Feasibility-Guided Exploration and Adaptation for Constrained Robotic Manipulation

Robots operating in unstructured environments must safely and effectively modulate contact forces with unfamiliar objects; a requirement that underlies tasks as diverse as collaborative object handling with humans and bulky-object manipulation through pushing or pivoting. Such interactions pose significant challenges, such as multi- modal dynamics, long-horizon planning with sparse rewards. Furthermore, the constraints inherent in such tasks amplify these difficulties and make it hard even to identify a feasible motion, let alone an optimal one. Paradoxically, however, these very constraints can also serve as guiding principles, narrowing the robot's exploration and steering it toward viable solutions. Motivated by this insight, the present thesis investigates strategies for incorporating and managing constraints to simplify and accelerate robotic interactions.

First, we demonstrate that representing feasible robot configurations on a low-dimensional robust manifold enables a humanoid robot to maintain stability while allowing a human user to control its motion directly on that manifold. However, identifying such a stable manifold in the full configuration space can itself be challenging, and in many cases it is preferable to tackle the original optimization problem directly. To that end, in our second contribution, we show how incorporating expert demonstrations can seed the solvers with these demonstrations (aka, warm-start) and augment gradients in regions of sparse cost, which accelerates convergence. Practically, this sample-then-project approach first generates candidate trajectories from expert data and then refines them via gradient descent in the full space. Extending this, our third contribution introduces a "project-then-sample" framework that offers more explorative behavior and faster convergence. By decomposing the problem into separate feasibility and optimality subproblems, we can sample trajectories from their combined solution space, ensuring sampled candidates are simultaneously feasible and near-optimal. Our final contribution tackles the challenging scenario where robots lack explicit environmental constraints and task models, particularly in imitation learning without access to unsuccessful demonstrations. We demonstrate that by combining multiple experts learned solely from successful demonstrations, the robot can interactively refine its sampling area and proactively avoid previously failed actions. These approaches are validated in an extensive experimentation, featuring human-humanoid collaboration and diverse contact-rich manipulation scenarios, including door-opening, object pushing, pivoting, etc.