In robotics, software intelligence has advanced faster than hardware capability. Artificial intelligence can plan, reason, and simulate, but physical execution still depends on motor–gearbox actuators designed decades ago. This imbalance creates a bottleneck: robots think faster than they move.

Adaptive Machines was founded to remove that bottleneck. We develop actuators with Physical Intelligence—hardware that collaborates with physics rather than fighting against it. Our mission is to make robots safer, faster, stronger, and more energy-efficient by embedding adaptability directly into their mechanical core.

The Actuator Bottleneck

Robotic performance today is constrained by hardware not designed for dynamic, variable, or human-centered tasks. Traditional actuators rely on rigid components that waste energy, add inertia, and reduce responsiveness. Each improvement in artificial intelligence or control software eventually collides with these physical limits.

Nature demonstrates a different approach. Muscles and tendons store and release energy and adjust stiffness to balance speed and safety. Adaptive Machines applies these same principles to engineered systems, creating actuators that interact constructively with physics rather than resisting it.

Why This Matters

Robotics is entering a new era. Collaborative and humanoid robots are moving from prototypes to real deployments. Artificial intelligence is no longer the main barrier; execution and hardware are.

Custom-built actuators have shown that improved performance is possible, but they are expensive and platform-specific. Scaling robotics requires standardized adaptive actuators—off-the-shelf components that combine high performance with broad reusability. Adaptive Machines delivers that foundation.

From Research to Scalable Solutions

Adaptive Machines is built on a decade of research in mechanically adaptive robotics and energy-efficient actuation. This work has demonstrated that hardware can embody intelligence—reducing power consumption and improving interaction safety without sacrificing precision.

We transform these insights into deployable technology, bridging the gap between theory, innovation, and industrial application.

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Dynamics is a branch of Mechanics that studies the motion of objects under the influence of forces. It is fundamental to engineering, bridging theoretical principles from physics with practical applications to predict the motion of systems such as rockets, cars, and robots. Introduction to Dynamics is the first course on this topic, studied by engineering, math, and science students.

My Expertise

I specialize in teaching Mechanics, focusing on both theoretical and computational aspects of:

• Newtonian Mechanics: Principles governing motion and forces.
• Lagrangian Mechanics: Energy-based methods for dynamic systems.
• Hamiltonian Mechanics: Advanced formulations that extend dynamics to optimal control.

My goal is to ensure students develop both a solid theoretical foundation and effective problem-solving skills.

Teaching

My teaching focuses on clarity and engagement, helping students navigate complex topics with confidence. Key features include:

• Bite-Sized Video Lectures: Pre-class videos introducing core concepts and examples.
• Interactive Lectures: Expanding on pre-class material with deeper theoretical insights.
• Emphasizing Mathematical Formalism: Leveraging formal methods to overcome the limitations of intuition-based problem-solving.

Why Study Dynamics?

Consider a simple question: If you drop a pen from your desk, what truly determines its trajectory? The intuitive answer might involve gravity, but a rigorous approach demands an understanding of differential equations, constraints, and possibly even perturbation theory. What if the pen is in freefall on the Moon? Or inside a rotating space station? The same fundamental principles govern everything from planetary orbits to the stabilization of legged robots.

This course will challenge you to refine your thinking, stripping away assumptions and replacing them with precise models that describe reality with mathematical accuracy. The tools you develop here will extend far beyond the classroom—whether you are designing autonomous drones, optimizing mechanical systems, or advancing theoretical physics.

Dynamics is not about memorization or following recipes; it is about learning to see structure in motion and gaining the ability to predict and control it. If that is the kind of challenge you are looking for, you are in the right place.

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Optimization and Optimal Control are essential tools for designing systems that operate efficiently while minimizing cost, time, or resources. These methods provide a systematic approach to decision-making in engineering and science, enabling solutions for problems ranging from fuel-efficient spacecraft trajectories to real-time energy optimization in robotics and improving machine learning models. By translating abstract mathematical principles into real-world applications, this course equips you with the ability to bridge theory and practice in optimization.

My Expertise

I specialize in Optimization and Optimal Control, focusing on both theoretical foundations and computational methods related to:

• Non-linear Programming: Techniques for solving static optimization problems—minimizing functions subject to constraints.
• Calculus of Variations: Methods for solving dynamic optimization problems—minimizing functionals subject to constraints.
• Optimal Control:
  • Maximum Principle: A powerful framework to solve optimal control problems and determine feedforward control inputs.
  • Dynamic Programming: A general framework to solve optimal control problems and derive feedback control laws or control policies.

