Behaviour cloning is a commonly used strategy for imitation learning and can be extremely effective in constrained domains. However, in cases where the dynamics of an environment may be state dependent and varying, behaviour cloning places a burden on model capacity and the number of demonstrations required. This paper introduces switching density networks, which rely on a categorical reparametrisation for hybrid system identification. This results in a network comprising a classification layer that is followed by a regression layer. We use switching density networks to predict the parameters of hybrid control laws, which are toggled by a switching layer to produce different controller outputs, when conditioned on an input state. This work shows how switching density networks can be used for hybrid system identification in a variety of tasks, successfully identifying the key joint angle goals that make up manipulation tasks, while simultaneously learning image-based goal classifiers and regression networks that predict joint angles from images. We also show that they can cluster the phase space of an inverted pendulum, identifying the balance, spin and pump controllers required to solve this task. Switching density networks can be difficult to train, but we introduce a cross entropy regularisation loss that stabilises training.
Our work is inspired by sequential composition theories in robotics @cite_23 , where tasks are solved by moving between sub-controllers lying within the domains of one another. Here, we seek to identify the sub-controllers required for a given task in an end-to-end fashion, from demonstration sequences. Learning from demonstration (LfD) @cite_1 is widely acknowledged as a particularly useful paradigm for robot programming. Significant progress has been made in LfD, moving beyond the direct replication of motions to produce more robust approaches @cite_7 through the introduction of more general schemes for modelling motion like dynamic motion primitives @cite_8 , linear dynamical attractor systems @cite_25 , sparse online Gaussian processes @cite_15 @cite_19 or conditionally linear Gaussian models @cite_20 @cite_21 that can be used for trajectory optimisation. It is important to note that each of these systems behaves as a hybrid system, decomposing a state space into specific regions, and learning appropriate dynamics for each region.
@cite_7 @cite_8 @cite_21 @cite_1 @cite_19 @cite_23 @cite_15 @cite_25 @cite_20
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We consider an imitation learning approach to model robot point-to-point (also known as discrete or reaching) movements with a set of autonomous Dynamical Systems (DS). Each DS model codes a behavior (such as reaching for a cup and swinging a golf club) at the kinematic level. An estimate of these DS models are usually obtained from a set of demonstrations of the task. When modeling robot discrete motions with DS, ensuring stability of the learned DS is a key requirement to provide a useful policy. In this paper we propose an imitation learning approach that exploits the power of Control Lyapunov Function (CLF) control scheme to ensure global asymptotic stability of nonlinear DS. Given a set of demonstrations of a task, our approach proceeds in three steps: (1) Learning a valid Lyapunov function from the demonstrations by solving a constrained optimization problem, (2) Using one of the-state-of-the-art regression techniques to model an (unstable) estimate of the motion from the demonstrations, and (3) Using (1) to ensure stability of (2) during the task execution via solving a constrained convex optimization problem. The proposed approach allows learning a larger set of robot motions compared to existing methods that are based on quadratic Lyapunov functions. Additionally, by using the CLF formalism, the problem of ensuring stability of DS motions becomes independent from the choice of regression method. Hence it allows the user to adopt the most appropriate technique based on the requirements of the task at hand without compromising stability. We evaluate our approach both in simulation and on the 7 degrees of freedom Barrett WAM arm. Proposing a new parameterization to model complex Lyapunov functions.Estimating task-oriented Lyapunov functions from demonstrations.Ensuring stability of nonlinear autonomous dynamical systems.Applicability to any smooth regression method. We present a probabilistic architecture for solving generically the problem of extracting the task constraints through a Programming by Demonstration (PbD) framework and for generalizing the acquired knowledge to various situations. In previous work, we proposed an approach based on Gaussian Mixture Regression (GMR) to find a controller for the robot reproducing the statistical characteristics of a movement in joint space and in task space through Lagrange optimization. In this paper, we develop an alternative procedure to handle simultaneously constraints in joint space and in task space by combining directly the probabilistic representation of the task constraints with a solution to Jacobian-based inverse kinematics. The method is validated in manipulation tasks with two 5 DOFs Katana robotic arms displacing a set of objects. Programming robotic assembly tasks usually requires delicate force tuning. In contrast, human may accomplish assembly tasks with much less time and fewer trials. It will be a great benefit if robots can learn the human inherent skill of force control and apply it autonomously. Recent works on Learning from Demonstration (LfD) have shown the possibility to teach robots by human demonstration. The basic idea is to collect the force and corrective velocity that human applies during assembly, and then use them to regress a proper gain for the robot admittance controller. However, many of the LfD methods are tested on collaborative robots with compliant joints and relatively large assembly clearance. For industrial robots, the non-backdrivable mechanism and strict tolerance requirement make the assembly tasks more challenging. This paper modifies the original LfD to be suitable for industrial robots. A new demonstration tool is designed to acquire the human demonstration data. The force control gains are learned by Gaussian Mixture Regression (GMR) and the closed-loop stability is analysed. A series of peg-hole-insertion experiments with H7h7 tolerance on a FANUC manipulator validate the performance of the proposed learning method. We consider the problem of designing controllers to steer mobile robots to the source (the minimizer) of a signal field. In addition to the mobility constraints, e.g., posed by the nonholonomic dynamics, we assume that the field is completely unknown to the robot and the robot has no knowledge of its own position. Furthermore, the unknown field is randomly switching. In the case where the information of the field (e.g., the gradient) is completely known, standard motion planning techniques for mobile robots would converge to the known source. In the absence of mobility constraints, convergence to the minimum of unknown fields can be pursued using the framework of numerical optimization. By considering these facts, this paper exploits an idea of the stochastic approximation for solving the problem mentioned in the beginning and proposes a source seeking controller which sequentially generates the next waypoints such that the resulting discrete trajectory converges to the unknown source and which steers the robot along the waypoints, under the assumption that the robot can move to any point in the body fixed coordinate frame. To this end, we develop a rotation-invariant and forward-sided version of the simultaneous-perturbation stochastic approximation algorithm as a method to generate the next waypoints. Based on this algorithm, we design source seeking controllers. Furthermore, it is proven that the robot converges to a small set including the source in a probabilistic sense if the signal field switches periodically and sufficiently fast. The proposed controllers are demonstrated by numerical simulations.