Biped Locomotion on the HOAP-2 robot Biped Walking HOAP-2 Computer - PowerPoint PPT Presentation

Biped Locomotion C. Lathion Introduction Biped Locomotion on the HOAP-2 robot Biped Walking HOAP-2 Computer Science Master Project The controller Coupling Trajectories Implementation Christian Lathion Pressure Sensors Parameters Extensions Speed Stabilization 10 January 2007 Results Performance Robustness Conclusion

Outline Biped 1 Introduction Locomotion Biped Walking C. Lathion The HOAP-2 Robot Introduction Biped Walking 2 The controller HOAP-2 Coupling The controller Coupling Joint Trajectories Generation Trajectories Implementation 3 Implementation Pressure Sensors Feet Pressure Sensors Parameters Extensions Finding Optimal Parameters Speed Stabilization 4 Extensions to the controller Results Speed Control Performance Robustness Stabilization Techniques Conclusion 5 Obtained results Performance Robustness of the Gait 6 Conclusion

Biped Walking Biped Locomotion C. Lathion Introduction Biped Walking HOAP-2 • The goal of this project is to implement biped locomotion on a The controller humanoid robot, based on an existing controller. Coupling Trajectories • Not an easy task, even if we are used to do it naturally: Implementation Pressure Sensors • Nonlinear dynamics of the body (inverted pendulum). Parameters • Many degrees of freedom. Extensions • Interactions with the environment. Speed Stabilization • . . . Results Performance • Main difficulty: achieve stability. Robustness Conclusion

Biped Walking Biped Locomotion C. Lathion Introduction • Several different methods have been proposed for artificial biped Biped Walking HOAP-2 locomotion: The controller • Trajectory-based : Use offline optimization and constraint Coupling Trajectories satisfaction algorithms. Implementation • Heuristics : Similar technique, but uses heuristic or evolutionary Pressure Sensors Parameters algorithms. Extensions • Central Pattern Generators : Bio-inspired approach, model the Speed nodes – located in the spinal cord – that control vertebrates Stabilization locomotion. Results Performance • . . . Robustness • But still no perfect solution. Conclusion

The HOAP-2 Robot Biped Locomotion C. Lathion Introduction Biped Walking HOAP-2 The controller Coupling Trajectories Implementation Pressure Sensors Parameters Extensions Speed • The controller is applied to the HOAP-2 robot: Stabilization • Humanoid for Open Architecture Platform Results Performance • Developed by Fujitsu Automation Ltd. Robustness • 7kg, 50cm Conclusion • 25 degrees of freedom • Modelized under Webots

Frequency and phase coupling Biped Locomotion C. Lathion • The controller ( φ c ) and robot ( φ r ) phases follow a differential Introduction equations system: Biped Walking HOAP-2 The controller ˙ φ c = ω c + K c sin ( φ r − φ c ) Coupling Trajectories ˙ φ r = ω r + K r sin ( φ c − φ r ) Implementation Pressure Sensors Parameters Extensions Speed • This synchronizes the controller dynamics with the robot. Stabilization Results • In practice, φ r is obtained through the feet pressure sensors, as Performance the robot natural frequency ω r and coupling constant K r are Robustness Conclusion usually unknown. • Controller phase equation is solved by numerical integration.

Frequency and phase coupling Biped Locomotion • A strong coupling value is necessary to obtain the desired C. Lathion locking effect: Introduction • K c = 2 . 0 Biped Walking HOAP-2 The controller 1 Coupling ω r ω c (K c = 2) Trajectories Implementation Pressure Sensors 0.5 Parameters Extensions Speed Stabilization 0 Results Performance Robustness -0.5 Conclusion -1 0 1000 2000 3000 4000 5000 6000 time [ms]

Frequency and phase coupling Biped Locomotion • A strong coupling value is necessary to obtain the desired C. Lathion locking effect: Introduction • K c = 4 . 0 Biped Walking HOAP-2 The controller 1 Coupling ω r ω c (K c = 4) Trajectories Implementation Pressure Sensors 0.5 Parameters Extensions Speed Stabilization 0 Results Performance Robustness -0.5 Conclusion -1 0 1000 2000 3000 4000 5000 6000 time [ms]

Frequency and phase coupling Biped Locomotion • A strong coupling value is necessary to obtain the desired C. Lathion locking effect: Introduction • K c = 5 . 0 Biped Walking HOAP-2 The controller 1 Coupling ω r ω c (K c = 5) Trajectories Implementation Pressure Sensors 0.5 Parameters Extensions Speed Stabilization 0 Results Performance Robustness -0.5 Conclusion -1 0 1000 2000 3000 4000 5000 6000 time [ms]

