A Rapid Trajectory Optimization and Control Framework for Resource-Constrained Applications

TL;DR

The paper addresses real-time trajectory optimization for resource-constrained autonomous space systems by introducing an integral Chebyshev collocation-based MPC framework. By mapping dynamics to the Chebyshev domain with $\tau \in [-1,1]$ and formulating the continuous-time cost $J$ into a quadratic program via Gaussian quadrature, the method yields a precomputable Hessian $H$ and gradient $\mathbf{f}$ for efficient online optimization. Constraints are handled with a slack variable and linear inequalities/equalities, and collision avoidance is achieved through differential collision detection for convex polytopes (DCOL) coupled with a soft keep-out mechanism. The approach demonstrates substantial computational savings on edge hardware, enables larger horizons without prohibitive resource use, and is validated in a TPODS docking scenario with robust KOC/DCOL-based safety, offering practical impact for fast, reliable autonomous space operations.

Abstract

This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem and recursive re-evaluation of the optimal trajectories, minimization of the L2 norms of the state and control errors are transcribed into a quadratic program. Control and state variable constraints are parameterized using Chebyshev polynomials and are accommodated in the optimal trajectory generation programs to incorporate the actuator limits and keep-out constraints. Differentiable collision detection of polytopes is leveraged for optimal collision avoidance. Results obtained from the collocation methods are benchmarked against the existing approaches on an edge computer to outline the performance improvements. Finally, collaborative control scenarios involving multi-agent space systems are considered to demonstrate the technical merits of the proposed work.

Figures (6)

• Figure 1: Comparison of trajectories and optimal input for double integrator for $T_s = 0.5$ s, $p = 5$ samples, and $n = 3$.
• Figure 2: Computational performance of MPC$^3$ for different state dimensions and control horizon. Generated on a computer with $11^\text{th}$ Gen Intel® Core™ i5-1135G7 @ 2.40GHz, 16 GB RAM, for running a MATLAB® script. MATLAB® interface for OSQP is used to integrate OSQP osqp-codegen.
• Figure 3: Computational performance of MPC$^3$ for different state dimensions and control horizon, with fixed n = 3. Generated on Teensy 4.1 development board, for running a single iteration of optimization routine, built and deployed from a MATLAB® script.
• Figure 4: Guidance algorithm for docking of TPODS with a stationary target consists of three distinct guidance modes. For each mode, TPODS is commanded to move along the optimal trajectory, which passes through the target if no collision avoidance maneuver is executed. The availability of vision measurements is depicted by a color change of the FOV cone.
• Figure 5: Time history of translation velocities and desired forces for docking scenario shown in Fig. \ref{['fig:guidance']}