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Movers and Shakers: Kinetic Energy Harvesting for the Internet of Things

Maria Gorlatova, John Sarik, Guy Grebla, Mina Cong, Ioannis Kymissis, Gil Zussman

arXiv:1307.0044v3cs.ETcs.NIcs.PF

TL;DR

Motion energy availability and its effect on adaptive IoT algorithms remain limitedly understood, particularly because human motion contains variable low-frequency vibrations. The paper estimates harvester output from acceleration traces, analyzes large-participant and long-term motion data, and develops allocation algorithms for practical IoT nodes. It reports highly variable motion power comparable to indoor-light availability, while trace-based evaluations show good performance from approximation and online algorithms and the importance of storage modeling.

  • Problem

    Limited understanding of motion-energy availability and its impact on energy-harvesting adaptive algorithms motivates characterization for IoT nodes.

  • Method

    The paper processes acceleration traces to estimate inertial-harvester energy, analyzes human-motion datasets and long-term measurements, and develops offline, approximation, and online allocation algorithms.

  • Results

    Motion power availability is comparable to indoor-light availability and highly variable, while approximation and online algorithms perform well on collected traces.

  • Takeaways & Limitations

    Real-world motion traces and storage properties should be incorporated when evaluating energy-harvesting adaptive algorithms for practical IoT nodes.

  • Takeaways & Limitations

    No performance guarantee exists for any online algorithm in some cases because the harvested-energy process cannot be represented by a Markov or i.i.d. process.

Abstract

from arXiv · show

Numerous energy harvesting wireless devices that will serve as building blocks for the Internet of Things (IoT) are currently under development. However, there is still only limited understanding of the properties of various energy sources and their impact on energy harvesting adaptive algorithms. Hence, we focus on characterizing the kinetic (motion) energy that can be harvested by a wireless node with an IoT form factor and on developing energy allocation algorithms for such nodes. In this paper, we describe methods for estimating harvested energy from acceleration traces. To characterize the energy availability associated with specific human activities (e.g., relaxing, walking, cycling), we analyze a motion dataset with over 40 participants. Based on acceleration measurements that we collected for over 200 hours, we study energy generation processes associated with day-long human routines. We also briefly summarize our experiments with moving objects. We develop energy allocation algorithms that take into account practical IoT node design considerations, and evaluate the algorithms using the collected measurements. Our observations provide insights into the design of motion energy harvesters, IoT nodes, and energy harvesting adaptive algorithms.

1. INTRODUCTION

The paper addresses limited understanding of motion-energy availability and its implications for harvesting-adaptive IoT algorithms. It characterizes human and object motion, develops trace-based energy estimates, and designs allocation algorithms for practical ultra-low-power nodes.

  • Motivation: Motion harvesting is more complex than light harvesting because human motion combines variable low-frequency vibrations below 10 Hz.Harvested power is maximized when harvester and motion frequencies are reasonably matched.
  • Motion characterization: The study estimates harvested energy from acceleration traces and analyzes common human activities using data from over 40 participants.The dataset covers walking, running, cycling, and other motions, while dedicated sensing units support long-duration collection.
  • Findings: The analysis finds motion power availability comparable to indoor-light availability and highly variable over time.These observations motivate evaluating adaptive algorithms with real-world traces rather than only i.i.d. or Markov models.
  • Object motion: The paper also measures moving objects, including writing, doors, luggage, vehicles, trains, and shipped packages.The experiments include everyday activities and objects in transit.
  • Contributions: The work contributes a publicly available long-term human-motion acceleration dataset and design insights for harvesters, IoT nodes, and adaptive algorithms.The dataset is described as the first publicly available long-term human-motion acceleration dataset to the authors’ knowledge.
  • Energy allocation: The authors develop optimal offline, approximation, and online energy-allocation algorithms for ultra-low-power IoT nodes.The model accounts for discrete spending rates, utility functions, and capacitor-based storage; evaluations use collected traces.

2. RELATED WORK

The paper positions its long-term human-motion and object-motion experiments as unique contributions relative to the related work discussed elsewhere.

  • Related work: The authors identify their long-term human-activity and object-motion experiments as unique contributions.The statement introduces the related-work discussion for the paper’s other contributions.

