Optimizing Control-Friendly Trajectories with Self-Supervised Residual Learning

TL;DR

The paper tackles the challenge of accurate tracking for aggressive robotic motions by explicitly modeling residual physics that are not captured by nominal dynamics. It introduces a self-supervised residual-learning framework that augments a nominal closed-loop model into a hybrid dynamics system, enabling stable long-horizon predictions with arbitrary integration steps. A residual-minimizing trajectory optimizer then generates control-friendly reference trajectories that are easier to track with standard controllers, demonstrated on quadrotor platforms both in simulation and real-world experiments. The results show reduced tracking error and the ability to produce aggressive yet trackable trajectories without re-tuning controllers, highlighting practical impact for high-speed robotic flight and planning under model mismatch. Limitations include offline learning and potential computational costs, with future work pointing to online adaptation and alternative, simpler regressors to improve real-time applicability.

Abstract

Real-world physics can only be analytically modeled with a certain level of precision for modern intricate robotic systems. As a result, tracking aggressive trajectories accurately could be challenging due to the existence of residual physics during controller synthesis. This paper presents a self-supervised residual learning and trajectory optimization framework to address the aforementioned challenges. At first, unknown dynamic effects on the closed-loop model are learned and treated as residuals of the nominal dynamics, jointly forming a hybrid model. We show that learning with analytic gradients can be achieved using only trajectory-level data while enjoying accurate long-horizon prediction with an arbitrary integration step size. Subsequently, a trajectory optimizer is developed to compute the optimal reference trajectory with the residual physics along it minimized. It ends up with trajectories that are friendly to the following control level. The agile flight of quadrotors illustrates that by utilizing the hybrid dynamics, the proposed optimizer outputs aggressive motions that can be precisely tracked.

Figures (9)

• Figure 1: The schematic of the quadrotor system with the definitions of the earth-fixed and the body-fixed frame.
• Figure 2: The proposed hybrid model. Given an open-loop dynamics and a control policy, the closed-loop dynamics could be constructed and augmented with a learning-based part to capture residual physics.
• Figure 3: Trajectory tracking results of the proposed trajectory optimization and the compared methods. Using a nominal MPC for trajectory tracking, the minimum-residual trajectory achieves the best tracking performance among others. The mean aerodynamic drag of the minimum-residual trajectory is $0.817N$, which is significantly lower than the $1.845N$ that appeared in the minimum-snap trajectory and $1.483N$ in the minimum-control-R trajectory.
• Figure 4: Trajectories generated with random waypoints for aerodynamic drag learning. Each trajectory contains 5 random waypoints and 200 discrete nodes with a step size of $0.02 \sec$.
• Figure 5: Learning curves of 5 trials with random initial guesses around zero initialization. At around epoch 100, all trials achieve promising regression results.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4