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.
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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 Tin and Text 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 ( Fopen , Fclose ). (f) Effective energy profile of a bistable capsule, combining elastic and gas-pressure contributions, and the energy barriers ΔE1 and ΔE2 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, Fclose or Fopen , 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 Fclose and Fopen . (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 Fclose or Fopen , and purple dashed line denotes a sudden current increase by 4 A leading to multiple snaps. Residual gas forces are represented by Fi . 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 Tin , Text . 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, Felastic , gas, Fgas , and external force, Fext , activated through electromagnetic force at TF to induce snap-down. (b3) Capsule length x and velocity v abruptly transitioning during snap events. (b4) The interplay between gas energy, Ug , and the elastic energy, Eel . After snap-up, cooling is insufficient to trigger snap-down, resulting in residual stored energy ΔEel↑ . (b5) The energy induced in the solenoid by the magnet motion, Eemf , the energy accumulated and retained in the system, Estored , and the usable work, W . (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, W , 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 Text driving changes in the internal capsule temperature Tin via heat transfer. (b2) Internal elastic and gas forces, Felastic and Fgas , interchanging according to the external temperature conditions and the capsule state. (b3) Capsule length x indicating the state, and edge velocity v which peaks during state transitions corresponding to high kinetic energy. (b4) Energy components: internal gas energy, Ug , and the elastic energy, Eel . (b5) Electromagnetic energy induced as a magnet at the capsule edge moves within a solenoid, Eemf , which accumulates as stored energy, Estored , 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 ( 75∘ C), inducing snap-up, and a cold, ice-water reservoir ( 0∘ 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 ( τa=110 ms, I±10 A) that advances the capsules clockwise, followed by a dwell for thermal equilibration ( τe=5 s). (c) Tube and capsule-internal temperatures for four circulating capsules with τa+τe 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 lc and lo 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, Lopen=115±9.8,Lclosed=82±5.6 , nominal extension ΔL=39.5% . 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 E0 , extending it through harvested energy Eh at each snap-through event, yielding a total possible range Er . (f) A path optimized with stronger harvesting incentive, achieving comparable range Er , despite a smaller initial stored energy E0 relative to (e), by traversing a greater number of energy-harvesting locations along the route.
Safely moving through environments affected by fire is a critical capability for autonomous mobile robots deployed in disaster response. In this work, we present a novel approach for mobile robots to understand fire through building real-time thermal radiation fields. We register depth and thermal images to obtain a 3D point cloud annotated with temperature values. From these data, we identify fires and use the Stefan-Boltzmann law to approximate the thermal radiation in empty spaces. This enables the construction of a continuous thermal radiation field over the environment. We show that this representation can be used for robot navigation, where we embed thermal constraints into the cost map to compute collision-free and thermally safe paths. We validate our approach on a Boston Dynamics Spot robot in controlled experimental settings. Our experiments demonstrate the robot's ability to avoid hazardous regions while still reaching navigation goals. Our approach paves the way toward mobile robots that can be autonomously deployed in fire-affected environments, with potential applications in search-and-rescue, firefighting, and hazardous material response.
Anton R. Wagner, Madhan Balaji Rao, Xuesu Xiao +1
Department of Computer Science, Kiel University, Germany · Department of Computer Science, George Mason University, USA
With the rapid development of simulation tools, the development and validation of autonomous robotic systems have become more efficient before real-world deployment. This paper presents a simulation-to-real implementation of an autonomous mobile robot based on an existing mechanical platform. Instead of focusing on mechanical design, our work concentrates on the development of the onboard control, self-localization, and autonomous navigation system. The proposed robot is equipped with onboard sensing and computation to estimate its pose and navigate autonomously in the environment. The overall framework is first developed and tested in simulation, and then deployed on the real robot for experimental evaluation. The results demonstrate the feasibility of the proposed approach and show that simulation provides an effective foundation for developing reliable autonomous mobile robot systems. The source code will be released at https://ntdathp.github.io/outdoor-robot-web.
Vinh Nguyen, Gia-Uy Le, Tien-Dat Nguyen +2
Faculty of Electrical and Electronic Engineering, Ho Chi Minh City University of Technology, VNU-HCM Ho Chi Minh City, Vietnam
Motor thermal management is often overlooked in the context of electrically-actuated robots, particularly legged robots, but motor overheating is a key factor that limits long-duration locomotion especially under payload conditions. This paper integrates a whole-body thermal model of a quadruped robot into the reinforcement learning pipeline to update motor temperatures, and proposes a two-stage training framework for motor thermal management. In this framework, a nominal policy is first pre-trained as a locomotion baseline capable of traversing diverse terrains. A residual policy is then trained on top of the nominal policy to provide corrective actions based on the robot's thermal state, ensuring high performance under low-temperature conditions and preventing motor overheating under high-temperature conditions. Simulation results demonstrate that the proposed policy achieves an effective balance between motor thermal safety and locomotion performance. Real-world experiments on a Unitree A1 quadruped robot further validate the approach: under a 3 kg payload, the robot achieves stable locomotion across multiple terrains for over 13 minutes, while the nominal policy alone leads to motor overheating in about 5 minutes.
Yuhang Wan, Weixian Lin, Letian Qian +5
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China