3 MODELS & MEASUREMENT SETUP

The paper models inertial harvesters and IoT nodes, collects acceleration with dedicated sensing units, and converts traces into estimated harvested power and data rates.

  • Inertial harvester model: The harvester is modeled as a second-order mass-spring system with proof mass, displacement limit, spring constant, and damping factor.The model represents the inertial harvesting mechanism used throughout the measurements and estimates.
  • Inertial harvester model: Harvester mass and displacement are constrained by IoT size and weight, while spring constant and damping are tuned for motion-specific energy harvesting.The selected configuration uses m = 1 · 10^-3 kg and ZL = 10 mm.
  • Inertial harvester model: Maximum power requires matching harvester resonant frequency fr to dominant motion frequency fm, while quality factor Q controls spectral width.Small Q covers a wider frequency range with lower peak power; large Q is more finely tuned.
  • Measurements: Dedicated ADXL-based sensing units record triaxial acceleration at 100 Hz across placements including shirt pocket, waist belt, and trouser pocket.The measured acceleration magnitude is high-pass filtered to remove the constant gravity component.
  • Power estimation: The analysis computes motion deviation D and dominant frequency fm, then transforms acceleration into proof-mass displacement and power.The procedure limits displacement by ZL and calculates P(t) = b(dz(t)/dt)^2 before averaging power.
  • Node characterization: The resulting average harvested power is converted into wireless-node data rates using a practical harvester efficiency assumption of ηh = 20%.A MATLAB and Simulink implementation demonstrates the trace-to-power procedure for a walking sample.

4 HUMAN MOTION

The paper characterizes human-motion energy and formulates trace-based allocation for a slotted IoT node whose storage may be a battery or capacitor.

  • Wireless node model: The node controls energy spending rates s(i) over K time slots to determine transmission power, duty cycle, sensing rate, or communication rate.The model represents an ultra-low-power wireless node that harvests and stores environmental energy.
  • Wireless node model: The optimization maximizes the sum of per-slot utility values associated with energy allocations and resulting data rates.The utility function may represent the data rate obtained from a selected spending rate.
  • Storage model: Storage level B(i) evolves from prior storage, harvested energy Q, leakage L, and energy spending, with capacity and conversion efficiency constraints.The harvested-energy function may depend on storage level for capacitor-based nodes.
  • Algorithmic design: The algorithmic model includes discrete spending rates, general utility functions, and capacitor storage rather than assuming continuous rates, concave utilities, or batteries.These design aspects distinguish the considered model from several earlier formulations.
  • Storage model: The study distinguishes battery and capacitor models because capacitor output voltage depends on storage level, producing nonlinear conversion efficiency.The battery model uses η(i, B(i)) = 1, whereas the capacitor model uses a nonlinear η(i, B(i)).

4. HUMAN MOTION

The study characterizes harvested kinetic energy across seven common human motions using measurements from over 40 participants and three sensing-unit placements. Motion frequency is generally consistent for common periodic activities, while harvested power varies substantially by activity and placement.

  • Dataset and measures: Over 40 participants performed 7 common motions, with acceleration traces used to calculate D, fm, P, and r.The motions included relaxing, walking, fast walking, running, cycling, and stair ascent and descent.
  • Motion frequency: Running samples produced dominant frequencies consistent with typical foot-strike cadence, including the 3 Hz optimal cadence reference.The observed frequency range was physiologically plausible for running.
  • Harvested power: Relaxing generated less than 5 µW, whereas walking produced median power of 155 µW at shirt-pocket placement.The passage gives the relaxing threshold and one walking-placement median; other placement values are truncated.
  • Harvested power: Going downstairs produced 1.65–2.1 times the median power of going upstairs, depending on sensing-unit placement.Downstairs motion had higher motion magnitude and frequency despite lower perceived exertion than upstairs motion.
  • Motion frequency: For shirt, waist, and trouser placements, the same motion generally produced similar fm values, except cycling differed at the trouser placement.The torso-adjacent placements experienced similar stresses; cycling differed because sitting changes stresses across body locations.

5 LONG-TERM HUMAN MOBILITY

Dominant motion frequency depends on participant physiology even when it is broadly consistent across people. Taller and heavier participants generally take fewer steps per unit time, while taller runners generated more power in one measured configuration.

