汽车案例Automotive Cases

Verifiable Safety Motion Planning

安全运动规划：面向复杂运动约束的可验证安全层 Safe Motion Planning: A Verifiable Safety Layer for Complex Motion Constraints

在网络输出与执行器之间建立基于物理与几何规则的可验证安全兜底层，让模块化、E2E 与 VLA 架构的输出轨迹始终不越界。 A verifiable, physics- and geometry-based safety layer between neural-network outputs and actuators—keeping trajectories within hard boundaries across modular, E2E, and VLA stacks.

Nonlinear Hard Constraints Millisecond Solving White-box Safety
01Architecture Evolution

自动驾驶规划必须满足物理安全约束Autonomous-Driving Planning Must Satisfy Physical Safety Constraints

自动驾驶软件正从全白盒模块化向 AI/数据驱动的端到端（E2E/VLA）快速演进。但深度学习的黑盒属性无法在物理层面给出 100% 的安全证明。

因此，无论上层采用规则、学习还是多模态模型，都需要在规划输出与执行器之间建立一层可验证、可重现、与架构解耦的运动安全底座。

Autonomous-driving software is rapidly moving from fully transparent modular stacks to AI- and data-driven E2E/VLA architectures. Yet black-box deep learning cannot provide a 100% physical safety proof.

Whether the upper layer is rule-based, learned, or multimodal, a verifiable, reproducible, architecture-agnostic motion-safety foundation is still required between planning outputs and actuators.

Safety Architecture

Modular
E2E
VLA
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OPTIMake

可验证安全优化层Verifiable Safety Layer

HARD CONSTRAINTS
GeometryPhysicsDynamics
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转向 · 驱动 · 制动执行器Steering · Drive · Brake Actuators
02Challenges vs. Advantages

传统方法 vs. OPTIMakeTraditional Challenges vs. OPTIMake Advantages

Traditional Bottleneck

弱求解能力倒逼“场景驱动调参”Weak Solvers Force Scenario-Driven Tuning

在密集交互、非规则道路及精细泊车等复杂工况下，避障约束本质上是高维、非凸且非线性的。传统开发面临严峻困局：

In dense interactions, irregular roads, and precision parking, collision-avoidance constraints are inherently high-dimensional, nonconvex, and nonlinear. Conventional development faces a severe dilemma:

01

复杂约束被迫简化Forced Simplification of Complex Constraints

受限于传统求解方法（如常规 c-iLQR）的求解能力，工程师被迫将硬约束“软化”为惩罚项，或将复杂物理几何体粗暴简化为点或半空间。

Limited by conventional solvers such as standard c-iLQR, engineers must soften hard constraints into penalties or reduce complex physical geometry to points and half-spaces.

02

算法退化与算法维护迭代成本高Algorithm Degradation and High Iteration Costs

几何建模失真使算法对初始值极度敏感，工程师不得不编写海量边缘逻辑，在不同场景下反复凑权重与调参（Scenario-driven tuning）。一旦遭遇无解工况，传统求解器往往直接报出 failure，缺乏明确的数值解释能力。

Distorted geometry makes the algorithm highly sensitive to initialization, forcing extensive edge-case logic and scenario-driven weight tuning. When a problem is infeasible, conventional solvers often return only “failure,” without a clear numerical explanation.

OPTIMake Breakthrough

以系统化求解能力与可解释分析突破瓶颈Break Through with Systematic Solving and Explainable Analysis

01

统一吸纳并直接求解复杂物理约束Unify and Directly Solve Complex Physical Constraints

OPTIMake 改变了“牺牲模型真实性迎合弱求解器”的逻辑，凭借底层高性能的优化引擎，将高维、非凸、非线性几何与物理硬约束系统化地统一考虑并直接优化，在保留精确几何与物理约束的前提下，实现毫秒级轨迹规划求解。

OPTIMake reverses the logic of sacrificing model fidelity to accommodate a weak solver. With its high-performance underlying optimization engine, it systematically unifies and directly optimizes high-dimensional, nonconvex, nonlinear geometric and physical hard constraints, delivering millisecond-level trajectory planning while preserving exact geometry and physics.

02

数值可解释的分析与“最小违背解”兜底Numerically Explainable Analysis and Minimal-Violation Fallback

OPTIMake 可在指定区域内精确评估求解可行性（Feasibility）。当遭遇极限不可行工况时，求解器能够根据用户预设的优先级，返回当前数学条件下的最小违背解（Minimal Violation Solution），而不是简单报出 failure。

清晰的数值解释使工程人员能够在车辆动力学极限、不同环境要素间距等约束之间进行精准 Trade-off，确保系统在极限安全边缘下依然平滑、可控、不崩溃。

OPTIMake precisely evaluates feasibility within a specified region. Under extreme infeasibility, it follows user-defined priorities and returns the Minimal Violation Solution under the current mathematical conditions instead of simply reporting failure.

