the planner chooses between alternative corridors. The continuous workspace is reduced to a graph that preserves its important passage structure. This bias is well matched to a shape-shifting robot. A shortest path running close to a wall is not necessarily desirable when the body must bend, cool, and maintain clearance along its entire length. The medial axis instead exposes where the widest routes are and, crucially, where the bottlenecks occur. The planner analyzes which Voronoi passages are theoretically traversable given the physical thickness and bending limits of the robot. A narrow edge is not immediately rejected simply because the straight body does not fit. It remains useful if the robot can place its front, center, and rear along compatible portions of the corridor while respecting curvature limits. Voronoi construction also gives VAMP a strong narrow-passage prior. Sampling-based planners often spend most of their computation exploring spacious, irrelevant regions. Here, the graph explicitly identifies constrictions and focuses the subsequent morphology optimization on them. The trade-off is that the medial axis is only a geometric scaffold. It is not itself a dynamically or kinematically feasible robot trajectory. That is why the next two stages are necessary. Stage Two: Plan for Three Critical Body Points. Representing the complete soft-rigid body during graph search would largely undo the computational benefit of the Voronoi decomposition. VAMP instead tracks three critical points: the front locomotion unit, the middle of the robot, and the rear locomotion unit. Together, these points provide a low-dimensional description of the robot’s gross geometry. If the three can be placed sensibly along a corridor, the two constant-curvature segments can often be fitted between them. The front and rear points constrain where the locomotion units must go, while the middle point anchors the overall path and captures whether the body should bow to one side or reverse curvature. This abstraction is more expressive than planning only for the body center. A centerline path can tell a rigid disc where to go, but it says little about how an extended articulated body should occupy a corner. Three paths encode the spatial phase difference needed for the front to enter a constriction before the middle and rear follow. It is also much cheaper than searching over every body point. This use of task-critical landmarks is one of the most transferable ideas in the paper. A continuum arm, deformable drone, snake robot, or articulated inspection platform may have many physical degrees of freedom, yet a small set of landmarks can be sufficient for topological planning. Stage Three: Lift the Point Paths Into Feasible Shapes. The critical-point paths are geometric suggestions, not commands. VAMP must now find a full five-dimensional robot configuration at each step whose front, middle, and rear points match the suggested locations. The paper formulates this as a sequential optimization. For every step, it chooses the central position, body orientation, and two curvatures while balancing four objectives. First is positional accuracy. The optimizer tries to place the three robot landmarks at their desired points, with the middle point normally receiving greater weight because it is the primary path reference. Second is motion smoothness. Large changes from the preceding configuration are penalized. Abrupt orientation and curvature changes are especially undesirable because they correspond to jerky or mechanically difficult shape transitions. Third is orientation alignment. The main body orientation is encouraged to follow the tangent direction of the middle-point path. Without this term, the three landmarks might fit while the robot’s overall heading oscillates or points awkwardly across the corridor. Fourth is shape simplicity. The absolute curvatures of both bridge segments are penalized, so a straight or mildly curved body is preferred whenever several collision-free solutions exist. The segments are also constrained to remain within their physical bending range; under the constant-curvature model, each is limited to a total bend of roughly 90 degrees. That curvature penalty has an important behavioral consequence. The robot does not contort merely because it can. In open regions it remains nearly straight, preserving a stable rigid-mobile configuration. Significant deformation appears only where additional curvature is required to pass a bottleneck. This can be viewed as a mechanical regularizer. In a learned policy we might penalize control effort, action variation, or deviation from a nominal posture. Here the planner penalizes morphological complexity directly. That reduces unnecessary deformation, limits model error, and should also reduce the number and duration of thermal stiffness transitions. The previous configuration provides a natural warm start for the next optimization. As the critical points advance along their paths, the fitted body changes gradually. The result is a dense sequence of complete poses and shapes rather than isolated inverse-kinematic solutions. Stage Four: Extract the Traverse Configurations. The