Power consumption optimization is crucial for extending robot operational time and enhancing efficiency. This topic explores various energy sources, including , , and fuel cells, as well as strategies for effective power management in robotic systems.

The notes cover efficient actuator design, sensor system optimization, and energy-efficient computing. They also delve into thermal management, software optimization, and bio-inspired energy solutions, providing a comprehensive overview of power consumption considerations in robotics and bioinspired systems.

Energy sources for robots

  • Power consumption optimization plays a crucial role in robotics and bioinspired systems by extending operational time and enhancing overall efficiency
  • Energy source selection impacts robot design, functionality, and environmental adaptability, influencing the development of autonomous and sustainable robotic systems

Battery types and characteristics

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  • Lithium-ion batteries offer high and long cycle life, commonly used in mobile robots
  • Nickel-metal hydride (NiMH) batteries provide a cost-effective alternative with moderate energy density
  • Lead-acid batteries suit stationary robots due to their low cost and high current output
  • Factors affecting battery performance include capacity, voltage, discharge rate, and temperature sensitivity

Solar power for robotics

  • convert light into electrical energy, enabling solar-powered robots
  • Amorphous silicon solar cells offer flexibility and better performance in low-light conditions
  • (MPPT) optimizes solar efficiency
  • Solar-powered robots often incorporate energy storage systems to operate during low-light periods

Fuel cells in robotics

  • Proton exchange membrane (PEM) fuel cells generate electricity through hydrogen and oxygen reactions
  • (SOFCs) operate at high temperatures, suitable for larger robotic systems
  • Fuel cells provide longer operational times compared to batteries but require fuel storage and management
  • harness energy from organic matter, inspiring bio-inspired robotic power systems

Power management strategies

  • Effective power management extends robot operational time and enhances overall system efficiency
  • Implementing adaptive power strategies allows robots to optimize energy consumption based on task requirements and environmental conditions

Dynamic power scaling

  • Voltage and frequency scaling adjusts processor performance to match computational demands
  • (DVFS) algorithms optimize power consumption in real-time
  • techniques shut down unused components to reduce static power consumption
  • adjusts the active-to-idle ratio based on workload and energy availability

Sleep modes and hibernation

  • Light sleep modes maintain minimal functionality while reducing power consumption
  • Deep sleep states power down non-essential components for extended periods of inactivity
  • Hibernation saves system state to non-volatile memory before complete shutdown
  • Wake-up mechanisms (timers, sensors) reactivate the system when needed

Energy harvesting techniques

  • Piezoelectric materials convert mechanical stress into electrical energy
  • Thermoelectric generators harvest energy from temperature gradients
  • Electromagnetic induction captures energy from motion or vibration
  • Radio frequency (RF) energy harvesting collects ambient electromagnetic waves

Efficient actuator design

  • Actuator efficiency significantly impacts overall robot power consumption
  • Bioinspired actuator designs often draw inspiration from natural muscle systems to achieve high efficiency and power density

Low-power motors and servos

  • offer higher efficiency and lower maintenance compared to brushed motors
  • Stepper motors provide precise positioning without continuous power consumption
  • convert electrical energy into mechanical motion with high efficiency
  • Shape memory alloy (SMA) actuators change shape when heated, offering compact and low-power operation

Pneumatic vs hydraulic systems

  • Pneumatic systems use compressed air, offering lightweight and clean operation
  • Hydraulic systems provide higher force output but require more complex fluid management
  • Pneumatic artificial muscles mimic biological muscle contraction for efficient actuation
  • Soft robotics often utilizes pneumatic or hydraulic systems for flexible and adaptive movement

Passive dynamics in locomotion

  • exploits natural swing dynamics to reduce energy consumption
  • Compliant mechanisms store and release energy during motion, improving efficiency
  • Bio-inspired spring-mass models optimize energy use in legged locomotion
  • Passive stability designs reduce the need for active control and energy expenditure

Optimizing sensor systems

  • Efficient sensor systems contribute to overall power optimization in robotic platforms
  • Sensor optimization strategies often draw inspiration from biological sensory systems, balancing sensitivity and energy consumption

Low-power sensing technologies

  • MEMS (Micro-Electro-Mechanical Systems) sensors offer low power consumption and small form factor
  • activate only when specific conditions are met, reducing idle power consumption
  • Asynchronous sensors operate without a fixed sampling rate, conserving energy during periods of inactivity
  • Bio-inspired artificial skin sensors provide efficient tactile sensing with low power requirements

