Constraint-consistent task-oriented whole-body robot formulation: Task, posture, constraints, multiple contacts, and balance

We present a comprehensive formulation to the problem of controlling a high-dimensional robotic system involving complex tasks subject to a variety of constraints, obstacles, balance, and contact challenges. Using intuitive and natural representations, the approach is initiated by establishing individual objectives for a task and its constraints. Simple independent controllers using artificial potential fields are then designed for each objective to reach goals while enforcing the constraints. Dynamically consistent projections in nullspaces associated with task and constraint representations are employed to deliver a coherent whole-body robot control. In multi-link multi-contact tasks, contact forces produce both resulting and internal forces. Internal forces play a critical role in robot balance and stability, achieved in this framework through modeling and controlling virtual linkages that explicitly describe the relationship between active/passive contact force, resultant force, controlled/uncontrolled internal force for multi-link multi-contact underactuated robots. Control of contacts with the environment involves material considerations such as friction and geometric constraints. Potential barriers direct the selection of contact forces ensuring stability and balance. This approach of dynamic projection and the Virtual Linkage Model addresses robot underactuation. In addition, the framework introduces a coordinate completion mechanism to establish a generalized coordinates representation of the task, removing redundancy and maintaining the full operational space dynamics description. This enables task-space dynamic control based on the relevant inertial properties. We present the experimental validation on a physical humanoid platform.