Robust Trajectory Planning with Parametric Uncertainties

Abstract

In this paper we extend the previously introduced notion of closed-loop state sensitivity by introducing the concept of input sensitivity and by showing how to exploit it in a trajectory optimization framework. This allows to generate an optimal reference trajectory for a robot that minimizes the state and input sensitivities against uncertainties in the model parameters, thus producing inherently robust motion plans. We parametrize the reference trajectories with Béziers curves and discuss how to consider linear and nonlinear constraints in the optimization process (e.g., input saturations). The whole machinery is validated via an extensive statistical campaign that clearly shows the interest of the proposed methodology.

COP: Control & Observability-aware Planning

“…3) Control-aware Trajectories: To address this issue, the notion of Closed-Loop State and Input Sensitivities (S/I-S) has been recently introduced in [22], [23] as a suitable metric to be optimized. Minimizing the norm of the S/I-S generates a trajectory whose tracking results are minimally sensitive to model uncertainties of the robot states and inputs.…”

“…T ∈ R 4 track a desired motion r d (a, t) ∈ R 4 , where ϕ is the yaw (or heading) angle of the quadrotor. The DFL (Dynamic Feedback Linearization) controller with an integral term used in previous works [22], [23] is not robust against parameter uncertainties and is not capable of considering input constraints. Therefore, we chose to use a different controller, namely the so-called Lee controller [20], which performs slightly worse in an ideal case compared to the DFL, but it is much less complex to implement and tune.…”

“…In [23] 'plain polynomials' were used, with the drawback of introducing possible numerical instability during the optimization. Due to this reason, we switched in [22] to the use of Bézier curve representation, as they are more stable from a numerical point of view.…”

“…This work goes one step further by implementing piecewise Beziér curves for the trajectory representation to avoid the use of a single high degree Beziér curve as in [22]. An aditional abstraction happens on the parameter vector a, which now contains way-points (with velocity, acceleration, and even higher order constraints) instead of the control points themselves.…”

“…2) Input Sensitivity Metric: As natural evolution, [22] added to the state sensitivity metric the so-called input sensitivity metric which is defined as…”