Frequency and phase coupling Biped Locomotion • A strong coupling value is necessary to obtain the desired C. Lathion locking effect: Introduction • K c = 9 . 0 Biped Walking HOAP-2 The controller 1 Coupling ω r ω c (K c = 9) Trajectories Implementation Pressure Sensors 0.5 Parameters Extensions Speed Stabilization 0 Results Performance Robustness -0.5 Conclusion -1 0 1000 2000 3000 4000 5000 6000 time [ms]

Joint Trajectories Biped Locomotion C. Lathion • Trajectories are generated from the controller phase by using Introduction simple sinusoidal patterns. Biped Walking HOAP-2 • Divided in stepping and biped walking sub-movements. The controller Coupling Trajectories Implementation φ 1 θ d � � hip r ( φ c ) = A hip r sin Pressure Sensors c Parameters c − π � � θ d φ 1 ankle r ( φ c ) = A ankle r sin Extensions 4 Speed Stabilization φ 1 φ 2 θ d � � � � + θ res hip p ( φ c ) = A p sin + A hip s sin c c hip p Results Performance θ d � φ 1 � + θ res knee p ( φ c ) = − 2 A p sin Robustness c knee p Conclusion θ d φ 1 φ 2 + θ res � � � � ankle p ( φ c ) = A p sin − A ankle s sin c c ankle p

Joint Trajectories Biped Locomotion C. Lathion • Trajectories are generated from the controller phase by using Introduction simple sinusoidal patterns. Biped Walking HOAP-2 • Divided in stepping and biped walking sub-movements. The controller Coupling Trajectories Implementation φ 1 θ d � � hip r ( φ c ) = A hip r sin Pressure Sensors c Parameters c − π � � θ d φ 1 ankle r ( φ c ) = A ankle r sin Extensions 4 Speed Stabilization φ 1 φ 2 θ d � � � � + θ res hip p ( φ c ) = A p sin + A hip s sin c c hip p Results Performance θ d � φ 1 � + θ res knee p ( φ c ) = − 2 A p sin Robustness c knee p Conclusion θ d φ 1 φ 2 + θ res � � � � ankle p ( φ c ) = A p sin − A ankle s sin c c ankle p

Joint Trajectories Biped Locomotion C. Lathion • Trajectories are generated from the controller phase by using Introduction simple sinusoidal patterns. Biped Walking HOAP-2 • Divided in stepping and biped walking sub-movements. The controller Coupling Trajectories Implementation φ 1 θ d � � hip r ( φ c ) = A hip r sin Pressure Sensors c Parameters c − π � � θ d φ 1 ankle r ( φ c ) = A ankle r sin Extensions 4 Speed Stabilization φ 1 φ 2 θ d � � � � + θ res hip p ( φ c ) = A p sin + A hip s sin c c hip p Results Performance θ d � φ 1 � + θ res knee p ( φ c ) = − 2 A p sin Robustness c knee p Conclusion θ d φ 1 φ 2 + θ res � � � � ankle p ( φ c ) = A p sin − A ankle s sin c c ankle p

Joint Trajectories Biped Locomotion C. Lathion • Limb movements are synchronized by using four different Introduction phases: Biped Walking HOAP-2 • π phase difference for right/left limb movement. The controller 2 difference between stepping and walking. Coupling π • Trajectories ˆ 2 , π, 3 π ˜ • α i = 0 , π Implementation 2 ˙ Pressure Sensors φ r ( χ ) − φ i φ i � � c = ω c + K c sin c + α i Parameters Extensions • θ res angles define the rest posture of the robot joints. Speed i Stabilization • An additional phase difference of − π 4 was introduced in the Results ankle joint equation. Performance Robustness • Without it, over-oscillations occured, leading to the robot fall. Conclusion • As a side-effect, oscillations of the foot are present during the stance phase.

Joint Trajectories Biped Locomotion • Coupling changes the shape of the joint trajectories. C. Lathion • Simple sinusoidal trajectories are not sufficient to generate the Introduction walking pattern. Biped Walking HOAP-2 2 to ≃ 3 π • The resulting frequency also rises from π 2 . The controller Coupling 50 Trajectories hip roll ankle roll Implementation 40 hip pit Pressure Sensors knee pit ankle pit Parameters 30 Extensions Speed 20 Stabilization angle [deg] Results 10 (Uncoupled) Performance Robustness 0 Conclusion -10 -20 -30 0 2000 4000 6000 8000 10000 12000 14000 16000 time [ms]

Joint Trajectories Biped Locomotion • Coupling changes the shape of the joint trajectories. C. Lathion • Simple sinusoidal trajectories are not sufficient to generate the Introduction walking pattern. Biped Walking HOAP-2 2 to ≃ 3 π • The resulting frequency also rises from π 2 . The controller Coupling 50 Trajectories hip roll ankle roll Implementation 40 hip pit Pressure Sensors knee pit ankle pit Parameters 30 Extensions Speed 20 Stabilization angle [deg] Results 10 (Coupled) Performance Robustness 0 Conclusion -10 -20 -30 0 1000 2000 3000 4000 5000 time [ms]