  • Physiological dependence: Heavier and taller participants generally had lower fm for walking, running, and stair motions.The study relates this pattern to fewer steps per time interval among heavier and taller participants.
  • Physiological dependence: For stair ascent with waist placement, height and fm correlated at ρ = −0.34 (p = 0.03, n = 39).The taller half averaged 9 fewer steps per minute than the shorter half: 1.85 versus 2.05 Hz.
  • Physiological dependence: For running with trouser placement, weight and fm correlated at ρ = −0.46 (p < 0.01, n = 39).This supports a measurable relationship between participant weight and running frequency in that placement.
  • Harvested power: For running with trouser placement, taller participants had 20% higher average harvested power than shorter participants: 704 versus 582 µW.Height also correlated positively with D (ρ = 0.35) and P (ρ = 0.38) in this configuration.

5. LONG-TERM HUMAN MOBILITY

Longer measurements show that harvested motion power changes substantially during sustained activities and ordinary daily routines. Most daily energy arrives in brief active periods, making energy-management policies important for small IoT nodes.

  • Prolonged activities: During a 3-hour run, fm varied continuously from 2.6–3.4 Hz while D changed subtly over time.The measurements used 1-second acceleration intervals to track changing motion properties.
  • Day-long routines: Over 200 hours of traces from 5 participants across 25 days captured motion experienced by everyday carried objects.Participants carried sensing units in any convenient way during normal daily routines.
  • Energy budgets: For most participants, an inertial harvester could continuously support at least 1 Kb/s because Pd exceeded 5 µW.The resulting rate was comparable to estimates for similarly sized indoor-light harvesters.
  • Energy budgets: The amount of daily walking primarily explained differences in P and Pd among participants and days.Participant M2 had higher values alongside a relatively long and frequent walking routine.
  • Energy variability: Energy availability varied widely throughout the day because walking generated substantial energy while stationary periods generated little.The collected routines therefore combined long low-power periods with shorter active periods.

6 OBJECT MOTION ENERGY

The paper evaluates Scheme-LB energy allocation using measured traces and matched i.i.d. and Markov surrogates. Surrogate processes can substantially distort both performance levels and trends, supporting evaluation with real motion traces.

  • Policy evaluation: Scheme-LB performance with the ON/OFF process stayed close to measured-trace performance, with rate differences up to 17% and ON-time differences up to 7%.The comparison used participant M1’s trace and corresponding process representations.
  • Policy evaluation: i.i.d. and Markov processes differed from measured traces by over 105% in data rate and 63% in ON times.These differences were observed under the same Scheme-LB policy evaluation.
  • Policy evaluation: Measured-trace data rates differed by over 2.3 times across C values, while i.i.d. and Markov rates were nearly independent of C.The surrogate processes therefore produced different performance trends, not merely different absolute values.
  • Policy evaluation: Using measured traces, ON times could be low for small C, whereas i.i.d. and Markov evaluations produced nearly 100% ON times even at C = 15 mJ.The 15 mJ value was less than 15% of the average energy harvested per day.

6. OBJECT MOTION ENERGY

Object-motion harvesting is usually weak because inertial harvesters favor periodic motion, but purposeful shaking can produce substantially higher power. Measurements covered everyday activities and objects in transit.

  • Measurements recorded acceleration and calculated harvested power across everyday objects, shipping, luggage, cars, subways, and trains.
  • 120 ≤P ≤280 µW is the typical power range for human walking used as a reference.
  • P < 10 µW was observed when a sensing unit attached to a book was taken from a shelf, read, or returned.
  • Damped object motions yield little harvestable energy because dampers absorb most of the motion energy.
  • Up to 3,500 µW was measured for purposeful shaking, 12–29 times more than walking power.

7. ENERGY-AWARE ALGORITHMS

The paper formulates energy allocation for ultra-low-power IoT nodes under realistic storage and spending constraints, then develops offline and online solution methods. The problem is NP-hard, motivating exact dynamic programming, approximation, and online approaches.

  • The formulation jointly models discrete spending rates, general utility functions, and capacitor-based energy storage.
  • Measured environmental energy cannot be represented by a Markov or i.i.d. process, so algorithms avoid assuming a distribution for e(i).
  • The paper develops optimal and approximate offline algorithms plus an online algorithm proven optimal in some cases.
  • Constraint (1) limits spending to stored energy and fixed rates, constraint (2) models storage evolution, and constraint (3) imposes capacity and endpoint levels.
  • The Energy Allocation problem is NP-hard, even for simple cases such as B0 = BK = 0 and linear U(s(i)).

