Lego-Like Stiffness Configuration of Planar Compliant Modules for Task-Specific Flexible Interfaces
Authors: Siyue Yao, Xiaochi Xie, Shixuan Zhao, Yutong Li, Hao Li, Mark R. Cutkosky, Genliang Chen
Organizations: State Key Laboratory of Mechanical Systems and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China · Department of Mechanical Engineering, Stanford University, USA · Shanghai Key Laboratory of Intelligent Robotics; META Robotics Institute, Shanghai Jiao Tong University, Shanghai 200240, China · META Robotics Institute, Shanghai 200240, China
Compliant mechanisms provide compact and intrinsic structural compliance for regulating physical interactions between mechanisms and environments. However, different tasks demand distinct stiffness characteristics, often requiring task-specific optimization and redesign due to limited geometric design space and inherent coupling among multiple stiffness components. This paper presents a Lego-like stiffness configuration approach using stackable planar compliant modules. Three complementary module geometries are introduced, with their stiffness characteristics further regulated through beam width, plate thickness, and module orientation. A unified stiffness model is established for quantitative analysis of individual and composed modules. Further, a two-stage optimization method is presented to achieve desired stiffness profiles, combining a genetic algorithm for configuration and sequential quadratic programming for parameter refinement. Experimental verification shows deviations below 6.5% for simulated stiffness. A flexible wrist is further developed as a representative implementation, exhibiting distinct compliant and dynamic responses under different stiffness characteristics. An optimized modular composition realizes prescribed stiffness values and maintains compliant obstacle interaction during high-speed motion at 1 m/s, with a maximum tested angular compliance of approximately 15∘. The proposed framework provides a systematic approach for constructing flexible interfaces with task-specific stiffness characteristics.
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Fig. 1: Overview of the proposed Lego-like stiffness configuration framework. (A) Different tasks demand distinct stiffness requirements, especially differing along task and other directions. (B) Stiffness configuration through optimization using parallel composition of planar compliant modules. (C) Demonstrative flexible wrist implementation with desired stiffness.
Fig. 2: Planar compliant module design. (A) Several types of modules with different geometries and complementary stiffness characteristics. (B) Radar plot of normalized stiffness characteristics ( kri∗=5⋅kri⋅R−2,i∈{x,y,z} ) of modules with different geometries, widths, and thicknesses. (C) Discretization-based stiffness modeling method for one chain.
Fig. 3: Variance of principal stiffness components with respect to the (A) plate thickness t and (B) chain width w for modules with type-I geometry.
Fig. 4: Optimization of module combination for stiffness configuration. (A) Flowchart of the two-stage strategy for solving the optimization design problem. (B) Stiffness radar plots of optimal results under different requirements using a same scale. (i) Given target stiffness components. (ii) Requiring higher rotational stiffness and lower translational stiffness. (iii) Requiring a higher kdy and lower the remaining components other than kdx .
Fig. 5: Stiffness validation using a Type-I module. (A) Experimental setup. (B) Measurement configurations for the six principal stiffness components.
Fig. 6: Experimental stiffness results and comparison with the simulated model. (A) Force-displacement curves and linear fitting near the unloaded configuration. (B) Comparison between experimentally identified and simulated stiffness components. (C) Radar plot of relative errors of the six principal stiffness components.
Fig. 7: Demonstration of task-dependent contact responses using two compliant wrist configurations. (A) Flexible wrist setup and two compliant module configurations with their corresponding stiffness characteristics. (B) Low rotational stiffness enables the wrist to accommodate the obstacle after contact. (C) Low translational stiffness enables initial compliance after contact, whereas high rotational stiffness eventually tips the obstacle.
Fig. 8: Stiffness configuration and experimental evaluation of the optimized flexible wrist. (A) Optimized stiffness characteristics and corresponding modular composition. (B) Compliance and dynamic performance when interacting with an obstacle at high-speed.
