cond-mat.softOct 8, 2026
SaveAutonomous thermodynamic cycles via robotic mobility and sensing
Organizations: Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, 3200003, Israel.
Abstract
Thermodynamic cycles are the foundation of energy conversion across natural and engineered systems, transforming heat into useful work. However, these cycles traditionally operate between fixed thermal reservoirs, restricting them to specific locations and temperature differences. Here, we introduce autonomous thermodynamic cycles enabled by robotic mobility and sensing, allowing robots to perform thermodynamic cycles by accessing spatially varying temperature fields. We experimentally realize this concept using multistable gas-filled capsules that circulate within the system across a thermal gradient. Our model reveals that rapid transitions in the capsules' energy states allow the system to operate as a mobile heat engine that harvests and stores energy. By linking the capsule-scale internal energy dynamics to the robot's large-scale navigation strategy, we optimize locomotion paths that balance motion cost and energy harvesting. These findings demonstrate that thermodynamic cycles can emerge when autonomous systems navigate their environments, offering an artificial analog of organisms that forage for energy across spatial resources.
Figures & tables
Figure 1: Energy storage and harvesting mechanisms using gas-filled multistable capsules. (a1) Robot paths across a spatially varying thermal environment, illustrating two operating modes: (I) energy harvesting by traversing alternating hot and cold regions and (II) stationary operation using local temperature gradients. (a2) Corresponding internal capsule temperature along a representative trajectory (Path 3), showing thermal lag and state-transition events (marked by lightning symbols), where and denote are the capsule’s internal and external temperatures, respectively. (b1) Schematic of embedded capsules as distributed energy units within a robotic platform. (b2) Capsules that are transported within an internal vascular system, actuated by solenoids. (c) The sealed gas-filled multistable capsule composed of a series of bistable units with magnets at its edges. (d) Electromagnetic energy conversion during rapid capsule transition, induced by the motion of a mounted magnet relative to a surrounding coil. (e) Piecewise-linear approximation of the force-displacement response of a bistable unit, highlighting two stable states and snap force thresholds ( , ). (f) Effective energy profile of a bistable capsule, combining elastic and gas-pressure contributions, and the energy barriers and between closed and open states, respectively.
Figure 2: Equilibrium states of electromagnetically actuated capsules. (a) Experimental setup consisting of a sealed capsule with magnets at its edges, and a power supply to drive current through a coil. (b) Comparison of theoretical (solid lines) and measured (circles) electromagnetic forces as a function of magnet distance relative to the center of the solenoid for two representative solenoid currents and magnet numbers, alongside a schematic of the forces acting on the capsule. (c1) Net actuation force resulting from the applied magnetic force and opposing internal gas force. (c2) Elastic forces corresponding to different stable states of the capsule. Equilibrium positions occur at the intersection of the net force and elastic force. Varying the net force within a given stable state shifts the equilibrium along the corresponding elastic response. The shaded region represents all possible stable equilibria. Once the force exceeds the snap-through thresholds, or , instability occurs and the capsule transitions to another stable state. Transitions between elastic force responses associated with different stable states occur only through snap-through. The inset shows the snap force thresholds and . (c3) Close-up of the magnetically actuated cycles where currents are cyclically increased and decreased incrementally. Stable equilibria are indicated by filled black circles, the thick line denotes the net force in the absence of an external magnetic force. Red dashed arrows denote the unstable snap-through transitions when elastic forces exceed or , and purple dashed line denotes a sudden current increase by 4 A leading to multiple snaps. Residual gas forces are represented by . Gray arrow traces the initial trajectory and black arrows indicate the repeating cycle. The legend is shared between panels (c2) and (c3). (d) Effective spring model of the loaded capsule, used to determine equilibrium and stability. (e) Comparison between simulations and experiments for magnet location as a function of solenoid current. In panels (b) and (e) error bars are smaller than the marker size.