7 ENERGY-AWARE ALGORITHMS

The paper develops offline, approximation, and online energy-allocation algorithms for IoT nodes with practical discrete-rate, utility, and storage constraints, then evaluates them on motion traces. The evaluation shows generally strong performance, while capacitor behavior makes storage size an important design factor.

  • Algorithm design: The energy-allocation problem is NP-hard, motivating an optimal offline algorithm, an FPTAS, and online algorithms with scenario-specific guarantees.The greedy online algorithm is optimal under stated battery-model conditions, while no universal online guarantee exists in some cases.
  • Algorithm design: The offline dynamic program uses utility-indexed states to maximize achievable utility while respecting storage evolution and terminal energy constraints.Its stated space complexity is O(K · U_H), and its time complexity is O(K·|S|·U_H).
  • Algorithm design: The FPTAS runs in polynomial time in 1/ϵ and K and returns a (1 −ϵ)-approximation, while the greedy online algorithm selects the highest feasible utility each slot.The online rule prevents storage from falling below B_K.
  • Trace-based evaluation: The trace-based evaluations find approximation and online algorithms perform well and show that larger energy storage can worsen overall performance for capacitor nodes.Figure 10 compares approximation ratios and average data rates; Figure 11 reports battery-model and cross-storage comparisons.
  • Trace-based evaluation: For capacitor traces, ALG-FC stays close to optimal ALG-OC, whereas ALG-GC worsens for larger C and its data rate decreases when C > 60 µJ.The greedy capacitor algorithm obtains lower output voltage and conversion efficiency as storage changes.
  • Trace-based evaluation: For battery traces, ALG-GB is compared with ALG-OB at B_K = B_0 = 10 · s_min, while larger capacitor storage lets ALG-OC approach ALG-GB performance.The capacitor comparison is attributed to a wider charge range with conversion efficiency near one.

8. CONCLUSIONS

The paper characterizes motion energy for IoT applications using extensive human acceleration traces and measurements of moving objects, then develops adaptive allocation algorithms. Future work expands motion and participant coverage, jointly studies light and motion, tests real devices, and addresses multihop networks.

  • Conclusions: The study analyzes 200 hours of day-long human acceleration traces and a dataset of 7 common motions performed by over 40 participants.It also reports observations from measurements of moving objects.
  • Conclusions: The paper develops a wireless energy-harvesting node model and provides observations about human and object motion relevant to IoT applications.The conclusion frames motion energy availability as the central application setting.
  • Future work: Future work will add motions and participants, jointly measure light and motion energy, evaluate algorithms on real devices, and study multihop IoT networks.The planned evaluations include varied utility functions and energy consumption.

APPENDIX I Proof of Theorem 1

The appendix proves NP-hardness of the energy-allocation problem by reducing decision subset sum to a decision version of the problem. It also establishes the approximation guarantee and analyzes a limitation of online feasibility under certain storage conditions.

  • NP-hardness proof: The reduction transforms subset-sum instances through polynomial-time coefficient and slack-variable constructions before encoding them as energy-allocation instances.The resulting EA-D instance uses specified capacity, spending, harvesting, efficiency, and utility settings.
  • NP-hardness proof: The decision version EA-D asks whether a feasible spending vector achieves total utility at least U, and solving it would solve the optimization problem by binary search.The proof therefore reduces EA-D from decision subset sum.
  • NP-hardness proof: The constructed energy-allocation instance is a yes instance exactly when the corresponding transformed subset-sum instance is a yes instance.Feasible spending slots encode the transformed subset choices and achieve utility c.
  • Approximation proof: The FPTAS proof bounds its returned utility by (1 −ϵ)U*, using scaled utilities and dynamic programming over the scaled range.The resulting space and time complexities depend polynomially on K, |S|, and the scaled maximum utility.
  • Online limitations: For capacitor storage with B_K > 0 and K ≥ 2, any feasible online algorithm can perform arbitrarily worse than optimal.The appendix constructs an instance where delayed energy availability forces an online algorithm to obtain no utility, creating an arbitrarily large gap.
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