final stage identifies the key configurations that define the traversal. Instead of treating every small fitted update as an independent high-level command, the planner extracts the configurations needed to enter, negotiate, and leave each constriction. This matters because morphology changes are not free. Melting and resolidifying a low-melting-point alloy occurs on a slower timescale than commanding a wheel velocity. A practical planner should therefore avoid switching stiffness for insignificant geometric gains. The resulting plan is best understood as a hybrid motion script. Some intervals are ordinary rigid-body navigation. Others activate one or both deformable segments, move the locomotion units to generate a new curvature, lock that shape, and continue. The geometry planner supplies the desired body sequence, while the robot’s existing hybrid controller manages the appropriate movement and stiffness modes. The complete pipeline has a useful hierarchical character: topology first, landmark geometry second, full-body shape third, and hardware execution last. Each layer operates with just enough physical detail for its decision. Turning the Entire Body Into a Gripper. Reaching the target is only half the task. The robot must also manipulate it, and this is where the hardware’s multifunctionality becomes most apparent. The 2SR platform performs what the authors call full-body grasping. Rather than bringing a small end effector to a locally selected contact pose, it wraps its deformable bridge around the object. The grasp resembles a hug: the robot conforms to a substantial portion of the object boundary, then solidifies the bridge to preserve the enclosing geometry. The grasping problem includes more than selecting a final curve. The robot needs an approach configuration that does not prematurely disturb the object, an appropriate sequence of stiffness transitions, and a final shape that is both secure and convenient for subsequent transport. The authors study this for curvilinear objects of varied geometry rather than for a single gripper-specific primitive. The overall manipulation sequence is mechanically intuitive. The robot navigates toward the object in a comparatively rigid and compact state. Near the target, selected bridge segments become compliant. The wheel units move around the object and bend the bridge into an enclosing configuration. The structure then becomes rigid again, after which the robot transports the object using ordinary omnidirectional motion. This is not conventional prehensile manipulation, because there is no independent arm and hand. Nor is it simply pushing. The locomotion system creates the grasp, and the grasping structure becomes the chassis during transport. The broader implication is that whole-body manipulation can eliminate part of the traditional navigation-versus-reach trade-off. A conventional mobile manipulator needs enough base clearance to position an arm, plus enough arm workspace to reach the target without collisions. The 2SR robot instead brings its grasping surface through the corridor as part of its body. What the Experiments Actually Establish. The dense-clutter experiments show the robot traversing four different environments with the VAMP-generated motion and morphology sequences. The planned shapes include straight sections, single-curvature C-shapes, S-shapes, and more complex combinations as the geometry demands. Transitions remain gradual rather than snapping between unrelated configurations. The most visible result is the minimal-deformation behavior induced by the optimizer. Where clearance is generous, the robot stays straight. As it approaches a bottleneck, the relevant segment begins to curve. Once clear, the body relaxes toward a simpler configuration. The shape sequence is therefore tightly coupled to local environmental geometry. The RRT*-APF failure example helps clarify what VAMP adds. The earlier method is not merely returning a longer or less elegant route; it cannot reach a target surrounded by obstacles because it lacks an effective mechanism for reasoning about coordinated deformation. VAMP finds a passage by explicitly planning where different portions of the robot should lie. For manipulation, the reported autonomous grasping trials incurred larger errors than more controlled cases, but the system nevertheless completed all of the demonstrated transport tasks. The thesis emphasizes robustness to imperfect final grasp configurations: even when the robot did not achieve the nominal envelope exactly, the distributed full-body contact was often sufficient to carry the object. That is an encouraging property of conformable grasping. A small parallel-jaw gripper can lose an object when a few millimeters of pose error move the contacts outside the frictional region. An enveloping body has more geometric redundancy, although its actual stability still depends on friction, object mass, curvature, and the stiffness achieved after cooling. The evidence should nevertheless be read as a system demonstration rather than a benchmark-scale evaluation. It establishes that the hardware, geometric planner, configuration fitting, stiffness sequencing, and manipulation controller can operate as an integrated physical pipeline. It does not yet establish broad statistical generalization across arbitrary three-dimensional clutter, dynamic obstacles, or large object distributions. How This Differs From Related Morphology-Aware Robots. The most direct predecessor is the team’s own 2023 2SR paper. That work introduced the soft-rigid mobile platform, derived a unified hybrid kinematic model, and demonstrated target shape formation, conformity around a cylinder, and transport of a cube. The new paper advances from “the robot can take these shapes” to “the robot can autonomously decide which shapes are needed to traverse clutter and grasp a target.”