[ICRA 24 REVIEW] A Multi-Stable Curved Line Shape Display

This document is structured as follows:

• Meta Information about the Paper (논문 정보)

• Researcher's Affiliation Site (저자 연구실 정보)

• Content for General Readers (일반 독자를 위한 내용)

• Content for Readers Who Want to Know More about the Paper (관련 분야 전문가를 위한 내용)

• Value for HCI(HCI에서의 가치)

• In conclusion (마치며)

let’s start.

Meta Information about the Paper

Law, W. S., Wyetzner, S. D. T., Zhen, R., & Follmer, S. (2024, May). A Multi-Stable Curved Line Shape Display. In 2024 IEEE International Conference on Robotics and Automation (ICRA) (pp. 9696-9703). IEEE.

Video:

Researcher's Affiliation Site

Prof. Sean Follmer

https://shape.stanford.edu/

Content for General Readers

motivation

1. Physical prototyping is important in design, but many shape-changing displays are made of individually actuated rigid bodies, which makes them mechanically complex and unable to form smooth surfaces.

2. The authors propose a curved line display inspired by physical splines as a step toward minimally-actuated, continuous surface displays.

한글 요약:

물리적 프로토타이핑은 디자인에서 중요하지만, 많은 모양 변형 디스플레이는 개별적으로 작동하는 강체로 이루어져 있어 기계적으로 복잡하며 부드러운 표면을 형성할 수 없습니다. 이에 저자들은 물리적 스플라인에서 영감을 받아, 최소한의 구동을 통해 연속적인 표면을 형성할 수 있는 곡선형 디스플레이를 제안합니다

contribution

• Proposed a curved line display inspired by physical splines, providing a significant step toward minimally-actuated, continuous surface displays.

• Designed and built a system that manipulates a flexible rod by controlling rod length, boundary positions, and boundary angles.

• Employed a discrete elastic rods model to determine the actuation strategy for the under-actuated, multi-stable system.

• Developed a novel optimization scheme over circular splines to initialize the simulator.

• Demonstrated the physical display's ability to reliably generate a variety of shapes.

• Simulated a multi-segment version of the curved line display to show scalability.

• Tested the system's loading response to assess its suitability for haptic exploration.

한글요약:

• 물리적 스플라인에서 영감을 받은 곡선형 디스플레이를 제안하여 최소한의 구동으로 연속적인 표면 디스플레이를 향한 중요한 단계 제공.

• 유연한 막대를 조작하는 시스템을 설계하고 구축하여, 막대의 길이, 경계 위치 및 경계 각도를 제어.

• 유연한 막대의 다중 안정성 특성을 활용하기 위해 이산 탄성 막대 모델을 사용하여 구동 전략 결정.

• 원형 스플라인을 기반으로 한 새로운 최적화 기법으로 시뮬레이터 초기화.

• 물리적 디스플레이가 다양한 형태를 안정적으로 생성할 수 있는 능력을 검증.

• 다중 세그먼트 버전의 곡선형 디스플레이를 시뮬레이션하여 확장 가능성을 시연.

• 시스템의 하중 반응을 테스트하여 촉각 탐사에 적합한지 평가.

Content for Readers Who Want to Know More about the Paper

Physical prototyping

• allow multiple users to simultaneously view and interact with a tangible design, from automotive design [1] to architecture [2]

• give a richer impression of a prototype’s aesthetic and function than would be available through a digital image alone, mitigating design fixation [3]

• However such models are often static and must be entirely re-fabricated to reflect iteration

Previous works of shape-changing displays

• Pin displays

  • array of linear actuators that move up and down in concert to discretely approximate 1.5D [4] and 2.5D surfaces [5]–[7].

  • used as a computational design tool [8]

• displays that approximate shapes using an articulated series [9]

• grid of rigid bodies connected by actuated hinges [10]–[12],

limitation in shape-changing displays

• mechanically complex

  • difficult to scale

• only discretely approximate smooth surfaces

  • due to being composed of discrete, rigid bodies

Related works

<continuous surfaces>

• Pin Display Augmentation: The pin display has been enhanced with a spatial low pass filter, allowing a material to stretch over its surface to better display continuous surfaces [5], [17].

  • Limitations: While this method partially smooths the pins, it does not perfectly interpolate a smooth surface, resulting in bumpy artifacts [18].