Figure 3: Energy storage in capsules via energetic minima and its on-demand release as mechanical work. (a) Robot trajectory across a thermal field, illustrating energy storage through thermally driven snap-up, with subsequent energy release using electromagnetically driven snap-down. (b) Simulation of capsule dynamics: (b1) Internal and external temperatures , . Expansion and snap-up upon heating, which induces heat rejection from the capsule, followed by contraction without snap-down during cooling. (b2) Force balance between elastic, , gas, , and external force, , activated through electromagnetic force at to induce snap-down. (b3) Capsule length and velocity abruptly transitioning during snap events. (b4) The interplay between gas energy, , and the elastic energy, . After snap-up, cooling is insufficient to trigger snap-down, resulting in residual stored energy . (b5) The energy induced in the solenoid by the magnet motion, , the energy accumulated and retained in the system, , and the usable work, . (c) The thermodynamic cycle of the capsule showing multiple stable states for the same temperature. (c1) Pressure-temperature and (c2) entropy/enthalpy-temperature diagrams showing near-isentropic snap-through behavior. The green triangle and the red square denote the start and the end states, respectively. (d) The mechanical work, , used to lift a load produced by a snap-through event.
Figure 4: Energy harvesting from cyclic thermal variations . (a) Energy scavenging via snap-through events through (I) a mobile system sampling temperature variations on route, or (II) a stationary system leveraging temperature gradients across the system. (b) Simulation of capsule dynamics under cyclic heating and cooling. (b1) External temperature driving changes in the internal capsule temperature via heat transfer. (b2) Internal elastic and gas forces, and , interchanging according to the external temperature conditions and the capsule state. (b3) Capsule length indicating the state, and edge velocity which peaks during state transitions corresponding to high kinetic energy. (b4) Energy components: internal gas energy, , and the elastic energy, . (b5) Electromagnetic energy induced as a magnet at the capsule edge moves within a solenoid, , which accumulates as stored energy, , through repeated snap-through events. (c) Capsule thermodynamics. Gas pressure, enthalpy and entropy as functions of internal temperature, showing mixed thermodynamic cycles.
Figure 5: Experimental demonstration of thermally induced thermodynamic cycles. (a) Experimental setup in which magnet-edged capsules circulate within a closed tube loop between a hot reservoir ( C), inducing snap-up, and a cold, ice-water reservoir ( C), inducing snap-down. The capsules are transported through the water-filled tube via alternating magnetic fields generated by six solenoids (M1-M6). Black rectangles mark the locations corresponding to the state images of the capsules inpanels (f,g). (b) Repeated solenoid current waveform consisting of a pulse ( ms, A) that advances the capsules clockwise, followed by a dwell for thermal equilibration ( s). (c) Tube and capsule-internal temperatures for four circulating capsules with phase-shift (capsule 1 shown in bold). (d) Capsules length during circulation. (e) Capsule state evolution during operation, with a nearly equal split between open and closed capsules throughout. (f,g) Representative images of open and closed capsules at \raisebox{-0.35ex}{\small3}⃝ and \raisebox{-0.35ex}{\small5}⃝ , respectively, where and denote the lengths associated with the closed and open states of the individual bistable elements comprising each capsule. (h) Mean of measured capsules’ lengths associated with each state, , nominal extension . Error bars represent one standard deviation.
Figure 6: Optimal energy-aware path planning in a thermal field . (a) Start and goal locations within a temperature field. (b) Thermal thresholds define boundaries that separate between hot and cold regions. Crossing these boundaries alternatingly triggers snap-through transitions in the multi-stable capsules. (c) Graph-based representation of the temperature field, with representative incentivized transitions between alternating thermal zones that enable energy harvesting. (d) Optimal simulated trajectories for increasing energy-harvesting incentives: the shortest path, a moderately incentivized path allowing limited detours, and a highly incentivized path favoring extended traversal through energy-harvesting regions. (e) A path requiring a moderate harvesting incentive to reach a target beyond the initial boundary range achievable with stored energy , extending it through harvested energy at each snap-through event, yielding a total possible range . (f) A path optimized with stronger harvesting incentive, achieving comparable range , despite a smaller initial stored energy relative to (e), by traversing a greater number of energy-harvesting locations along the route.