. Other variable-stiffness robots often use stiffness to select where deformation occurs. Do and colleagues, for example, showed how layer jamming in an inflated growing robot could activate particular joints, allowing one actuator to control different sections at different times. Both systems use stiffness as a way to reconfigure the mapping from actuation to shape, but the inflated-beam work focuses on workspace expansion and growth, whereas 2SR couples stiffness selection to planar mobility and full-body object transport. There is also a broader family of robots that use body bending to improve narrow-space navigation. Multi-segmented legged robots can coordinate torso bending with their gait to steer around obstacles or negotiate narrow passages. In those systems the body motion mainly supports locomotion; in 2SR, the same deformation later becomes the manipulation mechanism. Passive morphology offers another contrast. Experiments inspired by discoid cockroaches showed that a thin, rounded shell could let a legged robot roll through dense vertical clutter without changing its controller. That is mechanical intelligence through a fixed, environmentally favorable shape. The 2SR approach is active: it selects a different shape for each passage and task. What distinguishes the present work is therefore not any one ingredient in isolation. Variable stiffness, deformable spines, whole-body grasping, Voronoi navigation, and trajectory optimization all have precedents. The distinctive contribution is their integration around a robot whose embodiment serves as both the thing being controlled and a resource the planner can spend. The Hard Limitations. The first limitation is dimensionality of the physical world. The reported planner is fundamentally planar. Its five-coordinate model assumes two constant-curvature arcs moving on a surface, while the Voronoi analysis is built over two-dimensional obstacle geometry. This is appropriate for the current wheeled platform but does not directly capture overhangs, ramps, body roll, bridge sag, or objects that must be approached from different heights. The word “clutter” should consequently be interpreted carefully. This is obstacle clutter around an extended mobile body, not the occluded heap of unknown objects usually associated with six-degree-of-freedom bin picking. The planner is solving a confined-navigation and whole-body-access problem. Second, the constant-curvature model is both an enabler and a source of mismatch. Real soft segments may develop uneven curvature because of thermal gradients, material hysteresis, gravity, wheel slip, or contact with an obstacle. The authors’ earlier measurements already show that approximation error increases at large bends. A robust deployment would need state estimation that continuously observes the actual body curve and replans around deviations. Third, the hardware has thermal dynamics. Stiffness transitions take time and consume energy, and cooling conditions may vary with ambient temperature, contact, and prior heating. The thesis reports a modular redesign that reduces transition time, while the earlier paper explicitly identifies faster phase transition as an important direction. Even so, thermal latency remains qualitatively different from ordinary motor actuation. The planning objective discourages unnecessary curvature, and key-configuration selection should reduce redundant transitions. A stronger formulation would model temperature and solidification explicitly. Transition time, residual heat, stiffness uncertainty, and energy could then appear in the plan cost rather than being handled mainly by execution logic. Fourth, the sequential decomposition can miss solutions. A path that looks excellent on the Voronoi skeleton may not lift into a feasible sequence of whole-body shapes. Conversely, a feasible path may lie away from the medial axis and never be proposed. The decomposition is computationally attractive precisely because it does not search the entire hybrid configuration space. A mature implementation should therefore support feedback between stages. Failed configuration fitting could trigger another landmark path, another Voronoi branch, or a local off-skeleton trajectory optimization. Multiple candidate topologies would be especially useful when the shortest high-clearance route demands difficult stiffness transitions. Fifth, navigation and grasping are treated largely through geometry. Geometry is necessary