Least Constraint: A Framework for the Control of Complex Mechanical Systems

We describe an approach to control in which control actions are specified as weakly as desired. We use large time-varying sets of non-zero measure as desired goals instead of specific trajectories, maintaining that we do not care where in such a region we actually are. Inequality constraints and their conjunctions are used to describe such regions. The constraints are satisfied at run time to produce the control. The approach has been successfully used to produce human-like walking in simulation. We also describe an implemented programming environment for this approach. We discuss the representation of control computations using computational graphs and automatic differentiation for efficiency. Constraint satisfaction is performed usig a fast relaxation method.