Keita Sugibayashi, Eiji Konaka* (Meijo Univ. Japan) Design of three-dimensional binary manipulators for pick-and-place task avoiding obstacles This research is an extension of the paper “Design of three-dimensional binary manipulators based on the KS statistic and maximum empty circles,” presented in IECON2023. IECON2024, 3-6 NOV. CHICAGO, USA.

Outline Background: Binary Manipulator Problem setup: task and performance index Summary of proposed method Numerical result and conclusion IECON2024, 3-6 NOV. CHICAGO, USA.

What is “Binary manipulator” ? ⚫Binary Manipulator consists of binary modules ⚫Binary module consists of binary actuator ⚫Binary actuator: its state is ON/OFF ⚫E.g. expand/contract ⚫Pros: lightweight, low-bit communication ⚫Design variable: ON/OFF length 𝑑max , 𝑑min ⚫Design objective: Pick-and-place avoiding obstacles One binary module ON:𝑑max ON:𝑑max OFF:𝑑min IECON2024, 3-6 NOV. CHICAGO, USA.

What is “Binary manipulator” ? ⚫Binary Manipulator consists of binary modules ⚫Binary module consists of binary actuator ⚫Binary actuator: its state is ON/OFF ⚫E.g. expand/contract ⚫Pros: lightweight, low-bit communication ⚫Design variable: ON/OFF length 𝑑max , 𝑑min ⚫Design objective: Pick-and-place avoiding obstacles IECON2024, 3-6 NOV. CHICAGO, USA.

What is “Binary manipulator” ? ⚫Binary Manipulator consists of binary modules ⚫Binary module consists of binary actuator ⚫Binary actuator: its state is ON/OFF ⚫E.g. expand/contract ⚫Pros: lightweight, low-bit communication ⚫Design variable: ON/OFF length 𝑑max , 𝑑min ⚫Design objective: Pick-and-place avoiding obstacles Before designing ON/OFF length Reachable points IECON2024, 3-6 NOV. CHICAGO, USA.

Outline Background: Binary Manipulator Problem setup: task and performance index Summary of proposed method Numerical result and conclusion IECON2024, 3-6 NOV. CHICAGO, USA.

Task: pick-and-place ⚫Task description: Pick and place workpieces from Working Areas 𝑊1 to 𝑊2 through Path Area 𝑃 avoiding obstacles ⚫Design problem: Given 𝑊1 , 𝑊2 and 𝑃, find the optimal 𝑑min , 𝑑max the minimizes the performance index 𝐽. ⚫𝐽 consists of: ⚫End-effecter positioning accuracy in 𝑊. ⚫Path existence in 𝑃. 𝑊1 𝑊2 𝑃 IECON2024, 3-6 NOV. CHICAGO, USA.

𝑊1 𝑊2 𝑃 Performance index ⚫The set of reachable points of end effecter should have … ⚫High density and small “hole” in working areas: Maximum Empty Circle (MEC) ⚫Uniformly distributed in working areas: Kolmogorov-Smirnov (KS) statistic IECON2024, 3-6 NOV. CHICAGO, USA.

Performance index: Maximum Empty Circle (MEC) ⚫High density and small “hole” in working areas: Maximum Empty Circle (MEC) large small low high MEC radius density Small MEC radius = small positioning error & high density IECON2024, 3-6 NOV. CHICAGO, USA.

Performance index: KS-statistic ⚫KS-statistic measures distance from uniform distribution • 𝐺(𝑥): Hypothetical CDF(Cumulative distribution function) • CDF of uniform distribution • ෠ 𝐹(𝑥): Empirical CDF • CDF of reachable points of the manipulator 𝐷𝑥 = max 𝑥 ෠ 𝐹 𝑥 − 𝐺(𝑥) One-dimensional example 𝐷𝑥 IECON2024, 3-6 NOV. CHICAGO, USA.

Performance index 𝑤1 , 𝑤2 > 0 𝑤1 +𝑤2 = 1 𝐽 = 𝑤1 × 𝑟𝑚𝑒𝑐 + 𝑤2 × 𝐷 Radius of MEC KS-Statistic • Small MEC = high density • Small KS statistic = close to uniform distribution • Design of binary manipulator = minimize J IECON2024, 3-6 NOV. CHICAGO, USA.

Outline Background: Binary Manipulator Problem setup: task and performance index Summary of proposed method Numerical result and conclusion IECON2024, 3-6 NOV. CHICAGO, USA.

Proposed method: GA-based stochastic optimization ⚫Genetic Algorithm (GA) ⚫Gene: ON/OFF length of actuators ⚫Standard Elite strategy, crossover, mutation process ∆𝒅 = ∆𝑑1 , ⋯ ∆𝑑𝑖 , ⋯ ∆𝑑6×𝐵 𝑇 Genes in one gen. Elite strategy & feasibility check Crossover & mutation Next gen. IECON2024, 3-6 NOV. CHICAGO, USA.

𝑊1 𝑊2 𝑃 GA process: elite strategy and feasibility check ⚫Calculate reachable points and performance index for each gene (ON/OFF length) ⚫Feasibility check: if no path from 𝑊1 to 𝑊2 through 𝑃, remove the gene. ⚫Elite strategy: Genes with small 𝐽 are selected with high probability. Genes in one gen. Elite strategy & feasibility check IECON2024, 3-6 NOV. CHICAGO, USA.

GA process: crossover and mutation ⚫Crossover: select two parents, and mix their genes ⚫Mutation: randomly changes the value of genes Genes in one gen. Elite strategy & feasibility check Crossover & mutation Next gen. Repeat the process until we can find good design IECON2024, 3-6 NOV. CHICAGO, USA.

Outline Background: Binary Manipulator Problem setup: task and performance index Summary of proposed method Numerical result and conclusion IECON2024, 3-6 NOV. CHICAGO, USA.

Numerical example Parameters used in GA process ⚫Initial design Problem: Design ON/OFF lengths for a binary manipulator with 4 modules Symbol Value Weight (𝑤1 , 𝑤2 ) (0.75,0.25) Population 𝐼 50 Mutation ratio 𝑚 0.15 Generations 𝐺 500 Work areas Path area IECON2024, 3-6 NOV. CHICAGO, USA.

Main result: design process and result REACHABLE POINTS ACTUATOR LENGTHS IECON2024, 3-6 NOV. CHICAGO, USA.

Main result: design process and result REACHABLE POINTS (DESIGNED) ACTUATOR LENGTHS (DESIGNED) IECON2024, 3-6 NOV. CHICAGO, USA.

Main result: pick-and-place trajectory ⚫The proposed method realizes pick- and-place between work areas through path area (avoiding obstacle) We can verify that … ⚫Proposed performance index design is GOOD ⚫Proposed optimization algorithm (GA) is GOOD IECON2024, 3-6 NOV. CHICAGO, USA.