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Model predictive control for fast reaching in clutter
Model predictive control for fast reaching in clutter
Marc D. Killpack 0 1 2
Ariel Kapusta 0 1 2
Charles C. Kemp 0 1 2
0 Present Address: Brigham Young University , Provo, UT , USA
1 Georgia Institute of Technology , Atlanta, GA , USA
2 Marc D. Killpack is an Assis- tant Professor in the Depart- ment of Mechanical Engineer- ing at Brigham Young Univer- sity. He completed his doctorate in Robotics from the Woodruff School of Engineering at Georgia Tech (2013) as well as his MS in Mechanical Engineering (2008). He also completed a Master Pro Degree from ENSAM in Metz, France, and a BS in Mechan- ical Engineering from BYU. He founded the Robotics and Dynamics Lab at BYU (
A key challenge for haptically reaching in dense clutter is the frequent contact that can occur between the robot's arm and the environment. We have previously used single-time-step model predictive control (MPC) to enable a robot to slowly reach into dense clutter using a quasistatic mechanical model. Rapid reaching in clutter would be desirable, but entails additional challenges due to dynamic phenomena that can lead to higher forces from impacts and other types of contact. In this paper, we present a multi-timestep MPC formulation that enables a robot to rapidly reach a target position in dense clutter, while regulating wholebody contact forces to be below a given threshold. Our controller models the dynamics of the arm in contact with the environment in order to predict how contact forces will change and how the robot's end effector will move. It also models how joint velocities will influence potential impact forces. At each time step, our controller uses linear models to generate a convex optimization problem that it can solve efficiently. Through tens of thousands of trials in simulation, we show that with our dynamic MPC a simulated robot can, on average, reach goals 1.4 to 2 times faster than our previous controller, while attaining comparable success rates and fewer occurrences of high forces. We also conducted trials using a real 7 degree-of-freedom (DoF) humanoid robot arm with whole-arm tactile sensing. Our controller enabled the robot to rapidly reach target positions in dense artificial foliage while keeping contact forces low.
Clutter; Haptic; MPC; Multi-contact
B Marc D. Killpack
State-space matrices that are discrete time
linear approximations of the dynamics for a robot
in contact
Coriolis and centrifugal matrix
An integral term added to the cost function to
counter errors in gravity compensation
Approximate integral of end effector position
error
Current error in end effector position
External contact force vector on robot links
Measured normal force for contact i
User-defined allowable contact force threshold
Coulomb and viscous joint friction
Configuration dependent gravity joint torques
Estimate of configuration dependent gravity
joint torques used for gravity compensation
Number of time steps in the prediction model
where there is control authority
Number of time steps in the prediction model
with the control input set to zero
Geometric Jacobian at the end effector
Geometric Jacobian at contact i
Discrete time index
Cartesian stiffness matrix for contact i
Gain on the error integrator, eint
Diagonal joint stiffness matrix
Diagonal joint damping matrix
Configuration dependent joint-space inertia
matrix
Number of degrees of freedom of given robot
linkage
Unit vector normal to the surface of the robot
at the location of contact i
The number of contacts at any given time
instant
State variables of joint angle and velocity
Commanded equilibrium joint angles that are
sent to the joint impedance controller
Minimum allowable joint angle limits
Maximum allowable joint angle limits
Initial joint configuration at current time
Current time which is always the starting point
for the predictive model
Cartesian position for contact i
Cartesian position of the end effector
Scalar weighting terms for the multi-objective
cost function
Maximum desired rate at which the contact
force should be allowed to change at contact
i
Change in equilibrium joint angles, this is the
output of MPC
Maximum allowable change in commanded
joint angles
Time duration of an unexpected impact
Desired change in position at the end effector
Size of continuous time step used to generate
discrete-time difference equations for
prediction and dynamic MPC
Joint torques that result from the sum of all
external forces due to contact
Commanded joint torque that results from
“simple joint impedance control” and gravity
compensation calculations
Average torque due to impact forces occurring
during an unexpected collision
The integral term dgrav becomes effective
when e0 is below this threshold value
1 Introduction
The current state of capabilities for robot manipulation in
domains such as in-home assistance, search and rescue, and
natural or military disasters lags behind human capability
and speed. One particular capability at which humans (and
other animals) e (...truncated)