REAL-TIME MULTI-TASK OPTIMAKE

逆运动学与全身控制 Inverse Kinematics and Whole-Body Control

从机械臂到人形机器人,实现微秒级关节指令计算。 From manipulators to humanoid robots, computing joint commands in microseconds.

Inverse Kinematics and Whole-Body Control

让机器人在每个控制周期里都算得出、算得准 Solutions Available and Accurate in Every Control Cycle

任务场景The Task

逆运动学是机器人执行任何动作的第一步:把视觉、遥操作或上层规划给出的末端目标,实时转换成一组可执行、且不违反物理限制的关节角度。

  • 实时:视觉伺服、遥操作要求在毫秒级控制周期内持续给出解。
  • 可扩展:不管是多任务(例如人形机器人需要同时满足踩稳、重心稳定、双手到位等多个任务)还是多构型(不同类型的机器人),都能适应。
  • 可靠:目标不可达或接近奇异时,仍需给出安全可用的结果。
  • 高精度:直接处理非线性问题,实现微米级精度

Inverse kinematics is the first step of every robot motion: converting end-effector targets from vision, teleoperation, or high-level planning into joint angles that are executable and physically feasible.

  • Real-time: visual servoing and teleoperation require solutions to be delivered continuously within millisecond-level control cycles.
  • Scalable: it adapts to multiple tasks (for example, a humanoid robot must keep its feet planted, stay balanced, and place both hands at the same time) as well as to multiple configurations (different types of robots).
  • Reliable: even when the target is unreachable or close to a singularity, a safe and usable result must still be produced.
  • High accuracy: the nonlinear problem is solved directly, achieving micrometer-level accuracy.
Inverse Kinematics
μs级求解μs-Level Solving
关节角度实时解算Real-time joint-angle computation
强扩展性Highly Scalable
多任务/多构型Multi-task / multi-configuration
安全可靠Safe and Reliable
100% 求解成功率100% solve success rate
SOLVE TIME 0 20 40 60 80 100 120 36 μs 12 μs 122 μs 55 μs Cold Start Hot Start Cold Start Hot Start 7 DOF MANIPULATOR IK 29 DOF HUMANOID WBC TIME (μs)
01 Real-Time

微秒级求解,直接嵌进控制环 Microsecond Solve Times, Directly Inside the Control Loop

在典型 x86 计算平台上,7 轴机械臂 IK 冷启动约为 36 μs,热启动约为 12 μs。

29 自由度人形机器人的多任务全身控制(Whole-Body Control, WBC)冷启动约为 122 μs,热启动约为 55 μs。

微秒级 IK 求解结合求解器热启动机制,实现高频连续轨迹点求解与精准在线微调。

A 7-axis manipulator solves in about 36 μs cold-started and 12 μs warm-started on a typical x86 platform; whole-body multi-task IK on a 29-DoF humanoid takes about 122 μs cold-started and 55 μs warm-started.

Microsecond IK solving combined with the solver's warm-start mechanism enables high-frequency solving of consecutive trajectory points and precise online fine-tuning.

Scalable Robotics Diagram
02 Scalability

同一套建模,覆盖机械臂到人形、单任务到多任务 One Modeling Approach: From Arms to Humanoids, Single to Multi-Task

换机型只需替换运动学模型:从工业机械臂、人形机器人到多足机器人均可直接建模,求解耗时随规模平稳增长。

多任务通过“硬约束 / 软约束 / 目标函数”三层结构自然表达优先级,无需分层求解与启发式调参。

Switching robots only means switching the kinematic model: industrial manipulators, humanoid robots, and legged robots can all be modeled directly, with solve time growing smoothly as the problem scales.

Multiple tasks express their priorities naturally through the three-layer structure of hard constraints, soft constraints, and objective function, without hierarchical solving or heuristic tuning.

03 Reliability

Monte Carlo 随机测试,求解零失败 Zero Solve Failures in Monte Carlo Random Testing

Monte Carlo随机位姿测试, 求解零失败, 100%收敛至局部/全局最优解。

目标不可达时不会直接报错,而是返回最小约束违背解(例如距离目标位姿最近的可行折中解),让上层逻辑始终有稳定输入。

快速且可靠的局部求解,让 IK 任务的实时全局寻优成为可能。

Monte Carlo random pose testing shows zero solve failures, with 100% convergence to a local or global optimum.

When a target is unreachable, the solver does not simply report an error; it returns the solution with minimal constraint violation (for example, the closest feasible compromise to the target pose), so upper-level logic always receives a stable input.

Fast and reliable local solving makes real-time global optimization of IK tasks possible.

04 Accuracy

微米级求解精度 Micrometer-Level Solution Accuracy

得益于强大的非线性问题求解能力,非线性运动学、关节限位、支撑多边形等物理约束以精确形式引入,位姿精度不因近似而累积误差。

基于高精度求解算法,求解器能快速可靠地收敛到高精度解,在保证精度的同时保持计算效率。

Thanks to powerful nonlinear solving capabilities, physical constraints such as nonlinear kinematics, joint limits, and support polygons are introduced in exact form, so pose accuracy does not accumulate error from approximations.

Built on high-accuracy solving algorithms, the solver converges quickly and reliably to high-accuracy solutions, maintaining computational efficiency without sacrificing precision.

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