The role of time constraints in the design of control for the jogger´s problem

Control schemes in real-time sensor-based systems often operate under tight time constraints determined by the system sampling rate. One area where such constraints are especially severe is the sensor-based motion planning with dynamics in robotics. Though very important both theoretically and in practice, this problem has not been addressed so far. The typical sampling rates in such systems are 20 to 50 per second. This leaves only 20 to 50 msec for the whole cycle, including sensing, complex geometric (intelligence) analysis, calculations due to dynamics and control, and motion execution. As a first attempt to solve the problem, we show that the time constraints can be met by a combination of a simple model with a carefully chosen analytical solution of the dynamic equations. The resulting control scheme guarantees convergence and safety of motion, and blends well with kinematic path planning algorithms. Two such strategies are discussed, one using a simple heuristic and the other with local optimization