Sensor fusion for efficiency

  • Data fusion algorithms combine information from multiple sensors to reduce redundancy
  • Kalman filters optimize sensor data integration while minimizing computational overhead
  • Hierarchical sensor fusion architectures distribute processing load for improved efficiency
  • Context-aware sensor fusion adapts sensing strategies based on environmental conditions

Adaptive sampling techniques

  • reduces data acquisition and transmission requirements
  • Variable sampling rates adjust based on signal dynamics and information content
  • Sensor scheduling algorithms optimize the timing and frequency of sensor activations
  • Adaptive resolution techniques adjust sensor precision based on task requirements

Energy-efficient computing

  • Computing efficiency directly impacts power consumption in robotic systems
  • Bio-inspired computing architectures often mimic neural networks for energy-efficient information processing

Low-power microcontrollers

  • ARM Cortex-M series processors offer energy-efficient performance for embedded systems
  • Ultra-low-power microcontrollers (MSP430) provide extended for sensor nodes
  • Sleep modes and power-gating techniques reduce static power consumption in idle states
  • Energy-aware instruction sets optimize code execution for power efficiency

FPGA vs ASIC for robotics

  • Field-Programmable Gate Arrays (FPGAs) offer reconfigurability and parallel processing capabilities
  • Application-Specific Integrated Circuits (ASICs) provide highly optimized performance for specific tasks
  • FPGAs allow for rapid prototyping and updates, suitable for evolving robotic systems
  • ASICs offer better power efficiency for well-defined, high-volume applications

Cloud computing vs edge processing

  • Edge computing reduces communication overhead and latency for time-critical tasks
  • Cloud computing offloads computationally intensive tasks to conserve on-board power
  • Hybrid approaches balance local processing with cloud resources for optimal efficiency
  • Fog computing distributes processing across a network of devices, optimizing resource utilization

Thermal management

  • Effective thermal management ensures optimal performance and longevity of robotic components
  • Bio-inspired cooling mechanisms often draw inspiration from natural thermoregulation systems

Heat dissipation techniques

  • Heat sinks increase surface area for passive cooling through convection
  • Heat pipes efficiently transfer heat from hot spots to cooler regions
  • Thermal interface materials improve heat conduction between components
  • Phase-change materials absorb and release heat to maintain stable temperatures

Cooling system optimization

  • Active cooling systems (fans, pumps) adjust speed based on temperature and workload
  • Liquid cooling offers higher heat transfer capacity for high-power components
  • Thermoelectric coolers provide precise temperature control for sensitive components
  • Bio-inspired cooling designs mimic natural convection patterns for improved efficiency

Temperature-aware power control

  • adjusts system performance to maintain safe operating temperatures
  • Thermal sensors provide real-time feedback for adaptive power control
  • Predictive thermal modeling anticipates temperature changes for proactive power management
  • Thermal-aware task scheduling distributes workload to minimize hot spots

Software optimization

  • Efficient software design significantly impacts overall power consumption in robotic systems
  • Bio-inspired algorithms often provide energy-efficient solutions for complex robotic tasks

Energy-aware algorithms

  • Approximate computing trades off precision for energy savings in non-critical calculations
  • Anytime algorithms provide usable results with varying computational resources
  • Bio-inspired (genetic algorithms, particle swarm) efficiently solve complex problems
  • Energy-aware path planning minimizes energy consumption during robot navigation

Task scheduling for efficiency

  • Dynamic voltage and frequency scaling (DVFS) adapts processor performance to workload
  • Real-time scheduling algorithms balance task deadlines with energy constraints
  • Workload consolidation minimizes idle time and maximizes energy-efficient states
  • distributes tasks across multiple processors for optimal efficiency

Power-efficient communication protocols

  • Low-power wireless protocols (Bluetooth Low Energy, Zigbee) reduce energy consumption in sensor networks
  • Adaptive data rate selection optimizes transmission power based on link quality
  • Sleep scheduling in wireless sensor networks conserves energy during idle periods
  • Energy-efficient routing protocols minimize communication overhead in multi-robot systems

