Goal Directed Dynamics

We develop a general control framework where a low-level optimizer is built into the robot dynamics. This optimizer together with the robot constitute a goal directed dynamical system, controlled on a higher level. The high level command is a cost function. It can encode desired accelerations, end-effector poses, center of pressure, and other intuitive features that have been studied before. Unlike the currently popular quadratic programming framework, which comes with performance guarantees at the expense of modeling flexibility, the optimization problem we solve at each time step is non-convex and non-smooth. Nevertheless, by exploiting the unique properties of the soft-constraint physics model we have recently developed, we are able to design an efficient solver for goal directed dynamics. It is only two times slower than the forward dynamics solver, and is much faster than real time. The simulation results reveal that complex movements can be generated via greedy optimization of simple costs. This new computational infrastructure can facilitate teleoperation, feature-based control, deep learning of control policies, and trajectory optimization. It will become a standard feature in future releases of the MuJoCo simulator.

Authors

• Emanuel Todorov

Keywords

• Acceleration
• Robots
• Force
• Cost function
• Dynamics
• Optimization Problem
• Dynamical
• General Framework
• Center Of Pressure
• Quadratic Programming
• Trajectory Optimization
• Soft Constraints
• Robot Dynamics
• Actuator
• Optimal Control
• Dynamic Programming
• Equality Constraints
• Friction Force
• Contact Force
• Joint Space
• Cost Control
• Force Control
• Newton’s Second Law
• Humanoid Robot
• Inverse Dynamics
• Inverse Form
• Optimal Value Function
• Joint Limits
• Dry Friction
• Second-order System
• Frictional Contact
• Constraint Forces
• Numerical Efficiency
• Convex Optimization