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<article class="md-content__inner md-typeset">
<h1 id="-">视觉-语言-动作模型<a class="headerlink" href="#-" title="Permanent link">&para;</a></h1>
<p><em>视觉-语言-动作模型（VLA）将视觉理解、语言理解和行动控制统一到单个神经网络中。本章涵盖VLA架构、动作标记化、RT-2、Octo、OpenVLA、预训练策略、泛化能力、与具体形态无关的模型以及基准测试。</em></p>
<ul>
<li>
<p>在前面的文件中，我们涵盖了感知（感知世界）和机器人学习（控制身体）。传统上，这些是独立的流程：感知模块检测物体，语言模块解释指令，控制模块生成动作。每个模块独立设计、训练和调试。</p>
</li>
<li>
<p><strong>视觉-语言-动作模型（VLA）</strong>将这一流程压缩为单个神经网络。模型接收图像（视觉）和自然语言指令（语言），并输出电机命令（动作）。一个模型，端到端。</p>
</li>
<li>
<p>这沿袭了我们在第10章看到的统一趋势：正如多模态模型将视觉和语言理解合并到一个架构中一样，VLA将这一趋势扩展到物理行动。关键洞见在于，语言为指定任务提供了自然、灵活的接口（"拿起红色杯子放到架子上"），而大规模预训练的视觉-语言模型已经理解图像和指令。</p>
</li>
</ul>
<h2 id="-_1">从视觉-语言到行动<a class="headerlink" href="#-_1" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>回顾第10章，<strong>视觉-语言模型（VLM）</strong>如LLaVA和Flamingo接收图像和文本作为输入，并生成文本作为输出。它们理解场景、回答问题、遵循指令——全部通过语言完成。</p>
</li>
<li>
<p>VLA提出的问题是：如果输出不是文本而是<strong>机器人动作</strong>呢？模型不再生成"红色杯子在桌子的左侧"，而是生成一系列电机命令，驱动手臂去抓取那个杯子。</p>
</li>
<li>
<p>关键的架构洞见是，动作可以像单词一样表示为标记。如果VLM使用下一个标记预测逐个生成语言标记，那么VLA以同样的方式生成动作标记。Transformer从根本上并不关心输出标记表示"杯子"还是"将夹爪向前移动2厘米"。</p>
</li>
<li>
<p>这重新定义了机器人控制为序列建模问题，这正是transformer擅长的（第7章）。模型学习映射：（图像观测，语言指令）<span class="arithmatex">\(\\to\)</span>（动作标记序列）。</p>
</li>
</ul>
<h2 id="vla">VLA架构<a class="headerlink" href="#vla" title="Permanent link">&para;</a></h2>
<p><img alt="VLA架构：相机图像和语言指令被编码为标记，由LLM主干网络处理，并解码为机器人动作" src="../../images/vla_architecture.svg" /></p>
<ul>
<li>
<p>典型的VLA有三个组件：</p>
<ul>
<li>
<p><strong>视觉编码器</strong>：将相机图像处理为视觉标记。通常是预训练的ViT（第8章）或SigLIP编码器（第10章）。图像被分割成块，每个块嵌入为一个标记，与标准视觉transformer完全一样。</p>
</li>
<li>
<p><strong>语言模型主干网络</strong>：一个预训练的LLM（例如LLaMA、PaLM），处理交错的视觉标记和语言标记序列。这就是推理发生的地方：模型通过同时关注指令和视觉特征来理解"拿起<strong>红色</strong>杯子"。</p>
</li>
<li>
<p><strong>动作头</strong>：将LLM的输出映射到机器人动作。可以是一个简单的MLP，将最后的隐藏状态映射到连续动作值，或者是一种将动作转换为离散标记的方案，由LLM的现有词汇表来预测。</p>
</li>
</ul>
</li>
<li>
<p>架构看起来像：</p>
</li>
</ul>
<div class="arithmatex">\[\\text{图像} \\xrightarrow{\\text{ViT}} \\text{视觉标记} \\quad + \\quad \\text{指令} \\xrightarrow{\\text{分词器}} \\text{语言标记} \\quad \\xrightarrow{\\text{LLM}} \\quad \\text{动作标记}\]</div>
<ul>
<li>视觉标记和语言标记被拼接（或交错）并输入到transformer主干网络，后者自回归地生成动作标记。这与VLM（第10章）的架构相同，但输出模态是动作而非文本。</li>
</ul>
<h2 id="_1">动作标记化<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
<ul>
<li>机器人动作是连续的：关节速度、末端执行器位置、夹爪宽度。这些必须转换为离散标记才能让LLM生成。</li>
</ul>
<p><img alt="动作标记化：连续动作值被分箱为离散索引，LLM将其作为标记生成" src="../../images/action_tokenisation.svg" /></p>
<ul>
<li>
<p>最简单的方法是<strong>均匀离散化</strong>。每个动作维度被划分为<span class="arithmatex">\(N\)</span>个箱，覆盖有效值范围。例如，如果x方向速度范围从-0.1到0.1米/秒，使用256个箱，每个箱代表<span class="arithmatex">\(\\frac{0.2}{256} \\approx 0.8\)</span>毫米/秒。动作值被映射到最近的箱索引，该索引成为一个标记。</p>
</li>
<li>
<p>对于7个动作维度（6自由度+夹爪）和每个维度256个箱，动作词汇表有<span class="arithmatex">\(7 \\times 256 = 1792\)</span>个标记。这些被添加到LLM现有的文本词汇表中。模型每个维度生成一个动作标记，自回归地，就像生成单词一样。</p>
</li>
<li>
<p><strong>动作分块</strong>一次预测多个未来时间步，而不是单个动作。如果块大小为<span class="arithmatex">\(H\)</span>，模型输出<span class="arithmatex">\(H \\times d\)</span>个标记（其中<span class="arithmatex">\(d\)</span>是动作维度）。这对于平滑、时间连贯的运动至关重要。一次预测一步会产生抖动行为，因为每次预测都是独立的。分块迫使模型规划一个短轨迹，捕获时间结构。</p>
</li>
<li>
<p>更复杂的方法使用<strong>学习型标记化</strong>，通过VQ-VAE（第10章）。VQ-VAE编码器将连续动作序列映射到离散码本索引序列，解码器从这些索引重建连续动作。LLM然后生成码本索引，而不是均匀分箱的值。这类似于图像分词器（第10章）如何将视觉信息压缩为紧凑的离散编码。</p>
</li>
</ul>
<h2 id="vla_1">关键VLA模型<a class="headerlink" href="#vla_1" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p><strong>RT-2</strong>（机器人Transformer 2，Google DeepMind）是第一个大规模VLA。它使用预训练的VLM（PaLM-E或PaLI-X，参数高达55B）并在机器人示范数据上微调。动作表示为文本字符串：标记序列"1 128 91 241 5 101 127"编码了一个7维动作（每个数字是箱索引）。</p>
</li>
<li>
