sequential convex planning

Trajectory optimization for non-convex, differentially expensive or non-differentiable systems remains challenging, particularly under general equality and inequality constraints. Method: This paper proposes a gradient-free sequential convex programming (SCP) framework that constructs local convex approximations via interpolation of sampled points from dynamics, cost, and constraint functions—compatible with multiple-shooting and arbitrary constraints. Contribution/Results: It is the first to integrate sampling-based stochastic optimal control methods (e.g., Model Predictive Path Integral control) into the SCP paradigm, enabling derivative-free convexification. The framework unifies gradient-based deterministic and sampling-based stochastic approaches, drastically reducing reliance on gradient information while fully preserving compatibility with conventional SCP implementations. Empirical evaluation demonstrates high efficiency and robustness in motion planning and real-time control tasks.

This paper addresses the shortest-time trajectory planning problem for traversing a sequence of convex sets under velocity and acceleration constraints. To tackle its inherent nonconvexity, we propose a biconvex decomposition modeling approach that reformulates the original problem into an efficiently solvable biconvex structure. We further design an alternating convex optimization framework that requires no line search or trust-region parameters, guarantees strict feasibility of the trajectory at every iteration, and ensures global convergence. The method employs smooth B-spline parameterization and explicit modeling of sequential convex set constraints, enabling real-time execution while closely approximating the time-optimal solution. Experimental results demonstrate that our approach achieves speedups of several-fold over state-of-the-art nonconvex optimizers, matches the performance of industrial-grade waypoint planners, and generates trajectories significantly faster.

Generating optimal trajectories for dynamic systems—such as UAVs and robotic manipulators—under strong nonlinear dynamics, nonconvex input constraints, and real-time obstacle avoidance remains challenging. Method: This paper proposes a bilevel temporal decomposition optimization framework: an outer loop fixes the planning horizon, while an inner loop solves subproblems over dynamically constructed restricted convex sets. It innovatively couples temporal decomposition with an incremental convex set search mechanism. Contributions/Results: The framework ensures local optimality and feasibility while enabling efficient real-time computation; theoretical analysis proves convergence and reduced task completion time under mild conditions. Key techniques—including short-horizon convex reformulation, a customized incremental algorithm, and embedded obstacle constraints—significantly accelerate computation. Extensive simulations validate the method’s real-time performance, trajectory quality, and robustness against modeling uncertainties and environmental changes.

This work addresses the problem of constructing Safe Flight Corridors (SFCs) for autonomous navigation, aiming to efficiently approximate free space while ensuring trajectory safety. The proposed method introduces an online iterative convex covering optimization framework that alternately optimizes partially distributed variables and incorporates geometric heuristics. It jointly generates overlapping polyhedral segments—subject to waypoint constraints—balancing maximal volume coverage with kinematically feasible initialization. Its key contribution lies in the organic integration of convex optimization, polyhedral geometric modeling, and constraint-satisfaction optimization, enabling real-time SFC reconstruction within a two-stage motion planning pipeline. Extensive evaluation across diverse parametric environments demonstrates significant improvements in trajectory feasibility and computational efficiency. The approach provides a scalable theoretical and practical foundation for online safe navigation in complex, dynamic scenarios.

This work addresses the non-conservative collision avoidance problem between control-affine robotic systems and convex obstacles, formulating a differentiable Control Barrier Function (CBF) based on the minimum distance as the safety metric. The core challenge lies in the fact that the minimum distance is typically defined implicitly via optimization and is generally non-differentiable. To overcome this, we first introduce the class of strongly convex mappings, which rigorously guarantees the continuity and differentiability of the minimum distance. We then design an ordinary differential equation (ODE) derived from the Karush–Kuhn–Tucker (KKT) conditions to enable real-time analytical updates of both the minimum distance and its gradient. The framework supports heterogeneous convex set avoidance—e.g., ellipsoid–polyhedron interactions—and exact convex set algebraic operations without conservative approximations. In simulation, the method enables millisecond-scale quadratic programming (QP) solving for a quadrotor navigating a dense obstacle corridor, significantly improving safety guarantees and avoidance accuracy.

This work addresses the challenge of generating real-time, collision-free, and dynamically feasible trajectories for autonomous vehicles in complex environments by proposing a structured optimization approach based on Graphs of Convex Sets (GCS). The method models free space as a GCS and integrates Bézier curve path parameterization with polynomial time scaling within each convex region, embedding trajectory constraints under a simplified bicycle model and linear tire assumptions. By reformulating the nonlinear optimal control problem as a graph-based optimization that preserves convexity through continuous relaxation, the approach effectively unifies geometric and dynamic constraints. Experimental results demonstrate that the generated trajectories achieve efficient static obstacle avoidance and lane changes in CommonRoad scenarios, attaining solution accuracy comparable to nonlinear programming while significantly improving computational efficiency and reducing sensitivity to initial conditions.

This work addresses the problem of generating minimum-time smooth trajectories subject to high-order derivative constraints in environments with convex obstacles. The authors propose a biconvex optimization framework that jointly convexifies the time-optimal objective and dynamic constraints through a change of variables, while modeling collision avoidance via time-varying separating hyperplanes. This formulation yields an alternatingly optimizable biconvex structure that supports arbitrary-order derivative constraints, permits interruption at any iteration, and guarantees convergence while effectively escaping local minima. Notably, the method requires only a simple collision-free piecewise-linear path for initialization yet reliably converges to high-quality solutions. Evaluated on drone navigation and dual-arm box unloading tasks, the approach achieves trajectory quality and computational efficiency comparable to state-of-the-art decoupled planners, with broader applicability and strong robustness to poor initial guesses.

This work addresses the non-convex problem of planning high-order smooth (e.g., minimum-snap), collision-free trajectories for point robots amidst spherical obstacles. The authors formulate the task as a non-convex optimization over polynomial trajectories and present, for the first time, a theoretical analysis of its semidefinite programming (SDP) relaxation. Key contributions include establishing necessary and sufficient conditions for relaxation tightness, revealing the equivalence between relaxed solutions and globally optimal trajectories in an augmented space, and leveraging symmetry to reduce the SDP dimensionality so that it scales linearly with the polynomial degree—irrespective of the ambient environment dimension. Integrated into an RRT framework as a convex steering function, the method achieves 10–100× speedups over SNOPT/IPOPT in quadrotor C⁴-continuous minimum-snap planning, significantly reduces solution time variance, and reliably yields high-quality locally optimal trajectories.

本文提出一种基于ADMM的轨迹优化方法，快速稳健地解决满足时序逻辑要求的安全连续时间运动规划问题。

该论文介绍了一个名为OpenSCvx的开源Python框架，用于解决轨迹优化问题，通过提供符号建模接口自动生成并求解轨迹优化问题。