For many important tasks such as manipulation and locomotion, robots need to make and break contact with their environment. Although such multi-contact systems are common, they pose a significant challenge when it comes to analysis and control. This difficulty primarily stems from two key factors: 1) the rapid increase in the number of possible ways that a system can move or behave as the number of contacts increase (as a result of the hybrid structure), and 2) the inherent nonlinearities present in the system’s dynamics. As a result, for tasks which require initiating contact with the environment, many state-of-the-art methods struggle as the number of contacts increase. Considering the substantial difficulty of multi-contact problems, it’s only natural to raise the question: How can we solve such problems? In addressing this query, this thesis directs its attention toward the simplification of multi-contact problems. It does so by concentrating on local hybrid approximations, wherein the non-smooth, hybrid structure is retained, while linearizing the smooth elements within the dynamics to mitigate the complexities arising from nonlinearities. As a result, we focus on local hybrid models called linear complementarity systems which are simple models that qualitatively capture the underlying non-smooth, hybrid structure. Employing these local hybrid models, this thesis presents scalable and fast algorithmic solutions for challenging multi-contact problems. First, we present the first real-time MPC framework for multi-contact manipulation. The method is based on the alternating direction method of multipliers (ADMM) and is capable of high-speed reasoning over potential contact events. Then, we focus on utilizing tactile measurements for reactive control, which is very natural yet underexplored in the robotics community. We propose a control framework to design tactile feedback policies for multi-contact systems by exploiting the local complementarity structure of contact dynamics. This framework can close the loop on tactile sensors and it is non-combinatorial, enabling optimization algorithms to automatically synthesize provably stable control policies. Then, inspired by the connection between rectified linear unit (ReLU) activation functions and linear complementarity problems, we present a method to analyze stability of multi-contact systems in feedback with ReLU network controllers.
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