matlab expo pub - mathworks · matlab expo 2016 8 joint range of motion [deg] max. torque [nm] hip...
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ヒューマノイドロボットHYDRAの開発におけるMATLABの活用
東京大学 神永 拓
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開発の動機
フィールドで実用的に使用できるロボットをどうやったら作れるのか?
パワー
耐久性
操作性制御性
22016/10/19 MATLAB EXPO 2016
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なにをしなければならないか
(直感的)操作性・制御性
頑健性 自律性
駆動系
制御システム動作計画
センサ
人型構造 アクチュエータ
柔軟性の実現 機構の改善
多数のセンサ
高速制御
32016/10/19 MATLAB EXPO 2016
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力制御系に影響を与える要因
2016/10/19 MATLAB EXPO 2016 4
PlantController
SensorObserver
Reference OutputPlant
Sensor
Backdrivability
Force Measurement
Controller
Observer
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バルブを用いない油圧駆動系
MATLAB EXPO 2016 5
Humanoid robots withvalve controlled hydraulics[Cheng2006, Nelson2012, Hyon2015]
Humanoid robot withEHA [Alfayad2011]
2016/10/19
Torque Sensing
Strength
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バルブを用いない油圧駆動系
MATLAB EXPO 2016 6
Humanoid robots withvalve controlled hydraulics[Cheng2006, Nelson2012, Hyon2015]
Humanoid robot withEHA [Alfayad2011]
2016/10/19
Torque Sensing
Strength
Torque Sensing
Modularity
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電気静油圧アクチュエータ (EHA)
MATLAB EXPO 2016 7
Torque Sensing
Strength
Backdrivability
Built‐In Torque Limiter
Modularity
2016/10/19
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Conceptual Structure of the Robot
MATLAB EXPO 2016 8
Joint Range of Motion [deg] Max. Torque [Nm]
Hip Yaw ‐60 ~ 60 60
Hip Roll ‐22.5 ~ 22.5 144
Hip Pitch ‐105 ~ 13 85.5
Knee ‐10 ~ 120 120
Ankle Roll ‐24.2 ~ 24.2 117
Ankle Pitch ‐44 ~ 34 117
Waist Roll ‐22.5 ~ 22.5 147
Waist Pitch 0 ~ 50 94
Clavicle ‐30 ~ 90 60
Shoulder Roll ‐17.5 ~ 117.5 80
Shoulder Pitch ‐27.3 ~ 27.3 105
Shoulder Yaw ‐30 ~ 90 40
Elbow ‐117 ~ 9 82.5
Wrist Yaw ‐10 ~ 110 40
Wrist Roll ‐29.1 ~ 29.1 142.5
Wrist Pitch ‐66 ~ 85 77.2
2016/10/19
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EHAのモジュール化
MATLAB EXPO 2016 9
Max. Pressure~7MPa
2016/10/19
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閉リンクを用いた関節駆動
1自由度 2自由度
102016/10/19 MATLAB EXPO 2016
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ロボットの構造設計
MATLAB EXPO 2016 11
Modular Design
Parallel‐Serial Hybrid Kinematics
2016/10/19
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分散制御系の開発
Friction Compensation, DOB
Status Management
Protocol Stack Handling
Current Control
Serial Comm. Processing
RealtimeRequirement
Amount of Computation
Operational Space Control
Whole‐BodyCoordination
FPGA
MCU (CPU, no OS)
PC (CPU, RTOS)
122016/10/19 MATLAB EXPO 2016
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体内LANの種類
Speed ProtocolStack
Realtime
I2C 5Mbps N Y