Clear numerical explanations enable precise trade-offs among vehicle-dynamics limits and clearances to different environmental elements, keeping the system smooth, controllable, and operational at the safety limit.

03Native Collision Avoidance

一套求解内核，统一三类环境要素One Solver Core for Three Classes of Environmental Elements

从矩形表示的交互车辆，到由折线描述的道路边界，再到感知系统输出的占据栅格，OPTIMake 分别提供对应的避障约束接口，并在同一求解框架中统一处理。

From interacting vehicles represented as rectangles, to road boundaries described by polylines, to occupancy grids output by the perception system, OPTIMake provides a dedicated obstacle-avoidance constraint interface for each and handles them uniformly within the same solving framework.

01rect_to_rect

规则几何型要素：矩形—矩形避障Regular Geometry: Rectangle-to-Rectangle Avoidance

面向周边动态车辆与静态障碍车，精确计算带 Pose 的刚体矩形。车辆速度 v 与安全时距 tgap 可显式进入模型，以 length + v × tgap 形成随车速延展的安全区域。

Precisely models rigid rectangles with explicit poses for moving and parked vehicles. Speed v and time gap tgap can enter the model directly, extending the safety envelope as length + v × tgap.

工程收益：Engineering value: 覆盖高速 Cut-in 与密集路口多车交互，避免点/圆盘近似导致的几何失真、盲目急刹与低通行效率。Handles high-speed cut-ins and dense intersection interactions without point/disc distortion, blind emergency braking, or lost throughput.

Dynamic Safety Envelope

CONSTRAINT ACTIVE
v × t_gap EGO RECTANGLE + SPEED-ADAPTIVE BUBBLE
rect_to_rect.py
查看完整文档 ↗Full documentation ↗ 
dynamic_length = length_a + v * t_gap
rect2rect_ineq = rectangle_to_rectangle_inequality(
    x_a, y_a, phi_a, width_a, dynamic_length, x_b, y_b, phi_b, width_b, length_b,
    distance_to_avoid, center_point_avoidance=True)
prob.inequality(rect2rect_ineq)
02point_to_boundary

连续线型要素：polyline边界避障Continuous Linear Geometry: Polyline Boundary Avoidance

面向路缘石、车道边界、施工隔离墩、收费站通道与导流线，求解器原生计算车体几何点/圆盘到任意 Polyline 的物理距离，并严格满足安全阈值。

For curbs, lane edges, construction barriers, toll lanes, and channelizing lines, the solver natively computes physical distances from vehicle points/discs to arbitrary polylines and enforces the safety threshold.

工程收益：Engineering value: 覆盖 U-turn、环岛、连续 S 弯与狭窄通道，支持精确贴边行驶，避免规则包围盒在非规则空间内频繁报“无解”。Covers U-turns, roundabouts, S-curves, and narrow passages, enabling close boundary tracking without false infeasibility from regular bounding boxes.

Exact Polyline Corridor

CLEARANCE ≥ 0.3 m
CLEARANCE POLYLINE VERTICES · CONTINUOUS DISTANCE FIELD
point_to_boundary.py
查看完整文档 ↗Full documentation ↗ 
left_bound  = boundary('left_bound',  max_dim=50, left_positive=False)
right_bound = boundary('right_bound', max_dim=50, left_positive=True)
ineq_left  = point_to_boundary_inequality(left_bound, px, py, distance_to_avoid)
ineq_right = point_to_boundary_inequality(right_bound, px, py, distance_to_avoid)
prob.inequality(ineq_left)
prob.inequality(ineq_right)
03point_to_occ

非结构化离散要素：栅格避障Unstructured Discrete Geometry: Occupancy-Grid Avoidance

面向散落石块、立柱、矮墙与杂物等异形障碍，感知 OCC 网格可无损直连。求解器自动生成欧氏符号距离场（ESDF），将离散栅格转化为可高效优化的连续数学约束。

For irregular rocks, columns, low walls, and debris, perception occupancy grids connect without geometric extraction. The solver generates an Euclidean signed distance field (ESDF), turning discrete cells into efficient continuous constraints.