<p>RT-2展示了一个显著特性：来自VLM主干网络的<strong>涌现能力</strong>迁移到了机器人领域。模型可以遵循涉及从未在机器人数据中见过的概念的指令（例如，"将香蕉移动到以A开头的国家"需要视觉物体识别+世界知识+行动）。VLM的语言理解和视觉推理"免费"获得。</p>
</li>
<li>
<p>RT-2的局限性在于它是在单个机器人形态（特定的手臂和特定的夹爪）的数据上训练的。它不能泛化到不同的机器人。</p>
</li>
<li>
<p><strong>Octo</strong>（加州大学伯克利分校）是一个开源的、<strong>与具体形态无关</strong>的VLA，设计用于跨不同机器人平台工作。关键创新包括：</p>
<ul>
<li><strong>扩散动作头</strong>，而不是自回归标记预测。动作头获取transformer的输出，并通过去噪扩散过程（第8章）生成动作。这自然地处理了多模态动作分布（见下图），即存在多个有效的任务完成方式。</li>
</ul>
</li>
</ul>
<p><img alt="多模态动作分布：回归将两条有效路径平均为一条穿过障碍物的无效路径" src="../../images/multimodal_action_distribution.svg" /></p>
<div class="highlight"><pre><span></span><code>- **灵活的观测和动作空间**：Octo为不同的机器人配置使用特定于任务的标记化器。它在Open X-Embodiment数据集上预训练，该数据集包含来自22种不同机器人形态的示范。
- **高效微调**：Octo只需100个示范就可以微调到新机器人，使其适用于数据有限的实验室。
</code></pre></div>
<ul>
<li>
<p><strong>OpenVLA</strong>（斯坦福大学、加州大学伯克利分校）采用微调现有开源VLM（基于Llama）用于机器人技术的方法。它使用7B参数主干网络、均匀动作标记化（每个维度256个箱），并在Open X-Embodiment数据上训练。其优势在于简单性：架构是标准的VLM，动作标记被附加到词汇表中，使其易于使用现有的LLM基础设施进行训练和部署。</p>
</li>
<li>
<p><strong><span class="arithmatex">\(\\pi_0\)</span></strong>（Physical Intelligence）代表了当前最高水平。它使用预训练的VLM主干网络和<strong>流匹配</strong>动作头（第8章）。流匹配通过学习一个速度场将噪声传输到动作分布来生成动作，产生平滑、时间连贯的动作轨迹。<span class="arithmatex">\(\\pi_0\)</span>展示了卓越的通用性，在多种机器人形态（包括双臂操作和灵巧手控制）上执行任务。</p>
</li>
</ul>
<h2 id="_2">预训练配方<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>VLA极大地受益于预训练的VLM主干网络，这些网络已经理解视觉场景和语言。训练流程通常分为几个阶段：</p>
<ol>
<li>
<p><strong>VLM预训练</strong>：在数十亿来自互联网的图像-文本对（CLIP、SigLIP、LLaVA风格的训练，如第10章所述）上训练（或使用现成的）视觉-语言模型。</p>
</li>
<li>
<p><strong>机器人数据协同训练</strong>：在互联网数据和机器人示范数据的混合上微调VLM。互联网数据防止视觉和语言理解的灾难性遗忘，而机器人数据教授动作生成。混合比例很重要：机器人数据过多会降低语言理解，过少则无法学习动作。</p>
</li>
<li>
<p><strong>特定任务微调</strong>：可选地在特定任务或机器人的示范上进行微调，通常使用LoRA（第10章）保持可训练参数数量较少。</p>
</li>
</ol>
</li>
<li>
<p>机器人数据的数量比互联网数据少数个数量级。VLM可能在上数十亿张图像上预训练，但最大的机器人数据集（Open X-Embodiment）在所有形态上只有数百万帧。这种数据稀缺性正是从预训练VLM开始至关重要的原因：视觉和语言表示可以迁移，只有动作映射需要从有限的机器人数据中学习。</p>
</li>
</ul>
<h2 id="_3">泛化能力<a class="headerlink" href="#_3" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>VLA的承诺是<strong>泛化</strong>：执行训练中未见的任务，使用未见过的物体，在未见过的环境中，遵循未见过的指令。</p>
</li>
<li>
<p>VLA沿多个轴进行泛化：</p>
<ul>
<li>
<p><strong>新颖物体</strong>：VLM主干网络从互联网预训练中识别物体。如果模型从网络图像中知道"螺丝刀"长什么样，即使没有机器人示范涉及螺丝刀，它也能操作螺丝刀。</p>
</li>
<li>
<p><strong>新颖指令</strong>：组合语言理解使模型能够遵循已知概念的新组合。"将蓝色方块堆叠在绿色方块上"即使训练只展示了堆叠红色方块也能工作，因为模型从语言预训练中理解了颜色形容词。</p>
</li>
<li>
<p><strong>新颖环境</strong>：在一定程度上，VLA跨视觉域（不同的桌子、光照、背景）迁移，因为视觉编码器在多样化的网络图像上预训练。但这有局限性：在实验室训练的机器人可能在杂乱厨房中遇到困难。</p>
</li>
<li>
<p><strong>新颖形态</strong>：这是最难的轴。不同机器人有不同的动作空间（关节角度 vs. 末端执行器速度）、不同的传感器（腕部相机 vs. 头顶相机）和不同的物理能力。与形态无关的模型如Octo和<span class="arithmatex">\(\\pi_0\)</span>通过灵活的标记化器和跨多种机器人类型的预训练来解决这一问题。</p>
</li>
</ul>
</li>
<li>
<p>泛化能力通过<strong>保留任务</strong>进行评估：机器人被要求执行从未训练过的任务。在新颖任务上50-80%的成功率被认为是强劲的结果，而在分布内任务上成功率通常&gt;90%。随着模型规模扩大和机器人数据集增长，这一差距正在缩小。</p>
</li>
</ul>
<h2 id="_4">与形态无关的模型<a class="headerlink" href="#_4" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>该领域正朝着"一个模型，多种机器人"的方向发展。不再为每个机器人训练单独的策略，而是单个VLA处理多种形态。</p>
</li>
<li>
<p>这需要解决<strong>动作空间不匹配</strong>问题。一个7自由度手臂带平行夹爪有7个动作维度。双臂设置是14个。四足机器人有12个。类人机器人有30个以上。动作标记化必须足够灵活以处理所有这些。</p>
</li>
<li>
<p>解决方案包括：</p>
<ul>
<li><strong>填充动作向量</strong>：使用最大的动作空间，较小的用零填充。</li>
<li><strong>每种形态的动作头</strong>：共享的transformer主干网络，每种机器人类型有单独的小型MLP。</li>
<li><strong>归一化动作表示</strong>：在共同框架中表示所有动作（如世界坐标系中的末端执行器速度），使产生类似末端执行器运动的不同机器人共享相同的动作标记。</li>
</ul>
</li>
<li>
<p>共享主干网络学习通用的视觉和语言理解，加上通用的操作策略（从上方接近、对齐物体、闭合夹爪）。特定于形态的组件只需要将这些高层策略转化为具体的电机命令。</p>
</li>
</ul>
<h2 id="_5">基准测试与评估<a class="headerlink" href="#_5" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>评估VLA具有独特的挑战性，因为它需要物理机器人实验（或高保真仿真）。</p>
</li>
<li>