Bio-inspired energy solutions

  • Biological systems provide inspiration for energy-efficient robotic designs
  • often lead to novel and sustainable energy solutions for robotics

Metabolic processes in robotics

  • Artificial digestion systems convert organic matter into usable energy for robots
  • Microbial fuel cells harness bacterial metabolism to generate electricity
  • Enzymatic biofuel cells utilize specific enzymes for efficient energy conversion
  • Bio-inspired energy regulation mimics homeostatic processes in living organisms

Energy storage in artificial muscles

  • Dielectric elastomer actuators store and release energy during deformation
  • Shape memory polymers store energy in their molecular structure for later release
  • Hydrogel-based artificial muscles utilize osmotic pressure for energy-efficient actuation
  • Carbon nanotube yarn muscles store energy through electrochemical charge injection

Biomimetic power distribution

  • Decentralized power distribution systems inspired by biological circulatory systems
  • Bio-inspired energy sharing protocols optimize power allocation in multi-robot systems
  • Artificial vascular networks for efficient thermal management and power distribution
  • Biomimetic energy harvesting from ambient sources (vibration, heat, light)

Power consumption modeling

  • Accurate power modeling enables efficient design and optimization of robotic systems
  • Bio-inspired modeling approaches often incorporate adaptive and predictive elements

Energy budgeting techniques

  • Component-level identifies energy consumption hotspots
  • Hierarchical power modeling combines system-level and component-level models
  • Probabilistic energy estimation accounts for variability in task execution
  • Energy-aware design space exploration optimizes system configuration for efficiency

Simulation tools for optimization

  • Physics-based simulators model energy consumption in robotic systems
  • Hardware-in-the-loop simulation integrates real components for accurate power modeling
  • Multi-physics simulation tools combine mechanical, electrical, and thermal models
  • Bio-inspired simulation frameworks incorporate adaptive behaviors for realistic power estimation

Real-time power monitoring

  • On-board power sensors provide instantaneous energy consumption data
  • Software-based power estimation techniques utilize performance counters
  • Machine learning models predict power consumption based on system state
  • Adaptive sampling strategies balance monitoring accuracy with overhead

Energy efficiency metrics

  • Standardized metrics enable comparison and optimization of robotic energy efficiency
  • Bio-inspired metrics often consider adaptability and resilience in addition to raw efficiency

Performance per watt

  • MIPS/Watt measures computational efficiency for embedded systems
  • FLOPS/Watt evaluates energy efficiency in high-performance computing tasks
  • Locomotion cost metrics (Cost of Transport) quantify efficiency in mobile robots
  • Task-specific energy efficiency metrics (e.g., energy per grasped object)

Energy density considerations

  • Gravimetric energy density (Wh/kg) impacts weight and mobility of robotic systems
  • Volumetric energy density (Wh/L) affects the compactness of energy storage solutions
  • Power density (W/kg or W/L) determines peak performance capabilities
  • Cycle life and degradation factors influence long-term energy efficiency

Sustainability in robot design

  • Life cycle assessment (LCA) evaluates environmental impact throughout a robot's lifespan
  • Recyclability and repairability metrics promote sustainable robotic design
  • Energy payback time measures the time required to offset energy invested in production
  • Embodied energy considerations account for total energy input in robot manufacturing

Key Terms to Review (40)

