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 .
Assuming dynamics are known or can be estimated, Gillula and Tomlin @cite_34 applied reachability analysis to address bounded disturbances by computing a sub-region within a predefined safe region where the robot will remain safe under any disturbance for a finite horizon. This region is referred to as the discriminating kernel" by Akamet @cite_7 and @cite_36 who extended this theory to obtain safe policies that are less conservative under uncertainty. In their work, the safety controller is applied only on the boundary of the discriminating kernel while the robot's controller is freely applied in the interior, resulting in a switching policy. Although our objectives are similar, there are several key differences in our assumptions. First, we do not require the model or constraints to be specified explicitly to the robot. Also, safe reinforcement learning aims to facilitate exploration for policy improvement while our approach addresses safe execution of policies after learning.
@cite_36 @cite_34 @cite_7
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This paper presents a safe learning framework that employs an adaptive model learning method together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique, and the resulting model will be used in combination with control barrier certificates which constrain policies (feedback controllers) in order to maintain safety, which refers to avoiding certain regions of the state space. Under certain conditions, recovery of safety in the sense of Lyapunov stability after violations of safety due to the nonstationarity is guaranteed. In addition, we reformulate action-value function approximation to make any kernel-based nonlinear function estimation method applicable to our adaptive learning framework. Lastly, solutions to the barrier-certified policy optimization are guaranteed to be globally optimal, ensuring greedy policy updates under mild conditions. The resulting framework is validated via simulations of a quadrotor, which has been used in the safe learnings literature under stationarity assumption, and then tested on a real robot called brushbot , whose dynamics is unknown, highly complex, and most probably nonstationary. Reinforcement learning is a promising approach to learning control policies for complex robotics tasks. A key challenge is ensuring safety of the learned control policy---e.g., that a walking robot does not fall over, or a quadcopter does not run into a wall. We focus on the setting where the dynamics are known, and the goal is to prove that a policy learned in simulation satisfies a given safety constraint. Existing approaches for ensuring safety suffer from a number of limitations---e.g., they do not scale to high-dimensional state spaces, or they only ensure safety for a fixed environment. We propose an approach based on shielding, which uses a backup controller to override the learned controller as necessary to ensure that safety holds. Rather than compute when to use the backup controller ahead-of-time, we perform this computation online. By doing so, we ensure that our approach is computationally efficient, and furthermore, can be used to ensure safety even in novel environments. We empirically demonstrate that our approach can ensure safety in experiments on cart-pole and on a bicycle with random obstacles. In environments with uncertain dynamics exploration is necessary to learn how to perform well. Existing reinforcement learning algorithms provide strong exploration guarantees, but they tend to rely on an ergodicity assumption. The essence of ergodicity is that any state is eventually reachable from any other state by following a suitable policy. This assumption allows for exploration algorithms that operate by simply favoring states that have rarely been visited before. For most physical systems this assumption is impractical as the systems would break before any reasonable exploration has taken place, i.e., most physical systems don't satisfy the ergodicity assumption. In this paper we address the need for safe exploration methods in Markov decision processes. We first propose a general formulation of safety through ergodicity. We show that imposing safety by restricting attention to the resulting set of guaranteed safe policies is NP-hard. We then present an efficient algorithm for guaranteed safe, but potentially suboptimal, exploration. At the core is an optimization formulation in which the constraints restrict attention to a subset of the guaranteed safe policies and the objective favors exploration policies. Our framework is compatible with the majority of previously proposed exploration methods, which rely on an exploration bonus. Our experiments, which include a Martian terrain exploration problem, show that our method is able to explore better than classical exploration methods. The proven efficacy of learning-based control schemes strongly motivates their application to robotic systems operating in the physical world. However, guaranteeing correct operation during the learning process is currently an unresolved issue, which is of vital importance in safety-critical systems. We propose a general safety framework based on Hamilton-Jacobi reachability methods that can work in conjunction with an arbitrary learning algorithm. The method exploits approximate knowledge of the system dynamics to guarantee constraint satisfaction while minimally interfering with the learning process. We further introduce a Bayesian mechanism that refines the safety analysis as the system acquires new evidence, reducing initial conservativeness when appropriate while strengthening guarantees through real-time validation. The result is a least-restrictive, safety-preserving control law that intervenes only when (a) the computed safety guarantees require it, or (b) confidence in the computed guarantees decays in light of new observations. We prove theoretical safety guarantees combining probabilistic and worst-case analysis and demonstrate the proposed framework experimentally on a quadrotor vehicle. Even though safety analysis is based on a simple point-mass model, the quadrotor successfully arrives at a suitable controller by policy-gradient reinforcement learning without ever crashing, and safely retracts away from a strong external disturbance introduced during flight.