• Layer Jamming: This approach improves the formable crust display to showcase smoother surfaces by replacing rigid grids with flexible materials [19], [20].

  • Limitations: Although smoother than the pin display, this technique requires selectively locking segments along the surface, which constrains display resolution to the grid size.

• Combination of Rigid and Flexible Materials: Some studies have integrated aspects of both approaches by using rigid actuators to bend, stretch, and twist flexible materials by directly actuating points [21]–[23], or by actuating shape memory alloys embedded in flexible materials [24].

  • Limitations: While these devices can generate continuous surfaces, they are restricted in curvature by the area or elasticity of the flexible material used.

• Compliant Rods: Present a promising alternative to rigid or soft materials by employing two fixed actuators at either end to control a large state space [25]. Previous works in computer graphics have utilized this paradigm as an input method [26], a fabrication tool [27], and a haptic display.

  • Limitations: Although these devices can produce continuous surfaces, they are limited in curvature due to the material's area or elasticity.

=> 이 논문은 “injecting or removing material from a display” 으로 해결 시도

<Shape Generation Challenges>

The accuracy of shape generation in smooth displays presents challenges compared to their discretely actuated counterparts. In cases where devices directly actuate points on flexible materials [21]–[23], although there is positional control over the end effectors of the actuators, these devices do not measure or control the shapes of the intervening flexible material.

=> 이 논문은 인접한 액추에이터 사이의 막대 비선형 변형을 모델링하는 forward solution을 제안

<Multi-Stability and Control>

Understanding multi-stability under specific boundary conditions [14], [28] is crucial, as the system's multi-stability implies that controlling the output shape requires knowledge of how to reach a specific stable state.

=> 이 논문에서 안정 상태를 달성하기 위한 다양한 접근 방식을 탐색하고 다중 안정성에 대한 이해를 향상시킬 것

III. DESIGN OF A MULTI-STABLE CURVED LINE DISPLAY

Mechanical Design

• The display consists of a single segment featuring a flexible rod actuated between two individually operated nodes.

• Controllable dimensions of the system include:

  • Length of the flexible rod between the nodes (L)

  • Height between the nodes (y)

  • Angles of the tangent vectors at each end of the curved line (θ1 and θ2)

• The flexible rack used is the KHK DR1-2000 (Duracon), chosen for ease of actuation, although it is not perfectly elastic.

• The model assumes a perfectly elastic rod with a constant cross-section, while the actual rod is not fully elastic.

• Each node is equipped with three actuated mechanisms:

  • Extrude Mechanism:

    • A locally prismatic joint that allows the flexible rod to move.

    • Controls the length of the rod on either side of the node, affecting the value of L between the two nodes.

  • Biasing Mechanism:

    • A revolute joint that regulates the angle (θi) at which the rod passes through the node, corresponding to the node’s tangent vector (ti).

    • Rigid bearing surfaces above and below the rod constrain a 20 mm section of the rod to the desired angle at the center of rotation for the bias mechanism.

  • Translation Mechanism:

    • A prismatic joint that controls the position of the node along a 20 mm x 20 mm aluminum extrusion, corresponding to y.

    • Nodes are fixed at 500 mm apart horizontally.

Electronics and Communication

• Each node operates as an independent robot, with multiple nodes collaborating simultaneously to actuate the curved line display.

• The system utilizes N20 geared DC motors equipped with magnetic encoders (Adafruit 4641), controlled via a motor driver chip (Texas Instruments DRV8833RTYT).

• The actuated degrees of freedom include:

  • Extrusion

  • Bias adjustment

  • Translation

• A Teensy LC microcontroller manages logic computations and communication.

• The main computer wirelessly transmits pre-defined shape generation instructions to each node using a 2.4 GHz radio chip (nRF24L01+ chip on SparkFun WRL-00691 breakout board).

• The motors, encoders, and wireless communication module are integrated with the microcontroller using embedded electronics on a custom PCB (Bay Area Circuits).

• Each node is regularly polled for state information; once all nodes complete their current tasks, the main computer dispatches the next set of instructions.

IV. FORWARD SOLUTION USING DISCRETE ELASTIC RODS

• Analytical solutions for elastic rods [30], [31] are available but are limited to specific boundary conditions, necessitating numerical models for most practical applications.

• A well-known approach approximates a flexible rod or strip as a series of discrete segments, which is used to describe the positioning of continuous robotic components [32], [33] and estimate the shape of a deformed rod manipulated at its ends [26], [34]–[36].