Adaptive Duty Cycling: Adaptive duty cycling is a power management technique used in battery-operated systems, where the device alternates between active and low-power states based on workload requirements and environmental conditions. This approach helps to optimize power consumption, extending battery life while maintaining the performance necessary for the system's tasks. By dynamically adjusting the duty cycle, devices can efficiently respond to changes in usage patterns, allowing for better energy efficiency and longevity.
Batteries: Batteries are devices that store chemical energy and convert it into electrical energy through electrochemical reactions. They are essential components in various applications, especially in robotics and bioinspired systems, where efficient power management is crucial for optimizing performance and prolonging operational life.
Battery life: Battery life refers to the duration a battery can provide power to a device before it needs recharging or replacement. This term is crucial in the design and performance of various devices, especially in applications where energy efficiency is essential, such as in flying robots and systems that require power consumption optimization. Effective management of battery life can enhance operational efficiency, improve user experience, and extend the overall lifespan of the technology being used.
Bioinspired cooling mechanisms: Bioinspired cooling mechanisms refer to systems and technologies designed to replicate the natural cooling strategies observed in various organisms to enhance thermal management. These mechanisms draw inspiration from biological examples, such as how certain animals regulate their body temperature or how plants dissipate heat, ultimately leading to more efficient cooling solutions that optimize power consumption in devices and systems.
Bioinspired energy systems: Bioinspired energy systems refer to technologies and approaches that draw inspiration from natural processes and organisms to enhance energy efficiency, production, and consumption. By mimicking the mechanisms found in nature, these systems aim to optimize energy use and reduce waste, often leading to sustainable and environmentally friendly solutions. The study of bioinspired energy systems helps in understanding how biological entities efficiently manage energy, which can be leveraged to create innovative technologies.
Biomimetic approaches: Biomimetic approaches involve the design and development of technologies inspired by biological systems and processes found in nature. These strategies aim to emulate the efficiency, functionality, and adaptability of biological organisms to solve complex engineering problems, such as power consumption optimization. By studying how nature operates, engineers can create innovative solutions that reduce energy use and enhance performance in robotic systems.
Brushless dc motors: Brushless DC motors (BLDC) are electric motors that use electronic commutation instead of mechanical brushes to control the flow of current in the motor windings. This design reduces wear and tear, increases efficiency, and enhances performance by allowing precise speed and position control, making them ideal for applications requiring power consumption optimization.
C. L. Stong's Principles: C. L. Stong's Principles refer to a set of guidelines aimed at optimizing power consumption in robotic and bioinspired systems. These principles focus on reducing energy waste and enhancing the efficiency of energy use, which is crucial for the longevity and effectiveness of robotic applications in various fields. Understanding these principles helps engineers and researchers design systems that not only perform better but also minimize their environmental impact.
Compressive Sensing: Compressive sensing is a signal processing technique that enables the reconstruction of a signal from a small number of measurements, leveraging the idea that many signals can be represented with fewer data points due to their inherent sparsity. This method challenges traditional approaches that require sampling at a rate proportional to the signal’s bandwidth and allows for significant reductions in data acquisition and storage requirements, ultimately leading to lower power consumption in systems.
Control Theory: Control theory is a branch of engineering and mathematics that deals with the behavior of dynamic systems. It focuses on designing controllers that manage the behavior of systems to achieve desired outputs. This concept is essential for robotics, where it helps in interpreting sensor data, predicting system responses, managing remote operations, guiding movement through visual input, and optimizing energy use.
Dynamic thermal management: Dynamic thermal management refers to the adaptive strategies and technologies used to control and optimize the thermal conditions within a system, especially in response to varying operational demands. It plays a critical role in ensuring that devices and systems operate efficiently while minimizing energy consumption and preventing overheating. By continuously monitoring temperature and power usage, dynamic thermal management helps in maintaining optimal performance, improving reliability, and extending the lifespan of components.
Dynamic voltage frequency scaling: Dynamic voltage frequency scaling (DVFS) is a power management technique that adjusts the voltage and frequency of a processor in real-time, based on the current workload and performance requirements. This method helps to optimize power consumption by lowering the voltage and frequency during periods of low activity, thereby reducing energy usage while maintaining performance levels when needed. DVFS is essential for enhancing battery life in portable devices and reducing thermal output in various systems.
Dynamic Voltage Scaling: Dynamic voltage scaling (DVS) is a power management technique that adjusts the voltage and frequency of a processor dynamically to optimize power consumption based on the workload. By lowering the voltage during periods of low activity and increasing it when more processing power is needed, DVS helps in minimizing energy usage while maintaining performance levels. This adaptability is crucial in various applications, especially in mobile devices and embedded systems where battery life is critical.