Teaching

I use a teaching approach that makes complex concepts in optimization and control accessible and engaging. My method emphasizes:

• Step-by-Step Analogies: Building from simple, familiar problems like minimizing a quadratic function to more complex problems.
• Interactive Learning: Encouraging active participation, from hands-on MATLAB coding to solving real-world engineering problems.
• Bridging Disciplines: Linking optimization to applications in robotics, aerospace, and mechanics for a holistic understanding.

Why Study Optimization and Optimal Control?

Every engineering challenge ultimately involves making decisions—how to allocate resources, how to design efficient systems, and how to control them in real time. Optimization is the language that enables us to make these decisions systematically.

Consider a simple problem: if you are launching a spacecraft, should you aim for the shortest path or the most energy-efficient trajectory? The naive answer might be to take a direct route, but an optimal control perspective would reveal trade-offs between fuel, time, and orbital mechanics that must be mathematically optimized. The same principles apply whether you are designing an autonomous drone, optimizing neural network hyperparameters, or developing an exoskeleton to enhance human mobility.

Optimization is not about guessing or intuition—it is about constructing solutions with mathematical precision and algorithmic efficiency. If you are interested in developing the skills to systematically tackle the most complex problems in engineering and science, this course will give you the tools to do exactly that.

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Y. Y. Fu, A.U. Kilic and D.J. Braun, Energy Minimization using Custom-Designed Magnetic-Spring Actuators, IEEE International Conference on Intelligent Robots and Systems, pp. 3534-3539, October 14 – 18, Abu Dhabi, United Arab Emirates, 2024.

This paper presents a new actuator design that integrates a conventional motor with a custom rotary magnetic spring producing a non-uniform magnetic field. A computational framework is introduced to tailor the magnetic field for specific oscillatory tasks, minimizing energy consumption. Experiments with a prototype demonstrate significantly lower energy use during repetitive tasks such as pick-and-place or oscillatory limb motions compared to conventional motors.

Why it matters: Many robotic tasks involve oscillatory motion, which is often energy-inefficient with standard actuators. By embedding task-optimized non-uniform magnetic fields into motors, this approach enables substantial energy savings and could improve the efficiency of future robotic systems.

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D. Braun, C. W. Mathews, Method and apparatus for human augmentation and robot actuation, US Patent 17/872,164, 2022.

This patent discloses a Parallel Variable Stiffness Actuator (PVSA) that combines a direct-drive motor with a variable stiffness spring arranged in parallel. The design allows the motor to apply force directly to a load while the spring’s stiffness is modulated independently. The disclosure also describes a resonant energy accumulation method in which spring stiffness is adjusted only when no energy is stored, and the motor applies force in resonance with oscillatory motion to maintain constant amplitude.

Why it matters: Traditional actuators are limited by bandwidth and efficiency trade-offs. This invention enables precise force control, efficient energy storage, and resonance-based energy amplification—all within a compact design. The approach has applications in robotics and wearable devices where adaptable, energy-efficient actuation is essential.

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D. Braun, A. Sutrisno, and T. Zhang, Method and Apparatus for Augmented Locomotion, US Patent 17/127,080, 2020.

This patent discloses apparatuses for augmenting human locomotion using variable stiffness mechanisms that selectively store and release energy generated by human movement. By capturing and releasing this energy at the right time, the devices can provide force and power output that exceeds natural human capability. Applications include compliant mechanisms, artificial limbs, and wearable systems for enhanced mobility.

Why it matters: Human mobility is limited by the natural force and power capacity of muscles. This invention provides a pathway to extend those limits without external power, enabling faster and stronger movement through energy-efficient exoskeletons and assistive devices.

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Robotics is reaching new frontiers, with innovative designs reshaping how machines and humans interact. Mechanically adaptive robotics offers a path to enhancing mobility without relying on external power sources like motors or pneumatic actuators. By focusing on energy-efficient systems inspired by mechanisms like bicycles, this approach integrates programmable springs—mechanical elements with controllable stiffness—to redefine safety, adaptability, and efficiency in both robotic and human applications.

Programmable Springs: A Breakthrough in Mechanical Design

At the core of this research is the concept of programmable springs. These mechanical components allow precise energy storage and release independently of deformation, making them adaptable to various tasks at near-zero energy cost. This innovation eliminates the need for external power while enhancing the capabilities of robots and human-assistive devices. It also enables novel approaches to energy use, such as leveraging resonance-based control to optimize motion and efficiency.

Key Applications of Mechanically Adaptive Robotics

Mechanically adaptive robots have wide-ranging applications, including:

• Assistive Devices for the Elderly: Programmable springs can provide lightweight and efficient mobility assistance, helping older adults move more independently and safely.
• Emergency Response Tools: Robots equipped with these systems can assist first responders in carrying loads, navigating rough terrain, or performing physically demanding tasks.
• Energy-Efficient Transportation: Legged robots with programmable springs could provide sustainable alternatives to bicycles, offering new mobility options in diverse environments.