<p><strong>SIMPLER</strong>（机器人学习模拟操作策略评估）提供了标准化的仿真环境，无需物理硬件即可比较VLA性能。它与现实世界的成功率相关性良好，并实现了可复现的基准测试。</p>
</li>
<li>
<p><strong>现实世界评估</strong>仍然是金标准。典型协议：</p>
<ol>
<li>定义一组具有明确成功标准的任务（物体到达目标位置、选择正确物体、在时限内完成任务）。</li>
<li>每次任务运行<span class="arithmatex">\(N\)</span>次试验（通常10-50次）。</li>
<li>报告成功率及置信区间。</li>
<li>包括保留任务（从未训练过的）以衡量泛化能力。</li>
</ol>
</li>
<li>
<p><strong>Open X-Embodiment</strong>数据集和基准测试汇总了来自22个机构、跨越多个机器人平台的机器人数据。它提供了共享示范的标准格式和用于跨形态迁移的通用评估套件。</p>
</li>
</ul>
<h2 id="colabnotebook">编程任务（使用CoLab或notebook）<a class="headerlink" href="#colabnotebook" title="Permanent link">&para;</a></h2>
<ol>
<li>
<p>实现动作标记化：将连续动作离散化为箱并重建。观察量化误差随箱数量的变化。
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 连续动作：7个维度（6自由度+夹爪）</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">action_true</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.023</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.051</span><span class="p">,</span> <span class="mf">0.012</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.03</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">])</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">action_min</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">])</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">action_max</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">])</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">for</span> <span class="n">n_bins</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">64</span><span class="p">,</span> <span class="mi">256</span><span class="p">,</span> <span class="mi">1024</span><span class="p">]:</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="c1"># 标记化：将连续值映射为箱索引</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">normalised</span> <span class="o">=</span> <span class="p">(</span><span class="n">action_true</span> <span class="o">-</span> <span class="n">action_min</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">action_max</span> <span class="o">-</span> <span class="n">action_min</span><span class="p">)</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">tokens</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">clip</span><span class="p">((</span><span class="n">normalised</span> <span class="o">*</span> <span class="n">n_bins</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">),</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n_bins</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="c1"># 去标记化：将箱索引映射回连续值</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="n">reconstructed</span> <span class="o">=</span> <span class="p">(</span><span class="n">tokens</span> <span class="o">+</span> <span class="mf">0.5</span><span class="p">)</span> <span class="o">/</span> <span class="n">n_bins</span> <span class="o">*</span> <span class="p">(</span><span class="n">action_max</span> <span class="o">-</span> <span class="n">action_min</span><span class="p">)</span> <span class="o">+</span> <span class="n">action_min</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="n">error</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">action_true</span> <span class="o">-</span> <span class="n">reconstructed</span><span class="p">)</span>
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;箱数=</span><span class="si">{</span><span class="n">n_bins</span><span class="si">:</span><span class="s2">4d</span><span class="si">}</span><span class="s2"> 标记=</span><span class="si">{</span><span class="n">tokens</span><span class="si">}</span><span class="s2"> 误差=</span><span class="si">{</span><span class="n">error</span><span class="si">:</span><span class="s2">.6f</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
