Numerical solution of differential systems with algebraic inequalities arising in robot programming

Recently, new robot programming approaches have proposed the use of programmed constraints as an executable specification language for the desired behavior of a robot. The constraint-based approaches are intermediate level languages, promising a higher, more declarative level of programming than trajectory-based approaches, while being more tractable computationally than motion planning. This paper considers a numerical algorithm for solution of differential systems subject to algebraic inequality constraints. These are the mathematical structures behind the constraint-based approach. Our approach is based on a principle of 'least constraint', consisting of a dynamic integration of the equations of motion coupled with invocation of a control mechanism to ensure that the robot trajectory avoids all constraint boundaries. This is achieved by minimization of a barrier function defined using buffer zones near the constraint boundaries. Determination of the buffer zones is done dynamically, corresponding to a local planning strategy.