These examples showcase the potential to create practical, impactful solutions for everyday challenges.

Broader Impacts

This research extends beyond developing better robots—it contributes to advancing mobility, education, and public understanding:

• Redefining Mobility: By combining performance and energy efficiency, mechanically adaptive robotics addresses key challenges in human augmentation and autonomous systems.
• Inspiring Education: The project promotes engineering concepts centered on controlled energy storage and release, encouraging new approaches to mechanical design.
• Engaging the Public: Outreach efforts, including demonstrations and knowledge-sharing, aim to spark curiosity and innovation in robotics and mobility technologies.

Looking Ahead

The findings from this research pave the way for safer, more efficient mobility solutions that address critical needs in healthcare, emergency response, and sustainable transportation. By emphasizing energy efficiency and mechanical adaptability, these systems challenge traditional paradigms in robotics, inspiring innovations that balance practicality and impact.

This work is supported by the National Science Foundation CAREER Award (Award Number 2144551) under the Foundational Robotics Research Program within the Division of Civil, Mechanical, and Manufacturing Innovation.

If this topic resonates with you, I would love to hear your thoughts or discuss potential collaborations. Feel free to reach out and share your perspective.

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Compliant actuation, inspired by biological systems, offers robots mechanical adaptability and energy efficiency, making them suitable for tasks requiring both precision and power. However, controlling robots with compliant actuators is inherently challenging due to the complexity of their dynamics. My research tackled this problem by developing a constrained optimal variable impedance control framework to enable efficient and adaptive robot motion.

Key Contributions to Robotics

• Optimal Variable Impedance Control Framework:
  This framework optimizes robot performance under actuation constraints, balancing precision, energy efficiency, and adaptability. It provides a structured approach for achieving dynamic tasks with compliant actuators.
• Dynamic Motion Demonstration:
  The framework was applied to the DLR David robot, a highly advanced variable impedance system, in a dynamic throwing task akin to javelin throwing. Precise timing and energy-efficient execution were achieved, resulting in human-like throwing motions generated purely through optimization-based control methods, without relying on human data or demonstrations.

This was possible because, despite appearing as an open-loop control on the level of the robot joints, the optimal control formulation leveraged the intrinsic feedback capabilities of compliant actuators to reliably execute highly dynamic motions and achieve significant performance gains.

Recognition from the Field

This body of work was recognized with the 2014 IEEE Transactions on Robotics King-Sun Fu Memorial Best Paper Award, presented annually to the best paper published in IEEE Transactions on Robotics, a leading journal in the field. The award honors contributions that demonstrate technical merit, originality, practical significance, and potential impact on robotics research and applications.

Looking Forward

The insights from this research provide a foundation for addressing challenges in robotics, including dynamic motion control, energy efficiency, and adaptive performance. These principles have broad applications in areas such as assistive robotics, legged locomotion, and industrial automation.

If you are interested in discussing this work further or exploring its applications, feel free to reach out. Collaboration and shared perspectives drive the field forward, enabling new breakthroughs in robotics.

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Robotic intelligence is evolving beyond pre-programmed control, shifting towards systems that learn through real-world experience. A key challenge in this transformation is enabling robots to improve their performance on complex tasks—such as walking or riding a bicycle—without requiring highly accurate mathematical models or vast amounts of training data. This research introduces a novel concept: real-time optimal control for learner-helper robot pairs, where a learner robot refines its abilities through physical experimentation with the assistance of a helper robot. This approach bridges the gap between simulation and reality, unlocking new possibilities for autonomous learning in robotics.

Learner-Helper Pairs: A New Paradigm for Robot Training

At the core of this work is a robotic learning framework inspired by human skill acquisition. Just as a child learning to ride a bicycle benefits from an adult providing balance before riding independently, a learner robot receives structured assistance from a helper. The helper ensures the learner meets the minimum functional threshold—such as preventing a walking robot from falling—while gradually reducing support as learning progresses. This enables robots to refine their movements efficiently through repeated trials, without requiring highly accurate simulations or extensive datasets.

By shifting optimization from precomputed models to real-world experiments, this technique paves the way for new robotic control strategies that are adaptive, data-efficient, and capable of handling complex, unstable systems.

Key Applications of Learner-Helper Robotics

This research has broad applications across robotics and automation, including:

• Industrial Automation: Factory robots could learn tasks directly on the production line, improving efficiency without time-consuming reprogramming.
• Assistive Robotics: Medical robots and prosthetics could optimize their movements by interacting with users rather than relying on predefined control strategies.
• Autonomous Systems: Legged robots and exoskeletons could refine their locomotion in real-world environments, overcoming the limitations of rigid model-based control.