</code></pre></div></p>
</li>
<li>
<p>模拟动作分块与单步预测的比较。生成平滑轨迹，向单步预测添加噪声，并与分块预测比较。
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1"># 真实平滑轨迹（例如，伸手动作）</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">t</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">gt_x</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">gt_y</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">jnp</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="c1"># 单步：每次预测有独立噪声</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">rng</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="n">noise_ss</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">rng</span><span class="p">,</span> <span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.05</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="n">single_step</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">gt_x</span><span class="p">,</span> <span class="n">gt_y</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">noise_ss</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="c1"># 单步误差累积漂移</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="n">single_step_cumulative</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">noise_ss</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="mf">0.3</span> <span class="o">+</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">gt_x</span><span class="p">,</span> <span class="n">gt_y</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="c1"># 分块（块大小=10）：块内噪声关联，更平滑</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="n">chunk_size</span> <span class="o">=</span> <span class="mi">10</span>
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">rng2</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="n">chunks</span> <span class="o">=</span> <span class="p">[]</span>
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="n">chunk_size</span><span class="p">):</span>
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a> <span class="n">chunk_noise</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">fold_in</span><span class="p">(</span><span class="n">rng2</span><span class="p">,</span> <span class="n">i</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,))</span> <span class="o">*</span> <span class="mf">0.05</span>
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a> <span class="n">chunk</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">gt_x</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">chunk_size</span><span class="p">],</span> <span class="n">gt_y</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">chunk_size</span><span class="p">]],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a> <span class="n">chunks</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">chunk</span> <span class="o">+</span> <span class="n">chunk_noise</span><span class="p">)</span>
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="n">chunked</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">chunks</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a>
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">gt_x</span><span class="p">,</span> <span class="n">gt_y</span><span class="p">,</span> <span class="s2">&quot;k-&quot;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;真实轨迹&quot;</span><span class="p">)</span>
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">single_step_cumulative</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">single_step_cumulative</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span>
