An Optimization-Based Planner with B-spline Parameterized Continuous-Time Reference Signals

TL;DR

This paper tackles the persistent frequency gap between low-frequency high-level planners and high-frequency low-level controllers in robot navigation by introducing BSPOP, a planner that parameterizes continuous-time control inputs with B-splines. By optimizing control points rather than discrete control samples, BSPOP maintains a fixed number of decision variables regardless of horizon subdivision and exploits the convex hull property to automatically satisfy convex control constraints, reducing inequalities and speeding computation. The approach yields continuous-time references that high-frequency controllers can track, achieving planning quality comparable to high-frequency baselines but with lower onboard computational demands. Simulations and real-world experiments show smoother, more feasible trajectories under non-trivial control constraints and improved performance at the same planner frequency, highlighting BSPOP’s practical impact for computation-constrained autonomous systems.

Abstract

For the cascaded planning and control modules implemented for robot navigation, the frequency gap between the planner and controller has received limited attention. In this study, we introduce a novel B-spline parameterized optimization-based planner (BSPOP) designed to address the frequency gap challenge with limited onboard computational power in robots. The proposed planner generates continuous-time control inputs for low-level controllers running at arbitrary frequencies to track. Furthermore, when considering the convex control action sets, BSPOP uses the convex hull property to automatically constrain the continuous-time control inputs within the convex set. Consequently, compared with the discrete-time optimization-based planners, BSPOP reduces the number of decision variables and inequality constraints, which improves computational efficiency as a byproduct. Simulation results demonstrate that our approach can achieve a comparable planning performance to the high-frequency baseline optimization-based planners while demanding less computational power. Both simulation and experiment results show that the proposed method performs better in planning compared with baseline planners in the same frequency.

Figures (5)

• Figure 1: An illustration of discrete-time control inputs and B-spline parametrized continuous-time control signal within a convex set of control actions.
• Figure 2: The performance of the BSPOP and the baseline planners under boxed control constraints.
• Figure 3: The performance of the BSPOP and the baseline planners with control inputs under non-trivial control constraints.
• Figure 4: The performance of the baseline MPC performance when control inputs are constrained in diamond-shape area.
• Figure 5: Experiments using a Polaris Gem v-2 in a known environment.

Theorems & Definitions (1)

• Remark 1