The unmanned exploration of planets such as Mars requires a high level of autonomy because of the communication delays between robots in space and their Earth-based stations. This affects all the components of the system: planning, sensing, and mechanism. In particular, such a level of autonomy can be achieved only if each robot has a perception system that can reliably build and maintain models of the environment. The perception system is a major part of the development of a complete system that includes planning and mechanism design. The target vehicle is the Spider bot, a four-legged walking robot shown in Figure DP8.2(a), being developed at NASA Jet Propulsion Laboratory [18]. The control system of one leg is shown in Figure DP8.2(b).
(a) Sketch the Bode diagram for Gc(s)G(s) when K = 20. Determine (1) the frequency when the phase is -180° and (2) the frequency when 201og|GcG| = OdB. (b) Plot the Bode diagram for the closed-loop transfer function T(s) when K = 20.
(c) Determine Mpω ωr and ωB for the closed-loop system when K = 22 and K = 25. (d) Select the best gain of the two specified in part (c) when it is desired that the overshoot of the system to a step input r(t) be less than 5% and the settling time be as short as possible.