8.2 Underactuated mechanisms

Underactuated mechanisms are a game-changer in soft robotics. They use fewer actuators than degrees of freedom, allowing robots to adapt to various tasks and environments. This approach offers benefits like simplified control and reduced complexity.

These mechanisms come in two main flavors: tendon-driven and fluid-driven. Each type has its own perks and challenges. Understanding the pros and cons of underactuated systems is key to designing effective soft robots for real-world applications.

Types of underactuated mechanisms

• Underactuated mechanisms are robotic systems with fewer actuators than degrees of freedom, enabling them to adapt to various tasks and environments in soft robotics applications
• The two main categories of underactuated mechanisms are tendon-driven and fluid-driven systems, each with distinct advantages and challenges

Tendon-driven vs fluid-driven

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  Frontiers | SIMBA: Tendon-Driven Modular Continuum Arm with Soft Reconfigurable Gripper View original

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• Tendon-driven underactuated mechanisms use cables or tendons to transmit forces from actuators to the robot's links
  • Allows for remote actuation and reduces the weight of the robot's distal end
  • Enables the creation of complex, multi-degree-of-freedom systems with a minimal number of actuators (robotic hands)
• Fluid-driven underactuated mechanisms rely on pressurized fluids (pneumatics or hydraulics) to actuate the robot's links
  • Provides inherent compliance and adaptability to external forces and obstacles
  • Allows for the creation of soft, continuum-like structures with infinite degrees of freedom (soft grippers)

Compliant vs rigid links

• Underactuated mechanisms can be designed with either compliant or rigid links, depending on the desired performance characteristics
• Compliant links, often made from soft, elastomeric materials, provide passive adaptability and conformability to objects and environments
  • Enables safe interaction with delicate objects and human users (soft exosuits)
  • Allows for the creation of highly deformable and morphable structures (origami-inspired robots)
• Rigid links, typically made from stiff materials like metals or plastics, offer higher precision and force transmission capabilities
  • Enables the creation of underactuated mechanisms with well-defined kinematics and dynamics (underactuated robotic fingers)
  • Allows for the integration of traditional sensing and control techniques (underactuated parallel robots)

Advantages of underactuation

• Underactuation offers several key benefits in soft robotics, including adaptability, simplified control, and reduced system complexity
• These advantages make underactuated mechanisms well-suited for applications involving unstructured environments, human interaction, and resource-constrained scenarios

Adaptability to unstructured environments

• Underactuated mechanisms can passively adapt to uncertainties and variations in their surroundings without requiring explicit control or sensing
  • Enables robust grasping and manipulation of objects with unknown shapes and properties
  • Allows for traversal of irregular terrains and obstacles in locomotion tasks (underactuated legged robots)
• The inherent compliance of underactuated systems helps to mitigate the effects of external disturbances and impacts
  • Prevents damage to the robot and its environment during collisions or unintended contacts
  • Enables safe and stable interactions with human users in collaborative settings (assistive robots)

Simplified control strategies

• The reduced number of actuators in underactuated mechanisms simplifies the control problem, as fewer degrees of freedom need to be explicitly controlled
• Underactuation allows for the exploitation of natural dynamics and passive mechanical properties to achieve desired behaviors
  • Enables the creation of energy-efficient and self-stabilizing locomotion gaits (underactuated bipedal robots)
  • Allows for the design of compliant grasping strategies that automatically adapt to object shapes (underactuated robotic hands)
• The simplified control schemes of underactuated systems reduce the computational burden and latency associated with high-dimensional control problems
  • Enables real-time, onboard control implementations with limited computing resources
  • Allows for the deployment of underactuated robots in resource-constrained environments (space exploration)

Reduced system complexity

• Underactuation reduces the overall complexity of robotic systems by minimizing the number of actuators, sensors, and control components required
• The reduced mechanical complexity of underactuated mechanisms leads to lower manufacturing costs and increased robustness
  • Enables the creation of affordable and accessible soft robotic devices for various applications
  • Allows for the design of modular and reconfigurable underactuated systems (underactuated modular robots)
• The decreased system complexity also facilitates maintenance, repair, and troubleshooting of underactuated robots
  • Reduces downtime and operational costs associated with complex, fully-actuated systems
  • Enables the deployment of underactuated robots in remote or hazardous environments (underwater exploration)