Efficiency vs. Performance: Efficiency refers to the ability of a system or process to achieve maximum output with minimal wasted resources, while performance measures how well a system accomplishes its intended task under specified conditions. In many cases, a system can be efficient but not perform well, or vice versa, depending on various factors like design, resource allocation, and operational context.
Energy density: Energy density is defined as the amount of energy stored in a given volume or mass of a substance. This concept is crucial because it determines how efficiently energy can be stored and utilized in various applications, especially when it comes to powering devices and systems. High energy density materials allow for longer-lasting power supplies in compact forms, which is vital for technologies that demand portability and performance, like batteries and fuel cells.
Energy harvesting: Energy harvesting is the process of capturing and converting ambient energy from the environment into usable electrical energy. This technique is essential for powering low-energy devices, particularly in remote locations where traditional power sources are impractical. By optimizing energy collection methods, systems can be made more efficient, which directly relates to minimizing power consumption.
Energy Management Systems: Energy management systems (EMS) are integrated systems that monitor, control, and optimize energy consumption in various applications, including industrial, commercial, and residential settings. They play a crucial role in improving energy efficiency and reducing costs by analyzing energy usage patterns and implementing strategies to minimize waste.
Energy-aware algorithms: Energy-aware algorithms are computational strategies designed to optimize power consumption while performing tasks, balancing efficiency and performance. These algorithms help extend the lifespan of battery-operated devices, minimize energy waste, and reduce operational costs in various systems. They are increasingly important in the design of embedded systems, robotics, and other technologies where energy resources are limited or critical.
Energy-aware load balancing: Energy-aware load balancing is the strategic distribution of computational workloads across multiple systems to minimize energy consumption while maintaining performance and efficiency. This approach takes into account the energy usage of each node in a computing environment, making adjustments based on current demands and system capabilities. By optimizing how resources are allocated, this method helps reduce overall power consumption and can lead to more sustainable operations in various technological fields.
Energy-efficient algorithms: Energy-efficient algorithms are computational methods designed to minimize energy consumption while performing tasks, particularly in the context of devices with limited power resources. These algorithms focus on optimizing processing time and resource allocation, allowing systems to operate efficiently without compromising performance. In various applications, including robotics and bioinspired systems, these algorithms help extend the life of battery-operated devices and reduce overall operational costs.
Event-driven sensors: Event-driven sensors are types of sensors that operate based on specific events or changes in their environment rather than continuously monitoring. This approach significantly reduces power consumption, as these sensors activate only when triggered by a defined event, allowing them to remain in a low-power state during idle times. By focusing on significant changes, event-driven sensors enhance the efficiency and longevity of battery-operated devices.
Low-power motors and servos: Low-power motors and servos are compact electromechanical devices designed to provide movement while consuming minimal electrical energy. These components are essential in applications where energy efficiency is critical, such as in robotics and bioinspired systems, allowing for prolonged operation without frequent battery changes or overheating issues.
Low-power sensing technologies: Low-power sensing technologies refer to devices and systems designed to operate with minimal energy consumption while still effectively collecting data from their environment. These technologies are crucial for applications such as wireless sensor networks and portable electronic devices, enabling longer battery life and reduced energy costs. The optimization of power consumption in these systems directly influences their performance, reliability, and sustainability.
Maximum power point tracking: Maximum power point tracking (MPPT) is a technique used to optimize the power output of renewable energy systems, such as solar panels and wind turbines, by adjusting their operating conditions to find the maximum available power. This is particularly important in variable environmental conditions, as it ensures that energy systems operate at peak efficiency and deliver the highest possible power to the load or storage system. By continuously monitoring and adjusting the system's parameters, MPPT enhances energy conversion, contributing significantly to power consumption optimization.
Microbial fuel cells: Microbial fuel cells (MFCs) are bioelectrochemical devices that convert organic matter into electrical energy by harnessing the metabolic processes of microorganisms. These systems utilize bacteria to oxidize organic substrates, releasing electrons and protons, which then flow through an external circuit to generate power. MFCs play a crucial role in energy harvesting from waste materials and optimizing power consumption in various applications.
Optimization algorithms: Optimization algorithms are mathematical techniques used to find the best solution or outcome from a set of possible options, often under certain constraints. These algorithms play a crucial role in minimizing or maximizing specific objectives, such as power consumption in various systems, where efficiency and resource management are key considerations.
