Vrushabh Zinage

Vrushabh Zinage, Narek Harutyunyan, Eric Verheyden et al.

Legged locomotion in unstructured environments demands not only high-performance control policies but also formal guarantees to ensure robustness under perturbations. Control methods often require carefully designed reference trajectories, which are challenging to construct in high-dimensional, contact-rich systems such as quadruped robots. In contrast, Reinforcement Learning (RL) directly learns policies that implicitly generate motion, and uniquely benefits from access to privileged information, such as full state and dynamics during training, that is not available at deployment. We present ContractionPPO, a framework for certified robust planning and control of legged robots by augmenting Proximal Policy Optimization (PPO) RL with a state-dependent contraction metric layer. This approach enables the policy to maximize performance while simultaneously producing a contraction metric that certifies incremental exponential stability of the simulated closed-loop system. The metric is parameterized as a Lipschitz neural network and trained jointly with the policy, either in parallel or as an auxiliary head of the PPO backbone. While the contraction metric is not deployed during real-world execution, we derive upper bounds on the worst-case contraction rate and show that these bounds ensure the learned contraction metric generalizes from simulation to real-world deployment. Our hardware experiments on quadruped locomotion demonstrate that ContractionPPO enables robust, certifiably stable control even under strong external perturbations.

Lukas Taus, Vrushabh Zinage, Takashi Tanaka et al.

We revisit the problem of motion planning in the Gaussian belief space. Motivated by the fact that most existing sampling-based planners suffer from high computational costs due to the high-dimensional nature of the problem, we propose an approach that leverages a deep learning model to predict optimal path candidates directly from the problem description. Our proposed approach consists of three steps. First, we prepare a training dataset comprising a large number of input-output pairs: the input image encodes the problem to be solved (e.g., start states, goal states, and obstacle locations), whereas the output image encodes the solution (i.e., the ground truth of the shortest path). Any existing planner can be used to generate this training dataset. Next, we leverage the U-Net architecture to learn the dependencies between the input and output data. Finally, a trained U-Net model is applied to a new problem encoded as an input image. From the U-Net's output image, which is interpreted as a distribution of paths,an optimal path candidate is reconstructed. The proposed method significantly reduces computation time compared to the sampling-based baseline algorithm.

Vrushabh Zinage, Efstathios Bakolas

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems through the lens of linear systems and nonlinear control systems through the lens of bilinear control systems. The key idea of these methods lies in the transformation of the coordinates of the nonlinear system into the Koopman observables, which are coordinates that allow the representation of the original system (control system) as a higher dimensional linear (bilinear control) system. However, for nonlinear control systems, the bilinear control model obtained by applying Koopman operator based learning methods is not necessarily stabilizable. Simultaneous identification of stabilizable lifted bilinear control systems as well as the associated Koopman observables is still an open problem. In this paper, we propose a framework to construct these stabilizable bilinear models and identify its associated observables from data by simultaneously learning a bilinear Koopman embedding for the underlying unknown control affine nonlinear system as well as a Control Lyapunov Function (CLF) for the Koopman based bilinear model using a learner and falsifier. Our proposed approach thereby provides provable guarantees of asymptotic stability for the Koopman based representation of the unknown control affine nonlinear control system as a bilinear system. Numerical simulations are provided to validate the efficacy of our proposed class of stabilizing feedback controllers for unknown control-affine nonlinear systems.

Adhvaith Ramkumar, Vrushabh Zinage, Satadal Ghosh

Motion planning is an essential aspect of autonomous systems and robotics and is an active area of research. A recently-proposed sampling-based motion planning algorithm, termed 'Generalized Shape Expansion' (GSE), has been shown to possess significant improvement in computational time over several existing well-established algorithms. The GSE has also been shown to be probabilistically complete. However, asymptotic optimality of the GSE is yet to be studied. To this end, in this paper we show that the GSE algorithm is not asymptotically optimal by studying its behaviour for the promenade problem. In order to obtain a probabilistically complete and asymptotically optimal generalized shape-based algorithm, a modified version of the GSE, namely 'GSE*' algorithm, is subsequently presented. The forementioned desired mathematical properties of the GSE* algorithm are justified by its detailed analysis. Numerical simulations are found to be in line with the theoretical results on the GSE* algorithm.

Vrushabh Zinage, Senthil Hariharan Arul, Dinesh Manocha et al.

In this paper, we present an online motion planning algorithm (3D-OGSE) for generating smooth, collision-free trajectories over multiple planning iterations for 3-D agents operating in an unknown obstacle-cluttered 3-D environment. Our approach constructs a safe-region, termed 'generalized shape', at each planning iteration, which represents the obstacle-free region based on locally-sensed environment information. A collision-free path is computed by sampling points in the generalized shape and is used to generate a smooth, time-parametrized trajectory by minimizing snap. The generated trajectories are constrained to lie within the generalized shape, which ensures the agent maneuvers in the locally obstacle-free space. As the agent reaches boundary of 'sensing shape' in a planning iteration, a re-plan is triggered by receding horizon planning mechanism that also enables initialization of the next planning iteration. Theoretical guarantee of probabilistic completeness over the entire environment and of completely collision-free trajectory generation is provided. We evaluate the proposed method in simulation on complex 3-D environments with varied obstacle-densities. We observe that each re-planing computation takes $\sim$1.4 milliseconds on a single thread of an Intel Core i5-8500 3.0 GHz CPU. In addition, our method is found to perform 4-10 times faster than several existing algorithms. In simulation over complex scenarios such as narrow passages also we observe less conservative behavior.