Challenges in underactuated design

• Despite their advantages, underactuated mechanisms pose several design challenges that must be addressed to ensure effective performance in soft robotics applications
• These challenges include limited controllability, nonlinear dynamics, and coupling between degrees of freedom

Limited controllability

• The reduced number of actuators in underactuated systems limits the direct controllability of individual degrees of freedom
  • Requires the development of specialized control strategies that exploit the system's natural dynamics and constraints
  • Necessitates the use of redundancy resolution techniques to achieve desired end-effector poses (underactuated robotic arms)
• The limited controllability of underactuated mechanisms can lead to reduced precision and accuracy in certain tasks
  • Requires the integration of additional sensing and feedback control to compensate for the lack of direct actuation
  • Necessitates the development of robust control algorithms that can handle uncertainties and disturbances (underactuated aerial vehicles)

Nonlinear dynamics

• Underactuated mechanisms often exhibit highly nonlinear dynamics due to the coupling between actuated and unactuated degrees of freedom
  • Requires the development of advanced modeling and simulation techniques to capture the system's complex behavior
  • Necessitates the use of nonlinear control methods to ensure stability and performance (underactuated marine robots)
• The nonlinear dynamics of underactuated systems can lead to unexpected or emergent behaviors, such as self-stabilization or chaos
  • Requires the careful design and analysis of the system's parameters and initial conditions to avoid undesirable outcomes
  • Necessitates the development of robust control strategies that can handle the system's inherent nonlinearities (underactuated walking robots)

Coupling between degrees of freedom

• The underactuation of certain degrees of freedom leads to coupling between the actuated and unactuated joints, which can complicate the system's control and behavior
  • Requires the consideration of the system's kinematic and dynamic constraints in the design and control process
  • Necessitates the development of decoupling strategies or the exploitation of the coupling for desired behaviors (underactuated robotic hands)
• The coupling between degrees of freedom can lead to unintended motions or instabilities in the system
  • Requires the careful design of the system's mechanical structure and actuation scheme to minimize undesirable coupling effects
  • Necessitates the development of robust control algorithms that can compensate for the coupled dynamics (underactuated legged robots)

Modeling underactuated systems

• Accurate modeling of underactuated mechanisms is crucial for understanding their behavior, designing control strategies, and optimizing their performance in soft robotics applications
• Key aspects of modeling underactuated systems include the choice of kinematic or dynamic models, the Lagrangian formulation, and the Euler-Lagrange equations

Kinematic vs dynamic models

• Kinematic models describe the geometric relationships between the system's degrees of freedom, without considering the forces and torques acting on the system
  • Enables the analysis of the system's workspace, reachability, and motion planning
  • Allows for the development of inverse kinematics solutions for underactuated mechanisms (underactuated robotic fingers)
• Dynamic models capture the system's behavior under the influence of forces, torques, and inertial effects
  • Enables the analysis of the system's stability, controllability, and energy efficiency
  • Allows for the development of forward dynamics simulations and model-based control strategies (underactuated legged robots)

Lagrangian formulation

• The Lagrangian formulation is a powerful tool for deriving the equations of motion of underactuated systems using generalized coordinates and energies
• The Lagrangian is defined as the difference between the system's kinetic and potential energies, expressed in terms of generalized coordinates and velocities
  • Enables the systematic derivation of the system's dynamics, considering the effects of constraints and external forces
  • Allows for the identification of conserved quantities and symmetries in the system's behavior (underactuated pendulum systems)
• The Lagrangian formulation provides a unified framework for modeling underactuated systems with various types of actuators and constraints
  • Enables the modeling of tendon-driven and fluid-driven underactuated mechanisms using the same mathematical principles
  • Allows for the incorporation of compliant elements and nonlinear material properties in the system's dynamics (underactuated soft robots)

