Trajectory tracking for quadrotors: An optimization‐based planning followed by controlling approach

Abstract

We present an optimization-based reference trajectory tracking method for quadrotor robots for slow-speed maneuvers. The proposed method uses planning followed by the controlling paradigm. The basic concept of the proposed method is an analogy with linear quadratic Gaussian in which nonlinear model predictive control (NMPC) is employed for predicting optimal control policy in each iteration. Multiple-shooting is suggested over direct-collocation for imposing constraints when modeling the NMPC. Incremental Euclidean distance transformation map is constructed for obtaining the closest free distances relative to the predicted trajectory; these distances are considered obstacle constraints. The reference trajectory is generated ensuring dynamic feasibility. The objective is to minimize the error between the quadrotor's current pose and the desired reference trajectory pose in each iteration. Finally, we compared the proposed method with two other approaches and showed that the proposed method outperforms the said approaches in terms of reaching the goal without any collision. Additionally, we published a new data set that can be used for evaluating the performance of trajectory tracking algorithms.

Optimization-Based Trajectory Tracking Approach for Multi-Rotor Aerial Vehicles in Unknown Environments

“…In such planning, a global planner (Singh et al, 2017) tries to refine the desired trajectory considering safety constraints. Along with that, a local planner (Kulathunga et al, 2022a) ensures the dynamic feasibility and imposes safety constraints. However, incorporating fully-fledged system dynamics makes it harder to solve trajectory planning whilst avoiding obstacles in real time.…”

“…However, it arises various problems, including high computational demands, being stuck in local minima, low convergence rate, and real-time applicability. Hence, we decided to use a four-degree-of-freedom motion model, which was proposed in (Kulathunga et al, 2022a) f norm (x, u), that is appropriate enough since obstacle avoidance and low-speed maneuver are the main objectives of this work. Let f est (x, u) be the augmented quadrotor motion model:…”

“…where d o is the safe zone distance between a quadrotor and close-in obstacles, denoted by x o j ∈ R 3 , j = 1, .., N o . For the descriptive formulations of g 1 (w), g 2 (w), x ref k , and u ref k , refers to (Kulathunga et al, 2022a), (Kulathunga et al, 2022b).…”

“…Such learning helps improve the expressiveness (or reduce uncertainties) of the simplified motion model (or a nominal model) that is used in the planning stage. We used a planner that consists of two sub-planners: a local planner that consists of a 4 degree of freedom model (Kulathunga et al, 2022a) and a replanner (Kulathunga et al, 2022b) that can push the reference trajectory out of obstacle zones. The local planner is formulated as a hard constraint optimization problem, whereas the replanner is formulated as a box-constrained function minimization problem, which iteratively refines the reference trajectory by pushing away from the obstacle zones.…”

“…Hence, dynamic effects (external or/and internal) can be neglected, especially in the plan-based control paradigm. Therefore, a simplified motion model (Kulathunga et al, 2022a) was proposed to estimate the nominal dynamics in high-level planning. However, the residual dynamics that arise between the high-level planner and the low-level controller need to be minimized, which is unable to estimate analytically.…”