Passive dynamic walking: Passive dynamic walking refers to a bipedal locomotion strategy that relies on the natural dynamics of the human body and gravity to facilitate movement, minimizing the need for active energy input. This method allows for energy-efficient walking, particularly in robotic systems designed to mimic human gait. By utilizing the potential and kinetic energy during the gait cycle, passive dynamic walkers can achieve stable and efficient locomotion.
Photovoltaic cells: Photovoltaic cells are devices that convert light energy directly into electrical energy through the photovoltaic effect. These cells are crucial for harnessing solar energy, providing a renewable power source that reduces dependency on fossil fuels and minimizes environmental impact. Their ability to generate electricity from sunlight makes them integral in energy harvesting and optimizing power consumption in various applications.
Piezoelectric actuators: Piezoelectric actuators are devices that utilize the piezoelectric effect to convert electrical energy into mechanical motion. These actuators are known for their high precision and fast response times, making them suitable for applications in robotics, medical devices, and various industrial settings. By applying an electric field to piezoelectric materials, they can change shape or size, allowing for controlled movement and force generation.
Power Budgeting: Power budgeting refers to the systematic approach of estimating and allocating power consumption for various components within a system to ensure that energy resources are utilized efficiently. This process is essential for optimizing the performance of robotic and bioinspired systems, as it balances power needs with the limitations of power sources, contributing to overall efficiency and functionality.
Power Gating: Power gating is a technique used in electronic circuits to reduce power consumption by shutting off the power supply to sections of a chip that are not in use. This method allows for significant energy savings, especially in battery-operated devices and systems, by ensuring that components can be turned off when idle, thus optimizing overall power efficiency.
Power Profiling: Power profiling refers to the process of measuring and analyzing the power consumption of a system or device over time to identify patterns and optimize energy usage. This practice helps in understanding how different components contribute to overall power consumption, enabling more efficient designs and strategies for reducing energy costs and extending battery life.
Proton exchange membrane fuel cells: Proton exchange membrane fuel cells (PEMFCs) are a type of fuel cell that converts chemical energy from hydrogen and oxygen directly into electrical energy through electrochemical reactions. This technology utilizes a solid polymer electrolyte membrane to conduct protons while acting as an insulator for electrons, making it efficient and suitable for portable applications.
Shape Memory Alloy Actuators: Shape memory alloy actuators are devices made from materials that can return to a predetermined shape when exposed to a specific temperature change. These actuators leverage the unique properties of shape memory alloys, such as nickel-titanium (Nitinol), which enable them to undergo significant deformation and recovery, making them particularly useful in soft robotics for applications requiring flexibility and adaptability. Their ability to provide motion and force with minimal power consumption connects them to advancements in energy-efficient design in robotic systems.
Solar power: Solar power is the energy harnessed from the sun's rays using technologies like photovoltaic cells and solar thermal systems. This renewable energy source provides a clean alternative to fossil fuels, helping to reduce greenhouse gas emissions and dependency on non-renewable energy sources. With increasing awareness of climate change, optimizing power consumption with solar energy has become essential in various applications, including residential, commercial, and industrial sectors.
Solid oxide fuel cells: Solid oxide fuel cells (SOFCs) are a type of electrochemical cell that converts chemical energy directly into electrical energy through the reaction of a fuel, typically hydrogen or hydrocarbons, with oxygen. SOFCs operate at high temperatures, generally between 600°C to 1,000°C, which allows them to achieve high efficiencies and utilize a variety of fuels, making them an attractive option for power generation and optimization of energy consumption.
Supercapacitors: Supercapacitors are energy storage devices that combine the properties of traditional capacitors and batteries, allowing for rapid charging and discharging while providing high power density. They play a crucial role in power consumption optimization by offering a way to store and release energy quickly, which is essential for applications that require bursts of power without the slow recharge times associated with batteries.
Swarm robotics efficiency: Swarm robotics efficiency refers to the effectiveness and optimization of a group of robots working together to complete tasks, often inspired by the behavior of social insects. This concept emphasizes how individual robots can collaborate to achieve collective goals, minimizing resource use such as power consumption and maximizing task performance. The efficiency in swarm robotics is crucial for applications where energy resources are limited or where prolonged operation is necessary.
Trade-offs: Trade-offs refer to the balance between two competing factors where improving one may lead to a detriment in another. In power consumption optimization, trade-offs often arise when trying to enhance performance, reduce energy use, or lower costs. Understanding these trade-offs is crucial for making informed decisions in the design and operation of robotic systems.
Work of A. Y. Decker: The work of A. Y. Decker refers to significant contributions in understanding and optimizing power consumption in robotic systems. Decker's research primarily focuses on improving the energy efficiency of robotic designs and operations, emphasizing the importance of minimizing energy use without sacrificing performance or functionality. This body of work is essential for advancing sustainable practices in robotics and ensuring that robots can operate efficiently within their energy constraints.
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