工程收益：Engineering value: 覆盖 AVP/APA、园区与乡村非结构化道路，无需上层做几何特征提取和近似过滤，减少在杂乱栅格缝隙中“被卡住”的情况。Supports AVP/APA, campuses, and rural roads without upstream feature extraction or approximate filtering, reducing vehicles getting stuck in cluttered grid gaps.

Occupancy Grid · ESDF

D → R · SAFE PATH FOUND
TARGET SLOT PARKING AISLE D → R STAGE 1 · DRIVE FORWARD STAGE 2 · REVERSE INTO SLOT
point_to_occ.py
查看完整文档 ↗Full documentation ↗ 
occupancy_map = occupancy_map_2d(name, length, width, resolution, origin_x, origin_y, origin_phi)
ineq = point_to_occupancy_map_inequality(occupancy_map, px, py, distance_to_avoid)
prob.inequality(ineq)
04Flexible Configuration

不限构型：从标准矩形到任意关键点几何避障Any Configuration: From Standard Rectangles to Key-Point Geometry

真实量产场景中的 Ego 并不总是一个简单的矩形。窄车位泊车时，后视镜、车角等局部突出结构可能成为实际碰撞风险；卡车规划需要考虑牵引车 + 挂车的组合构型；船舶等特殊载体则可能具有连续曲线、非规则边界。

基于OPTIMake避障约束的原生接口，OPTIMake 在保留 rect_to_rect 标准矩形精确避障的同时，可通过 Point-to-Boundary 与 Point-to-OCC，在欧式空间中灵活选择 Ego 几何构型上的关键点，并直接定义这些关键点与环境之间的约束关系，无需将所有主体强行简化成统一几何模型。

A production Ego is not always a simple rectangle. Mirrors and body corners can determine clearance in tight parking; trucks require a coupled tractor-trailer footprint; marine craft may have continuous curves and irregular boundaries.

Building on the native OPTIMake obstacle-avoidance constraint interfaces, OPTIMake retains exact rect_to_rect avoidance for standard rectangles while also offering Point-to-Boundary and Point-to-OCC, so engineers can freely choose key points on the Ego geometry in Euclidean space and directly define the constraints between those points and the environment, without forcing every body into a single simplified geometric model.

CUSTOM EGO GEOMETRY · KEY-POINT CONSTRAINTS CURVED BOUNDARY OCCUPANCY GRID EGO Point-to-Boundary Point-to-OCC
用户定义的安全关键点User-defined safety points Point-to-Boundary Point-to-OCC
01 / SAFETY POINTS

任意构型，自由定义安全关注点Define Safety-Critical Points on Any Configuration

工程师可以根据不同载体和场景，选择车角、后视镜、挂车边缘、船艏船艉等关键点，构建与实际碰撞风险相匹配的几何表达。

Select corners, mirrors, trailer edges, bow, stern, or other critical locations to represent the actual collision risks of each platform and scenario.

02 / PRECISE OBSTACLE AVOIDANCE

精确避障距离，软硬可调Precise Obstacle Avoidance with Tunable Constraints

可直接建立 Ego 关键点到不规则障碍物及曲线边界的精确距离约束。支持根据安全优先级灵活配置硬约束（绝对不可越界）与软约束（带松弛变量），兼顾极致安全与可行解求解效率。

Directly constrain the precise distance from Ego key points to irregular obstacles and curved boundaries. Hard constraints (absolutely not to be violated) and soft constraints (with slack variables) can be configured flexibly according to safety priority, balancing uncompromising safety with efficient computation of feasible solutions.

05Engineering Value

从“让问题适应求解器”转向“让求解器还原真实问题”From Making Problems Fit the Solver to Making the Solver Represent Reality

OPTIMake 改变传统运动规划开发范式：工程师不再因为求解能力限制而牺牲模型真实性，而是将车辆、道路与非结构化障碍的复杂物理约束统一处理。最终形成一套面向架构演进、跨场景复用的安全底座。

OPTIMake changes the planning-and-control paradigm. Engineers no longer sacrifice model fidelity for a weak solver; vehicle, road, and unstructured-obstacle constraints are absorbed into one optimization core, forming a reusable safety foundation across architectures and scenarios.

Unified

统一多维环境约束Environmental constraints

Verifiable

物理安全可验证Physical safety

Robust

减少场景补丁调参Less scenario tuning

Real-time

毫秒级嵌入式求解Millisecond solving

让复杂物理约束成为系统能力，而不是场景负担 Make Complex Physical Constraints a System Capability, Not a Scenario Burden

了解 OPTIMake 如何处理复杂物理约束，我们将提供详细的演示案例与技术支持 Learn how OPTIMake handles complex physical constraints—we provide detailed demo cases and technical support.

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