The paper proposes a robot-agnostic compliant-control framework that extends the ROS control ecosystem with standardized joint and Cartesian command interfaces. It addresses a key limitation of existing control software: no reusable infrastructure for implementing compliant-control algorithms across different manipulators while preserving a common interface to higher-level applications. A plugin-based architecture separates controller infrastructure from control-law implementation. Generic wrappers use existing hardware abstractions to interface with different manipulators, while runtime-loaded plugins implement only the control law. Command interfaces support joint- and Cartesian-space references, stiffness and damping gains, nullspace targets, and feedforward terms, enabling variable impedance and diverse compliant-control formulations. Robot kinematics and dynamics are computed from URDF models using Pinocchio. The architecture facilitates the development of compliant-control strategies and enables the same implementation to be deployed across platforms unchanged. The complete framework, including reference controllers, high-level task interfaces, and example configurations for various manipulators, is open-sourced. The reference Cartesian impedance controller supports task-dependent compliance by rotating translational and rotational stiffness and damping, allowing the principal compliance directions to be updated online according to local task geometry rather than remaining fixed in the robot base or TCP frame. This is particularly important in contact-rich manipulation, where the desired directions of motion, constraints, and compliance directions may vary throughout task execution. Real-robot experiments demonstrate task-dependent compliance in contact-rich manipulation, while simulations show portability across manipulators with distinct kinematic and dynamic characteristics.
Mihael Simonič, Xiaocong Li
College of Information Science and Technology, Eastern Institute of Technology, Ningbo, Ningbo 315200, China · Zhejiang Key Laboratory of Industrial Intelligence and Digital Twin, Eastern Institute of Technology, Ningbo, Ningbo 315200, China
Realistic palpation training requires reliable rendering of soft tissue stiffness changes in real time, which is difficult to achieve with conventional simulators. This paper presents a compact, variable-stiffness tactile interface (VSTaI) based on vacuum-induced jamming of 3D-printed structured fabrics. A vacuum-sealed fabric layer is sandwiched between two silicone layers, and stiffness is tuned by regulating internal pressure. Four fabric patterns with different geometric parameters were fabricated and evaluated using force-indentation tests under atmospheric and vacuum conditions. Across the tested pattern and geometry combinations, vacuum jamming increased stiffness significantly, producing an effective modulus from sub-megapascal to megapascal levels. Specifically, one configuration exhibited a stiffness increase of up to 140% under the jammed state. Circular chainmail patterns provided the most spatially uniform distribution of tactile stiffness, while denser geometries reached higher peak stiffness. VSTaI was also shown to exhibit excellent conformability to the underlying geometry. These results support structured-fabric jamming as a practical approach for shape-conformable, tunable-stiffness displays aimed at physical examination training.
Yiting Mo, Xinyuan Mao, Jashan Preet Singh +1
Duke-NUS Medical School, National University of Singapore, Singapore · College of Design and Engineering, National University of Singapore, Singapore · Mechanobiology Institute, National University of Singapore, Singapore +1
Humanoids are increasingly capable of tracking complex whole-body motions, but physical interaction introduces a different challenge. When a robot makes contact with a person or the environment, it needs to respond to external forces while preserving the motion needed for the task. This response can vary across directions in the end-effectors and on the body. For example, an end effector may need to accommodate contact force in one direction while maintaining motion accuracy in another, while the robot body may resist an external force or move with it. We present a compliance framework for humanoid loco-manipulation that combines directional and tunable end-effector (EE) compliance with selectable root compliance for external force rejection or force following. A hierarchical reinforcement learning controller modulates a fixed whole-body tracking policy through high-level EE and root commands, while interaction forces are estimated from proprioceptive history. Our simulation and real-world experiments on a humanoid demonstrate directional stiffness control, online stiffness adjustment, distinct root compliance, compliant manipulation, and collaborative carrying.
Xinyuan Luo, Chunyuan Yang, Boyuan Chen +1
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA