1、Introduction to Biped Walking,Lecture 1 Background, simple dynamics, and control,Some Sample Videos,Human Walk.avi Hubo straight leg.avi,Human Leg Anatomy,Torso,Hip, 3DOF,Knee, 1DOF,Ankle, 2DOF,Toes, 2 DOF,Building Blocks of Biped Walking,Dynamic modeling Trajectory generation Inverse kinematic mode
2、l Trajectory error controllers Additional failure mode controllers Mechatronics Programming,Provides virtual experimentation platform The ideal path that the hips and feet follow. Specifies the joint movements to make feet and hips follow the trajectory Specify how the joints should move to compensa
3、te for trajectory error. Adjusts the trajectory to compensate for nonidealities. The structure and implementation and the limitations thereof Reading sensors, processing and filtering their data, sending joint position commands.,Walking Cycle (2D),Kim, Jung-Yup (2006),Stages,Kim, Jung-Yup (2006),Con
4、trollers,Damping Controller reduces reactive oscillations to swinging legs ZMP controller minimizes ankle torque and optimizes hip trajectory Landing controller limits impact forces at foot, controls foot angle,Torso/pelvis controllers follow prescribed trajectory Tilt-over controller adjusts foot p
5、lacement if ZMP becomes unstable Landing position controller adjusts foot landing to compensate for excess angular velocity,Kim, Jung-Yup (2006),Block Diagram of KHR-2,Kim, Jung-Yup (2006),Balance Control,Controls Center of mass location Prevents tiltover Controls foot placement during landings Cons
6、ists of: Torso sway damping controller ZMP controller Foot placement controller Foot Landing Controller,Single Support Vibration Modeling,Compliance between ankle and torso Model robot body as lumped mass Model flexible parts and joints as spring Use Torque along X axis of ankle to counteract motion
7、 Linearize with small angle,Vibration Damping Control,Apply Laplace Transform Factor out (s) and U(s) to form transfer function Substitute to find TF of Torque wrt input angle,Damping Controller,Substitute = K/ml2g/l =K/ml2 Apply derivative feedback of error Simulation shows effect of damping on vib
8、rations (See )“vibdamp.mdl”,Joint Motor Controller Basics,DC brush motors Harmonic drive gear reduction Simple governing equations Inefficient at low speeds,Joint Motor Controller,Motor Voltage/Speed constant (V-s/rad),Output Torque (N-m),Rotor Inductance (Henry),Rotor Resistance (),Input Voltage (V
9、),Motor equivalent viscous friction (N-m-s),Current (Amp),Block Diagram of System,Effects of Motor on Control,Torque limit due to R torque inversely proportional to speed High current (and heat) at zero speed,Ankle model with motor,Assume simple inverted pendulum Combine electrical and mechancal ODE
10、s,Zero Moment Point,Point about which sum of inertia and gravitational forces = 0 Requires no applied moment to attain instantaneous equilibrium Control objective: minimize horizontal distance between COM and ZMP,Single Support Model,Divide ZMP control into 2 planes Track hip center to ZMP Requires
11、dynamic model or experiment to determine model parameters Pole placement compensator (See “ZMP.mdl”),Kim, Jung-Yup (2006),Double inverted pendulum,Foot Landing Placement,IMU measures X and Y angular velocity Hip sway monitored by trajectory controllers Excess angular velocity reduced by widening lan
12、ding stance Reduced angular velocity maintains hip trajectory,Kim, Jung-Yup (2006),Landing Problem,Foot landing causes impact and shock to system Dynamics of shock are difficult to model Large reaction forces Angular momentum controlled with 1 ankle,Simplified Collision Dynamics,Governing FormulasIm
13、pact Energy LossesPower Input,Impact Before After,v2,v1,Deriving the ideal model,Ideal mass-spring-damper mT53kg (hubos mass) c, k = model constants Form transfer function Solve numerically,Dynamic Model of knee,Lump mass of torso at hip Lagrange method to derive dynamics Add artificial damping to r
14、educe simulation noise Use PID control to stabilize,mT,Knee Inverse Kinematics,Need to solve i(x,t) (i=1,2) Desired path along y axis (x=0) Setup constraint equations & solveApply as input to model,Trajectory Generation,“Goal” Control,Needs no knowledge of model Low computation overhead Non-optimal
15、path,Trajectory Feedforward,Requires mathematical model Input conditioned for system Requires online computation Allows path optimization,Hubos Hip Trajectory,Y=A*sin(t) A=sway amplitude = stride frequency (rad/s) Simplifies frequency domain design,X=c*A1cos (t)+(1-c)A2*t A2=A1*/(2 ) c controls star
16、t/end velocity Amplitude A1 controls step length,Basic foot trajectory,Continuous function of t 0 velocity at each full cycle Velocity adjustable by linear component,Cycloid function,Timing of walking cycle,Short double support phase (10% of half cycle) Knee compression and extension Short landing phase,Kim, Jung-Yup (2006),Trajectory Parameters,Whats Next,Biped Design Procedure,Concepts Dynamic modeling Simulations Trajectory generation,Next Lecture:,Fundamentals of dynamics Fundamentals of controls 2d dynamic modeling Implementing posture control systems Basic X and Z axis trajectories,