• However, this method has not yet been integrated into the design of shape-changing displays.

• This paper utilizes the discrete elastic rods method [15], [16], which discretizes Kirchhoff rods and calculates bending, twisting, and stretching energy across discrete segments.

• This choice is supported by the method's physical validation [37] and its ability to accommodate various rod material properties and cross-sectional shapes.

• The paper uses the provided Young’s modulus and density from the manufacturer, along with a rectangular cross-section, to approximate the notched rod in the device.

• The system exhibits multi-stability, characterized by different stable states existing at local minima due to the non-convex nature of the energy landscape of elastic rods.

Mathematical Boundary Conditions

• One module of this paper consists of an elastic strip connected at two points on a vertical frame.

• The boundary conditions of this system include:

  • The relative vertical position (y) of the left and right nodes and the tangent vectors (t1, t2).

  • The arc length (L) of the elastic strip between the nodes.

• These boundary conditions alone do not uniquely determine the final shape of the strip, as multiple stable states exist within the system.

• However, by varying the initial conditions, the solver can be utilized to converge on different final shapes.

• The strip can be approximated as a one-dimensional curve embedded in the frame plane, with endpoints defined as p1 and p2, where the origin is set at p1.

• The vertical coordinate y of p2 represents a degree of freedom, and each endpoint has tangent vectors t1 and t2 expressed as unit vectors.

• Additionally, the length of the injected material, L, is provided.

• Empirical observations indicate that for each set of boundary conditions, there exist at most two stable states, categorized as:

  1. When most of the rod material is above the endpoints.

  2. When most of the rod material is below the endpoints.

• Based on these observations, this paper reduced the infinite-dimensional problem space to a finite number of physically viable solutions using spline integration.

Finding Initializations to the Simulator

• The Kirchhoff model for elastic rods incorporates a term that minimizes geometric curvature to capture rod bending energy [15].

• The desired initial geometry should be smooth and twice differentiable, ensuring that curvature is a defined quantity.

• To describe this potentially complex initial curve, the paper opts to use a spline, allowing for easy editing through control points.

• The splines are based on a C² blending function, adapted from Yuksel et al. [29].

• Advantages of this approach include:

  • Interpolation capabilities, which enable encoding tangent constraints as two points along a vector of infinitesimal length.

  • This circular interpolation results in splines that are close to the final stable shapes they produce.

  • The geometric properties of Kirchhoff rods indicate that minimizing bending energy often corresponds with minimizing curvature inherent in circular splines.

• Each spline consists of five control points: two points on each end represent the endpoints and tangent constraints, while one central point (p) is used to control the end shape.

• The point p is adjusted to both satisfy the arc length constraint and achieve an initialization that closely resembles the final relaxed shape

• Discretizes the spline into n sample points.

• Calculates the edges between sample points.

• Approximates the arc length by summing the lengths of the discrete edges.

• Approximates the curvature by looking at changes in tangent directions between edges.

• Sets up the optimization problem to find the optimal control point p* that minimizes curvature while achieving the desired arc length.

• This optimization problem is solved using automatic differentiation, Newton's method, and line search. The initial value is set to a point slightly offset above and below the midpoint of the boundary points. It typically converges in fewer than 10 iterations.

<result and limitation of the paper>

• The physical display was able to consistently generate a variety of shapes, with an average standard deviation in height of 0.75 mm, which corresponds to 0.47% of the display's maximum vertical range.

• The simulation results matched well with the physical display, with a mean RMSE of 6.68 mm, or 3.85% of the display's maximum vertical range.

• The current system has key limitations, including a lack of tactile stiffness and no sensing for shape snap-through and recovery, requiring open-loop control.

Value for HCI

The key value of this paper to the HCI field is that it presents a novel shape-changing display that can generate smooth, continuous surfaces using a minimally-actuated, multi-stable system. This represents an advancement over previous shape-changing displays that were composed of discrete, rigid elements. The authors' use of a discrete elastic rods model and circular spline optimization to control the multi-stable system is also a technical contribution that could be applicable to other shape-changing interface designs. Overall, this work expands the design space for smooth, reconfigurable physical interfaces that can provide rich, tangible feedback to users.

In conclusion

Reference papers can be found below

https://ieeexplore.ieee.org/document/10610902

If you have any questions, please contact me at the email address below.

ehlkim0215@gmail.com