Euler-Lagrange equations

• The Euler-Lagrange equations are derived from the Lagrangian formulation and describe the system's dynamics in terms of generalized coordinates, forces, and torques
• The Euler-Lagrange equations are obtained by applying the principle of least action to the Lagrangian, resulting in a set of second-order differential equations
  • Enables the analysis of the system's equilibrium points, stability, and controllability
  • Allows for the development of model-based control strategies and trajectory optimization techniques (underactuated aerial vehicles)
• The Euler-Lagrange equations can be extended to include the effects of dissipative forces, such as friction and damping, using the Rayleigh dissipation function
  • Enables the modeling of realistic energy dissipation mechanisms in underactuated systems
  • Allows for the analysis of the system's energy efficiency and the design of energy-optimal control strategies (underactuated underwater robots)

Control strategies for underactuation

• Controlling underactuated mechanisms requires specialized strategies that address the challenges of limited controllability, nonlinear dynamics, and coupling between degrees of freedom
• Key control approaches for underactuated systems include open-loop and closed-loop control, feedforward and feedback control, and optimal control techniques

Open-loop vs closed-loop control

• Open-loop control strategies generate control inputs based on a predefined model or trajectory, without using feedback from the system's sensors
  • Enables the execution of fast and precise motions in the absence of external disturbances or uncertainties
  • Allows for the design of energy-efficient control sequences that exploit the system's natural dynamics (underactuated throwing robots)
• Closed-loop control strategies use feedback from the system's sensors to continuously update the control inputs based on the current state and desired behavior
  • Enables the compensation of external disturbances, model uncertainties, and nonlinear effects
  • Allows for the stabilization of unstable equilibrium points and the tracking of desired trajectories (underactuated balancing robots)

Feedforward vs feedback control

• Feedforward control strategies generate control inputs based on a model of the system's dynamics and the desired motion, without using real-time feedback
  • Enables the compensation of known disturbances and the execution of precise, high-speed motions
  • Allows for the design of energy-optimal control sequences that minimize the required control effort (underactuated manipulators)
• Feedback control strategies use real-time measurements of the system's state to generate control inputs that minimize the error between the current and desired behavior
  • Enables the rejection of unknown disturbances and the compensation of model uncertainties and nonlinearities
  • Allows for the stabilization of the system around desired equilibrium points or trajectories (underactuated legged robots)

Optimal control techniques

• Optimal control techniques aim to find control strategies that minimize a predefined cost function, such as energy consumption, time, or tracking error, while satisfying the system's dynamics and constraints
• Trajectory optimization methods, such as direct collocation or differential dynamic programming, discretize the control and state trajectories and solve a nonlinear programming problem
  • Enables the generation of energy-efficient and time-optimal motion plans for underactuated systems
  • Allows for the incorporation of state and control constraints, as well as nonlinear dynamics and cost functions (underactuated aerial vehicles)
• Model predictive control (MPC) techniques solve a finite-horizon optimal control problem in real-time, using the current state as the initial condition and applying the first step of the optimized control sequence
  • Enables the handling of constraints, disturbances, and model uncertainties in a receding-horizon fashion
  • Allows for the stabilization and tracking of desired trajectories in the presence of nonlinear dynamics and coupling effects (underactuated marine robots)

Applications of underactuated mechanisms

• Underactuated mechanisms find numerous applications in soft robotics, leveraging their adaptability, simplified control, and reduced complexity to enable novel functionalities and improved performance
• Key application areas for underactuated systems include grasping and manipulation, locomotion and mobility, and soft wearable devices

Grasping and manipulation

• Underactuated robotic hands and grippers can adapt to a wide range of object shapes and sizes without requiring complex control strategies or precise sensing
  • Enables robust and versatile grasping of unknown objects in unstructured environments (underactuated adaptive grippers)
  • Allows for the manipulation of delicate or deformable objects, such as food items or biological tissues (underactuated compliant hands)
• Underactuated manipulators can exploit their passive compliance and natural dynamics to achieve energy-efficient and safe interactions with the environment
  • Enables the execution of dexterous manipulation tasks, such as in-hand manipulation or tool use (underactuated anthropomorphic hands)
  • Allows for the development of collaborative robots that can safely operate in close proximity to human workers (underactuated cobot arms)

Locomotion and mobility

• Underactuated legged robots can achieve stable and efficient locomotion gaits by exploiting their natural dynamics and passive mechanical properties
  • Enables the traversal of irregular terrains and the navigation of cluttered environments (underactuated bipedal robots)
  • Allows for the development of energy-efficient and self-stabilizing locomotion strategies (underactuated quadrupedal robots)
• Underactuated aerial and aquatic vehicles can achieve agile and maneuverable motion by leveraging their inherent stability and control properties
  • Enables the execution of complex flight maneuvers, such as perching or grasping (underactuated aerial manipulators)
  • Allows for the exploration and monitoring of underwater environments with minimal energy consumption (underactuated underwater gliders)

Soft wearable devices

• Underactuated soft exosuits and assistive devices can provide adaptive support and assistance to human users without restricting their natural movements
  • Enables the development of comfortable and unobtrusive wearable robots for rehabilitation or performance augmentation (underactuated soft exoskeletons)
  • Allows for the creation of personalized and responsive assistive devices that adapt to the user's needs and preferences (underactuated soft orthotics)
• Underactuated soft haptic interfaces can provide realistic and immersive tactile feedback to users in virtual reality or teleoperation scenarios
  • Enables the simulation of complex object properties, such as texture, stiffness, and temperature (underactuated soft haptic gloves)
  • Allows for the development of intuitive and natural human-robot interaction modalities (underactuated soft haptic displays)

Design principles for underactuation

• Designing effective underactuated mechanisms for soft robotics applications requires careful consideration of material properties, geometric design, and actuation and sensing integration
• Key design principles for underactuated systems include material selection and properties, geometric design considerations, and actuation and sensing integration

Material selection and properties

• The choice of materials for underactuated mechanisms significantly influences their performance, compliance, and durability
• Soft, elastomeric materials, such as silicone rubbers or thermoplastic elastomers, provide inherent compliance and adaptability
  • Enables the creation of highly deformable and conformable structures that can safely interact with the environment (soft pneumatic actuators)
  • Allows for the design of mechanisms with tunable stiffness and damping properties (variable stiffness actuators)
• Rigid materials, such as metals or high-performance polymers, offer high strength and precision but may require additional compliant elements for underactuation
  • Enables the creation of underactuated mechanisms with well-defined kinematics and load-bearing capabilities (underactuated robotic fingers)
  • Allows for the integration of traditional manufacturing techniques and off-the-shelf components (underactuated modular robots)

Geometric design considerations

• The geometric design of underactuated mechanisms plays a crucial role in determining their kinematics, dynamics, and functionality
• Topology optimization techniques can be used to design underactuated structures with optimized compliance, stiffness, and load distribution
  • Enables the creation of lightweight and efficient underactuated mechanisms with reduced material usage (topology-optimized soft grippers)
  • Allows for the design of mechanisms with tailored deformation modes and force transmission characteristics (underactuated compliant transmissions)
• Bio-inspired design principles, such as those based on animal morphology or plant structures, can inform the development of underactuated mechanisms with enhanced performance and adaptability
  • Enables the creation of underactuated robots with efficient locomotion gaits and grasping strategies (underactuated bio-inspired hands)
  • Allows for the design of mechanisms with self-stabilizing and self-organizing properties (underactuated bio-inspired robots)

Actuation and sensing integration

• The integration of actuation and sensing components into underactuated mechanisms is essential for their control and performance
• Tendon-driven actuation, using cables or artificial muscles, allows for remote actuation and reduced distal mass
  • Enables the creation of underactuated mechanisms with high dexterity and force transmission capabilities (