COP: Control & Observability-aware Planning

Abstract

In this research, we aim to answer the question: How to combine Closed-Loop State and Input Sensitivity-based with Observability-aware trajectory planning? These possibly opposite optimization objectives can be used to improve trajectory control tracking and, at the same time, estimation performance.Our proposed novel Control & Observability-aware Planning (COP) framework is the first that uses these possibly opposing objectives in a Single-Objective Optimization Problem (SOOP) based on the Augmented Weighted Tchebycheff method to perform the balancing of them and generation of Bézier curve-based trajectories. Statistically relevant simulations for a 3D quadrotor unmanned aerial vehicle (UAV) case study produce results that support our claims and show the negative correlation between both objectives. We were able to reduce the positional mean integral error norm as well as the estimation uncertainty with the same trajectory to comparable levels of the trajectories optimized with individual objectives.

A Sensitivity-Aware Motion Planner (SAMP) to Generate Intrinsically-Robust Trajectories

“…To evaluate the effectiveness of our approach, we considered the model of a 3D quadrotor as described in [20]. The control inputs are the squared rotor speeds of the quadrotor u = [ω 2 1 ω 2 2 ω 2 3 ω 2 4 ].…”

“…T ← Extend(T, x rand ); end if 16: end while 17: return sol 3) Sensitivity-Aware shortcut (SAshortcut): In order to improve the sensitivity-based cost function, a local optimization is performed using a simple variant of the 'shortcut' smoothing algorithm [20], called SAshortcut and described in Algorithm 3. The reason for this variant, as already mentioned in Sec.III-A.2, is that the sensitivity of a trajectory portion is not invariant but instead depends on the previous portions since the start of the motion.…”

Controller and Trajectory Optimization for a Quadrotor UAV with Parametric Uncertainty

“…We now report the results of a statistical analysis for the three controllers of Sect. III when considering the three optimization problems (11)(12)(13). For the analysis we generate N traj = 25 initial trajectories s d (a, t) starting at the origin and coping with the initial/final state constraints and input saturations as in (11)(12)(13).…”

“…III when considering the three optimization problems (11)(12)(13). For the analysis we generate N traj = 25 initial trajectories s d (a, t) starting at the origin and coping with the initial/final state constraints and input saturations as in (11)(12)(13). These initial trajectories are restto-rest motions (from a hovering state to a hovering state) with a final position randomly generated inside a spherical shell of 4 to 6 m centered at the origin, and a final yaw angle randomly generated in the interval [−π/2, π/2].…”

“…One can then attempt to increase robustness against uncertain parameters by planning a suitable feedforward (or desired) trajectory that minimizes the sensitivity metrics, thereby generating an intrinsically-robust and control-aware motion plan. These ideas have also been extended to the problem of combining state observabilty with parametric robustness in [11], and in [12] a recent extension is proposed for obtaining the 'tubes' of perturbed trajectories given a known range of parametric deviation.…”