  Learning from human demonstrations can facilitate automation but is risky
because the execution of the learned policy might lead to collisions and other
failures. Adding explicit constraints to avoid unsafe states is generally not
possible when the state representations are complex. Furthermore, enforcing
these constraints during execution of the learned policy can be challenging in
environments where dynamics are difficult to model such as push mechanics in
grasping. In this paper, we propose Derivative-Free Recovery (DFR), a two-phase
method for generating robust policies from demonstrations in robotic
manipulation tasks where the system comes to rest at each time step. In the
first phase, we use support estimation of supervisor demonstrations and treat
the support as implicit constraints on states. We also propose a time-varying
modification for sequential tasks. In the second phase, we use this support
estimate to derive a switching policy that employs the learned policy in the
interior of the support and switches to a recovery policy to steer the robot
away from the boundary of the support if it drifts too close. We present
additional conditions, which linearly bound the difference in state at each
time step by the magnitude of control, allowing us to prove that the robot will
not violate the constraints using the recovery policy. A simulated pushing task
in MuJoCo suggests that DFR can reduce collisions by 83\%. On a physical line
tracking task using a da Vinci Surgical Robot and a moving Stewart platform,
DFR reduced collisions by 84\%.
