UTC was developed during investigating control of advanced skydiving maneuvers. The goal was reconstructing in simulation performance of these maneuvers by the means of changing the body posture of a virtual skydiver, as well as muscle tension (represented by dimensionless input moment coefficients and damping moment coefficients). Conventional methods, such as learning these coefficients via RNN and controlling the posture via classic control methods, didn’t allow to achieve the desired accuracy and robustness.
UTC utilizes the skydiver non-linear model to predict the skydiver’s inertial motion during a prediction horizon for a number of representative combinations of control variables (chosen via Unscented Transform). The outcome of each case is compared to the desired maneuver and a weighted average is assigned to the controller output. This controller showed a very good performance in simulations and could be conveniently tuned to obtain several different ways to execute the same maneuver, thus reconstructing the experience reported by skydivers.
However, stability and robustness of this controller needs to be further investigated. If applied to linear systems with prediction horizon of one step it can be proved that UTC satisfies a Discrete Algebraic Riccati Equation (DARE), and for the first simulation step the UTC controller is identical to LQR. From the second step onward the UTC controller has a part that depends on the previous con- troller’s output (as opposed to LQR). For linear systems and prediction horizon of multiple steps the stability condition of UTC has a structure of DARE with one additional term. The weight matrix R associated with control effort in DARE is related, in the case of UTC, to the scattering of sigma points. The solution of DARE – matrix P is related,
in the case of UTC, to the desired accuracy of tracking the state reference profile. In the case of multiple step prediction horizon – it is related also to the system dynamics: matrix A. The structure of the stability condition for one prediction step UTC for non-linear systems has the same structure as a state-dependent DARE. The stability of multiple step UTC for non-linear systems is yet to be explored.
From simulations with the skydiver model we get an impression that UTC is beneficial for highly non-linear systems with NMP dynamics and multiple actuators (with tight range and rate limits), which has many equilibrium points (stable and unstable) and is required to pass through their attraction regions during performing the desired maneuver. It seems important to find a less complex example system (or, alternatively, derive a smaller-dimension private case from the sky- diver model), but yet with meaningful dynamics, in order to acquire a better understanding of the physical meaning of UTC tuning matrices.
The robustness of UTC can be explored by providing it with an uncertain model of the plant, a partial state feedback, and adding noise to the feedback signals.