By removing the reliance on high-fidelity models and vast training datasets, this technique accelerates the adoption of intelligent, adaptable robots across industries.

Broader Impacts

Beyond specific applications, this research contributes to multiple domains:

• Bridging the Simulation-Reality Gap: Many control techniques struggle when transitioning from simulations to real-world implementation. The proposed approach ensures that robots optimize performance in real-time, adapting to uncertainties as they learn.
• Strengthening the Economy: Enabling robots to learn autonomously enhances manufacturing efficiency, reduces reliance on labor-intensive programming, and fosters technological innovation.
• Advancing Engineering Education: By integrating concepts from mechanical, electrical, and control engineering, this research promotes interdisciplinary learning and engagement.

Looking Ahead

The development of learner-helper robot pairs marks a step toward next-generation intelligent machines, where robots teach each other, refine their abilities through real-world trials, and adapt to uncertain environments. This work lays the foundation for more capable, autonomous robotic systems, pushing the boundaries of what machines can achieve.

This work was supported by the National Science Foundation Dynamics, Control, and System Diagnostics Program (Grant Number 2029181) under the Directorate for Engineering’s Division of Civil, Mechanical, and Manufacturing Innovation.

If this topic resonates with you, I would love to hear your thoughts or explore potential collaborations. Feel free to reach out and share your perspective.

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Have you ever wondered how much faster humans could run with just a little help from physics?

A new twist on the old idea of spring-driven shoes may hold the answer. By storing and releasing energy during the swing phase of each stride, these wearables offer a fresh way to rethink running, potentially achieving speeds far beyond what is possible today. This concept is explored in my work, “How to Run 50% Faster Without External Energy“, published in Science Advances. The study explains how unpowered, spring-driven devices, such as robot boots, can enhance human locomotion by offering mechanical advantages similar to those of a bicycle.

The Skeptics’ Guide to the Universe hosted an engaging discussion about this work, delving into the science behind spring-driven wearables and the potential they hold for shaping the future of human-powered mobility. Listen to the panel’s insights in Episode #776:

The Physics Behind Spring-Driven Devices

The simplest model of these wearable devices is a variable-stiffness springs which stores energy while the leg is airborne and release it upon foot contact. This approach eliminates the “dead time” during a runner’s stride, enabling continuous energy use and significantly boosting efficiency.

Performance Potential

Physics suggests that speeds of up to forty-four miles per hour—comparable to top cycling speeds—are achievable under ideal conditions. Even practical designs could enable speeds of forty miles per hour, representing a fifty percent increase over the current limits of unassisted human running.

Applications

Potential use cases include:

• Sports: Enhancing athletic performance and creating opportunities for new competitive events.
• Emergency Response: Rapid mobility for law enforcement, search and rescue missions.

The reliance on mechanical systems rather than external power sources makes these devices especially suited for off-grid or resource-limited scenarios, while also supporting the goal of sustainable transport.

Challenges to Overcome

Key challenges include:

• Maintaining stability at high speeds.
• Minimizing risks of injury, such as strain or falls.
• Helping users adapt to the new movement mechanics required by the device.

Similar challenges were faced during the development of the bicycle. Early designs struggled with stability, safety, and usability before evolving into the efficient and widely used vehicles we know today.

Redefining Human Potential

Over the past century, technological advancements have revolutionized athletic performance. Innovations such as lightweight running shoes, aerodynamic swimsuits, and synthetic track surfaces have consistently pushed the boundaries of what athletes can achieve. Spring-driven devices may represent the next leap forward, offering unprecedented possibilities in speed and efficiency.

As we have seen in the evolution of the Olympic Games, technology does more than enhance performance—it challenges us to rethink the limits of human potential. Devices like these could one day become a standard part of athletic competition or recreational activities, paving the way for a future where humans achieve feats once thought impossible.

What are your thoughts on the future of spring-driven running devices? Could they redefine athletic performance and human mobility?

I would love to hear your perspectives—feel free to comment below or reach out if you are interested in discussing this further.

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Welcome to the 19th IEEE/RAS-EMBS International Conference on Rehabilitation Robotics (ICORR 2025), the biannual conference on theoretical and experimental issues in the fields of Rehabilitation Robotics and Neuroscience. ICORR covers several disciplines with both theoretical and experimental challenges in robotics, control engineering, and neuroscience applied to healthcare. Focuses include cutting edge solutions to boost the rehabilitation process, providing robotic assistance to address and speed motor recovery, and trying to unveil mechanisms underlying brain plasticity. Enabling better societal inclusion, as well as improving independence and quality of life, are the main goals we aim to achieve, with the purpose of providing health systems with technological instruments to assist human beings in prevention, diagnosis, rehabilitation, and personal assistance.

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