CAN 1Mbps Y N(Y for siglemaster case)
FlexRay 10Mbps Y Y
CU‐Net 12Mbps Y Y
RS‐485 20Mbps N Y
SPI ~20Mbps N Y
SERCOS‐II 10Mbps Y Y
SERCOS‐III 100Mbps Y Y
Ethernet 1000Mbps Y N
EtherCAT 100Mbps Y Y
清水ら2001
Kaneko et al. 2011
Sugihara et al. 2005
Lohmeier et al. 2009
Englsberger et al. 2014
2016/10/19 MATLAB EXPO 2016 13
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制御ハードウェアのブロック図
2016/10/19 MATLAB EXPO 2016 14
MCU Board Driver Board Joint Actuation
Sensor Interface Board
F/T Sensor
Accelerometer
FOG
Sensor Interface Board
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駆動系制御ハードウェアMCU + FPGA
FPGA+SiC
LVDS
15
MD
MD
Master(RT PC)
EtherCAT
1 1..5
2016/10/19 MATLAB EXPO 2016
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計算の階層構造
FOC Current Control
FOC Current Control
FOC Current Control
EHA Position / Pressure Control
FOC Current Control
EHA Position / Pressure Control
Parallel – Serial Linkage Conversion
Whole Body Motion Generation Robot Status Management
Congnitive Systems
FPGA
MCU
RT‐PC
PC
High
Low
Real Tim
e Re
quire
men
t
16
ROS
EtherCAT
LVDS
1 kHz
5kHz
1 kHz
20kHz
shm + sem
2016/10/19 MATLAB EXPO 2016
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パラレルリンクの等価開リンク系への変換
MATLAB EXPO 2016 172016/10/19
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閉リンクのシンボリックな計算
2016/10/19 MATLAB EXPO 2016 18
Rp = [cos(q_1),0,sin(q_1);0,1,0;‐sin(q_1),0,cos(q_1)];Rr = [1,0,0;0,cos(q_2),‐sin(q_2);0,sin(q_2),cos(q_2)];pend_1 = [xend;yend;zend];pend_2 = [‐xend;yend;zend];pcyl_01 = [xcyl;ycyl;z_1+zcyl];pcyl_02 = [‐xcyl;ycyl;z_2+zcyl];pend_01 = Rp*Rr*pend_1;pend_02 = Rp*Rr*pend_2;d1 = pend_01‐pcyl_01;d2 = pend_02‐pcyl_02;l1sq = norm(d1)^2;l2sq = norm(d2)^2;z_1_sol = solve(l1sq==lc^2,z_1);z_2_sol = solve(l2sq==lc^2,z_2);
z_1_sol =(lc^2 ‐ abs(ycyl ‐ yend*cos(q_2) + zend*sin(q_2))^2 ‐abs(xend*cos(q_1) ‐ xcyl + zend*cos(q_2)*sin(q_1) + yend*sin(q_1)*sin(q_2))^2)^(1/2) ‐ zcyl ‐ xend*sin(q_1) + zend*cos(q_1)*cos(q_2) + yend*cos(q_1)*sin(q_2)zend*cos(q_1)*cos(q_2) ‐ (lc^2 ‐abs(ycyl ‐ yend*cos(q_2) + zend*sin(q_2))^2 ‐abs(xend*cos(q_1) ‐ xcyl + zend*cos(q_2)*sin(q_1) + yend*sin(q_1)*sin(q_2))^2)^(1/2) ‐ xend*sin(q_1) ‐ zcyl + yend*cos(q_1)*sin(q_2)
Symbolic MathToolboxによる求解
さらにシンボリックな微分によりヤコビ行列を計算
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FPGA(Verilog HDL)
複雑なマルチプロセッサシステムの組み込み開発
2016/10/19 MATLAB EXPO 2016 19
Control Objectives
MCU(C/C++)
Working with multiple language Difficulty of simulation
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Simulinkによる電流ベクトル制御系の統合シミュレーションと自動コード生成
2016/10/19 MATLAB EXPO 2016 20
FPGA2MCU FPGA1
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電流ループシミュレーション結果
2016/10/19 MATLAB EXPO 2016 21
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Simulinkによるモジュール化設計
2016/10/19 MATLAB EXPO 2016 22
