optimization-based full body control for the darpa robotics challenge
DESCRIPTION
Optimization-Based Full Body Control for the DARPA Robotics Challenge. Siyuan Feng Mar. 14 2014. Introduction. We want a generalized controller that works for a variety of tasks. This is a complex optimization problem, so we factor it into two stages. NOW. FUTURE. QP. DDP. - PowerPoint PPT PresentationTRANSCRIPT
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Optimization-Based Full Body Control for the DARPA Robotics Challenge
Siyuan FengMar. 14 2014
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Introduction
• We want a generalized controller that works for a variety of tasks.
• This is a complex optimizationproblem, so we factor it into two stages.
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NOW FUTURE
QP DDPFull model Simple model
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Related works
• Reference motion generation (Long term)– Preview control– Full dynamic programming– RHC with foot step adjustment
• Floating base inverse dynamics (Instantaneous)– Prioritized inverse dynamics– Reduced model using CoM and angular momentum– Orthogonal decomposition
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Outline
• Related works• Low level controller– Inverse dynamics– Inverse kinematics
• State estimation• High level controller– Walking– Ladder climbing– Manipulation
• Discussions
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Low level controller
• Both inverse dynamics and inverse kinematics– ID for compliance– IK to battle modeling errors
• ID and IK are formulated as quadratic programming problems optimizing for the current time step.
• Based on the full model (floating base)– Have control over full state– Easy to specify constraints
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QP formulation
Cost function: Each row represents an objective:
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Inverse dynamics
• • Uses desired motions from the high level
controller and estimated robot states to compute target acceleration with feedback
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Inverse dynamics
• Cost function:– Target CoM / torso / limb acceleration tracking– CoP tracking – Weight distribution– Change in torque and force– Regularization
• Constraints:– Equations of motion– CoP within the support polygon– Torque limits
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Inverse kinematics
• Maintains its own state• • Integrate to get • Uses desired motions from high level
controller and internal states to compute target velocity with feedback
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State estimation
• Simple kinematic filter (EKF) just for pelvis position and velocity estimation
• Process model: based on IMU’s acceleration measurement
• Observation model: assumes known stationary contact and kinematics
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Outline
• Related works• Low level controller– Inverse dynamics– Inverse kinematics
• State estimation• High level controller– Walking– Ladder climbing– Manipulation
• Discussions
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Simulated walking
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Optimizing CoM trajectory
• Generates CoM trajectory for a point mass model with Differential Dynamic Programming (DDP)
• Uses a nonlinear model
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x vs t
z vs t
y vs t
x vs y
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Atlas static walking
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Atlas static walking
• Foot step selection is entirely manual based on a live camera stream.
• Toe off is needed for stepping up or long stride• Ankle is purely torque controlled• Integrators– CoM– Swing foot
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Atlas ladder climbing
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Atlas ladder climbing
• Foot / hand reposition is scripted, but final adjustment is done by the operator.
• Intentionally leaning on railings to stop yaw rotation
• More kinematic constraint management due to tight spacing between railings
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Atlas full body manipulation
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Remarks about our controller
• 2-stage setup made concurrent development for multiple tasks possible.
• The low level controller is generic enough and seems to be effective for the 3 tasks.
• Inconsistency between IK and ID?– Can bias either solution to the other’s– Empirically consistent without constraint violation– Need to reason about the future to steer away from
constraints -> can’t be solved at this stage
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Remarks about Atlas
• Going slow made things much easier– Can use integrators– Delay is not a big deal
• Position and torque sensing are pre-transmission– FK has much more error– Joint friction is not measured at all
• Terms we used in the joint servos– k_q_p, k_qd_p– k_f_p, ff_qd is transformed by moment arm
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Next step
• Try to model modeling errors / better state estimation
• High level controller– Include angular momentum– Re-optimize step timing and location based on current
state• Low level controller– Coordinate IK and ID better– Add a notion of future in QPs through value function– Valve command in ID?
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Questions?
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