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a> <span class="s2">&quot;r-&quot;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.7</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;单步（漂移）&quot;</span><span class="p">)</span>
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">chunked</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">chunked</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">&quot;b-&quot;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.7</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;分块（稳定）&quot;</span><span class="p">)</span>
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">();</span> <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">);</span> <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;动作分块 vs 单步预测&quot;</span><span class="p">)</span>
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</code></pre></div></p>
</li>
<li>
<p>可视化VLA动作分布如何是多模态的。使用简单的2D高斯混合来展示为什么扩散/流匹配动作头优于回归。
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="c1"># 绕过障碍物的两种有效方式：左边或右边</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">rng</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">k1</span><span class="p">,</span> <span class="n">k2</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">rng</span><span class="p">)</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">mode1</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k1</span><span class="p">,</span> <span class="p">(</span><span class="mi">200</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.15</span> <span class="o">+</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">mode2</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k2</span><span class="p">,</span> <span class="p">(</span><span class="mi">200</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.15</span> <span class="o">+</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">samples</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">mode1</span><span class="p">,</span> <span class="n">mode2</span><span class="p">])</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="c1"># 回归预测均值 = 模态的均值（无效！）</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="n">mean_pred</span> <span class="o">=</span> <span class="n">samples</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">samples</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">samples</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">s</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;真实动作分布&quot;</span><span class="p">)</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">*</span><span class="n">mean_pred</span><span class="p">,</span> <span class="s2">&quot;rx&quot;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">markeredgewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;回归均值（无效！）&quot;</span><span class="p">)</span>
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="s2">&quot;g^&quot;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;模态1（向左）&quot;</span><span class="p">)</span>
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="s2">&quot;b^&quot;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;模态2（向右）&quot;</span><span class="p">)</span>
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">();</span> <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;多模态动作：为什么回归失败&quot;</span><span class="p">)</span>
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;动作维度1&quot;</span><span class="p">);</span> <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;动作维度2&quot;</span><span class="p">)</span>
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</code></pre></div></p>
</li>
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