Fixed Logic
Logic under work
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PWM波形生成
2016/10/19 MATLAB EXPO 2016 23
ton
tofftd
有効なhigh時間
有効なlow時間
短絡防止時間
上アーム
下アーム
キャリア波形
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State Flowによる実装
2016/10/19 MATLAB EXPO 2016 24
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MATLAB/Simulinkを使うメリット
• 複雑なロジックを検証しつつ実装できる
• 複数のプラットフォームに渡る開発を統合的に行うことができる
• 可視化が容易
2016/10/19 MATLAB EXPO 2016 25
開発の高速化
バグの最小化
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MATLAB/Simulinkを組み込みに使う上での難しさ
• 極めてリソースが限られている場合の難しさ– リソースの再利用
– データ幅の自由度
• FPGAならではの難しさ– 純粋なクロックのみを使ったマルチレート制御
– 各社提供IPの利用の難しさ
• マイコンならではの難しさ– 自分で書いたCの関数を使いにくい
• あまりスケールが大きくなるとシミュレーションが遅くなる
2016/10/19 MATLAB EXPO 2016 26
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reg [3:0] clk2_cnt;reg clk2;
always @(posedge clk) beginclk2_cnt <= clk2_cnt + 4b’1;if(clk2_cnt==4’b0) beginclk2 <= 1’b1;
end else beginclk2 <= 1’b0;
endend
always @(posedge clk) beginif(clk2 ==1’b1) begin
/* slow process */end
end
生成しにくいロジックの例
2016/10/19 MATLAB EXPO 2016 27
reg [3:0] clk2_cnt;reg clk2;
always @(posedge clk) beginclk2_cnt <= clk2_cnt + 4b’1;if(clk2_cnt==4’b0) beginclk2 <= 1’b1;
end else beginclk2 <= 1’b0;
endend
always @(posedge clk2) begin/* slow process */
end
内部でのイベント発生
外部クロック同期でのイベント実行
これはやりたくない
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MATLAB/Simulinkを組み込みに使う上での難しさ
• 極めてリソースが限られている場合の難しさ– リソースの再利用
– データ幅の自由度
• FPGAならではの難しさ– 純粋なクロックのみを使ったマルチレート制御
– 各社提供IPの利用の難しさ
• マイコンならではの難しさ– 自分で書いたCの関数を使いにくい
• あまりスケールが大きくなるとシミュレーションが遅くなる
2016/10/19 MATLAB EXPO 2016 28
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最適化を用いた可動域の計算
2016/10/19 MATLAB EXPO 2016 29
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CADとのインテグレーション
SolidWorks
MATLAB
OptimizationToolbox
MacroInterface
2016/10/19 MATLAB EXPO 2016 30
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開発した制限装置
2016/10/19 MATLAB EXPO 2016 31
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ヒューマノイドロボットHYDRA
MATLAB EXPO 2016 32
Height 1800mmWeight 130kg
2016/10/19
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まとめ
FOC Current Control
FOC Current Control
FOC Current Control
EHA Position / Pressure Control
FOC Current Control
EHA Position / Pressure Control
Parallel – Serial Linkage Conversion
Whole Body Motion Control Robot Status Management
Congnitive Systems
FPGA
MCU
RT‐PC
PC
332016/10/19 MATLAB EXPO 2016
HDL Coder
E Coder
Sym Math
SimulinkReal‐Time
E Coder
Rob.System
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結論
1. ヒューマノイドロボットHydraの設計を紹介した
2. Hydraのメカトロニクスを例にとり,MATLAB/ Simulinkがどのように開発に用いられたのか紹介した– C/HDLの統合的な開発
– シミュレーションのメリット
– 独自コードを組み込んだ開発の難しさ
3. SolidWorksとの統合によるOptimization Toolboxを用いた最適化設計を紹介した
4. 開発したロボットの動作を紹介した
2016/10/19 MATLAB EXPO 2016 34