for an enveloping grasp, but it does not fully determine grasp quality. Friction, object compliance, mass distribution, acceleration during transport, and the final rigidity of the bridge all affect whether the object slips. Distributed tactile or force sensing would make it possible to close the loop around actual grasp security rather than inferred conformity. Finally, the method assumes relatively dependable environmental geometry. Voronoi graphs can be sensitive to noisy obstacle boundaries, and narrow passages amplify even small perception errors. Clearance margins should ideally depend on uncertainty, not only nominal distance. A passage reconstructed with low confidence may need a larger safety buffer or a slower contact-tolerant execution mode. How Roboticists Could Reuse the Idea. The most reusable contribution is not the particular alloy or wheel layout. It is the planning pattern: reduce a difficult morphology-aware problem to a small number of spatial landmarks, use workspace topology to propose routes, and then lift those routes into full configurations through constrained optimization. For a continuum manipulator, the landmarks might be the tip, two intermediate backbone points, and the base. For a quadruped squeezing through a doorway, they might represent the shoulders, pelvis, and feet. For a deformable aerial vehicle, they could represent rotor hubs and the body center. The landmarks should capture the collision-relevant shape without forcing the global planner to reason over every actuator. The second lesson is to make nominal morphology an explicit regularizer. If the robot can bend, telescope, fold, or change width, a planner should not use those capabilities indiscriminately. Deformation may consume energy, reduce model accuracy, limit payload, or increase wear. Penalizing deviation from a simple, strong nominal shape produces behavior that reserves morphological adaptation for places where it creates real value. The third lesson is to price stiffness changes separately from ordinary motion. For 2SR, melting and resolidifying are expensive events. In a tendon-locking robot, the cost may be cable tension and wear. In a pneumatic system, it may be pressure and settling time. A morphology-aware planner should distinguish between moving through a fixed shape and changing the mechanical structure itself. For researchers working with learning, VAMP is an attractive model-based teacher. The planner could generate demonstrations across procedurally generated bottlenecks, providing supervision for a policy that predicts landmark paths, curvature profiles, or stiffness modes from local sensor observations. A learned proposal model could produce several candidate shape sequences, while the geometric optimizer enforces collision and curvature constraints. A residual policy would be another natural addition. VAMP could provide the nominal topology and shape plan, while a learned controller compensates for wheel slip, imperfect heating, contact, and deviations from constant curvature. This division preserves interpretability and constraint handling without requiring the analytical model to explain every physical effect. The planner could also serve as a warm start for model-predictive control. Rather than optimizing an entire long-horizon hybrid trajectory online, MPC would follow the VAMP plan locally, adjust landmark targets from live perception, and reconsider the stiffness schedule only when the observed corridor differs materially from the map. For three-dimensional systems, the Voronoi skeleton could be replaced with a medial surface, signed-distance-field ridge, topological roadmap, or learned connectivity graph. The same principle remains: use a coarse representation to choose the passage class, then solve the expensive morphology optimization only inside that class. Perhaps the most interesting extension is co-design. The number and location of variable-stiffness segments determine both mechanical versatility and planning complexity. A planner such as VAMP can quantify which bends are repeatedly required across a task distribution. Those statistics could guide where the next robot should place joints, heaters, stiffeners, sensors, or high-friction grasping surfaces. Final Takeaway. This paper asks a question that much of robotics quietly avoids: what if the robot’s body is not a boundary condition but part of the plan?. The 2SR robot can move while rigid, soften selected sections to reshape itself, lock those sections into a new load-bearing geometry, pass through a corridor that excludes its nominal form, and then use the same deformable body to grasp an object. VAMP makes that capability computationally manageable by planning over workspace topology, three body landmarks, and a regularized sequence of full configurations. The work is still planar, model-dependent, thermally limited, and demonstrated at modest scale. But its central idea is broad. Future embodied systems may need to choose not only what action to take, but also what body to present to the world. For these robots, planning will no longer mean merely finding somewhere to go. It will mean deciding what to become along the way.