《操作臂的力控制》PPT课件.ppt

1. 位置控制的局限性 当末端执行器与操作臂工作环境发生碰撞时，纯粹的位置控制已经不适用。. 考虑用海绵擦玻璃. 用刚性刮削工具从玻璃表面刮油漆.,如果末端执行器、工具或者环境刚性很高，则操作臂压贴在平面上的操作执行起来就非常困难.,2. 工业机器人在装配作业中的应用 简单的应用场合 流水线作业 目前，操作臂的灵巧性仍然较低，限制在自动化装配领域中的应用.,假设仅需要描述接触和自由状态，只考虑由于接触产生的力，主要是刚度较大的物体之间的接触力。 每一个操作任务可以分解为多个子任务，这些子任务都是由操作臂末端执行器和工作环境之间特定的接触状态定义的。对于每一个与这种子任务相关的约束，称为自然约束。 自然约束：位置约束、力约束,Example: 用扳手夹着笔从孔中拔出来. 我们假设: 笔可以垂直出入孔，而且忽略摩擦力. 整个工作过程是准静态的，忽略所有惯性力.,考虑和运动相关的约束 自然约束: 由于几何的约束关系，螺丝不能在x和y的方向移动: 也不能绕着x 和 y 轴转动: 人工约束: The remaining directions are linear and angular z axes. Velocities alone these two directions can be assigned arbitrarily, and may be controlled with position cantrol mode. We select:,考虑静态约束 自然约束: 由于做了准静态的假设，即忽略所有惯性力，所以笔在运动方向上不能有任何的加速度和力: 人工约束: 由于孔在几何上有约束，所以我们必须保证有如下的力输入:,自然约束和人工约束的坐标轴都是互相正交的. 自然约束中的运动学部分与人工约束的静态部分坐标相同. 自然约束中的静态部分与人工约束的运动学部分坐标相同.,Example: 摇手柄.,Example: 拧螺丝.,4. 装配策略 Assembly strategy is a term that refers to a sequence of planned artificial constraints that will cause the task to proceed in a desirable manner. The system can detect a change in the contacting situation so that transitions in the natural constraints can be tracked. With each such change in natural constraints, a new set of artificial constraints is recalled from the set of assembly strategies and enforced by the control system.,Example: An assembly sequence used to put a round peg into a round hole. For each of the subtasks shown, give the natural and artificial constraints. Also, indicate how the system senses the change in the natural constraints as the operation proceeds. First attach the constraint frame to the peg.,In Fig.(a), the peg is in free space, so the natural constrains are: Therefore, the artificial constrains in this case constitute an entire position trajectory, which moves the peg in the direction toward the surface.,In Fig.(b), the peg has reached the surface. To detect that this has happened, we observe the force in the direction. When this sensed force exceeds a threshold, we sense contact, which implies a new contacting situation with a new set of natural constraints. The peg is not free to move in ,or to rotate about or . In the other three DOF, it is not free to apply forces.,Hence, natural constraints: The artificial constraints describe the strategy of sliding along the surface in the direction while applying small forces to ensure that contact is maintained. Thus, we have:,In Fig.(c), the peg has fallen slightly into the hole. This situation is sensed by observing the velocity in the direction and waiting for it to cross a threshold. It signals that the natural constraints have changed, and strategy must change. The new natural constraints are: artificial constraints:,1. 位置/力混合控制 两种极端情况:,沿着自然力约束的方向进行操作臂的位置控制. 沿着自然位置约束的方向进行操作臂的力控制. 沿着任意坐标系C的正交自由度方向进行任意位置和力的混合控制.,2. 质量弹簧系统的力控制 In considering forces of contact, we must make some model of the environment upon which we are acting. We model contact with an environment as a spring: we assume the system is rigid and the environment has some stiffness, . The variable we wish to control is the force acting on the environment, , which is the force acting in the spring, .,The equation describing this physical system is: Written in terms of the variable we wish to control: Control law: We get: However, we cannot use knowledge of in control law.,If we choose to leave the out of control law: we find that: where , the effective force-feedback gain.,When the environment is stiff, might be small, and so the error is quite large. If we choose to use in the control law in place of the term : Therefore, the steady-state error is quite an improvement than before.,Generally, practical considerations change the implementation of force control servo quite a bit: First, force trajectories are usually constants. Another reality is that sensed forces are quite noisy, we can obtain the derivative of the force on the environment as .,3. 位置/力混合控制策略 1) 约束坐标系 C中的笛卡尔坐标系 Consider a manipulator having three DOF with prismatic joints acting in the directions. Assume that: The joint motions are lined up exactly with the constraint frame. The end-effector is in contact with a surface of stiffness that is oriented with its normal in the - direction.,这种情况下，力/位置混合控制问题的解比较清楚: 力控制在 方向，位置控制在 方向. 关节1和关节3用位置控制器，关节2用力控制器. 在 方向上设置位置轨迹，在 方向上设置力轨迹（很可能只是一个常数）,矩阵 来确定采用哪种控制模式.,2) 一般操作臂的控制,与约束坐标系一直的笛卡尔操作臂混合控制器.,3) 附加可变刚度 Controlling a degree of freedom in strict position or force control represents control at two ends of the spectrum of servo stiffness: An ideal position servo is infinitely stiff and rejects all force disturbances acting on the system. An ideal force servo exhibits zero stiffness and maintains the desired force application regardless of position disturbances. It could be useful to be able to control the end-effector to exhibit stiffnesses other than zero or infinite. In general, we might wish to control the mechanical impedance of the end-effector. Example: In dealing with plastic parts or springs, we could wish to set servo stiffness to other than zero or infinite.,真正的力控制并没用应用到工业机器人中，这主要是因为: 大量的计算; 缺少动力学模型的精确参数; 缺少可靠耐用的力传感器; 力/位置混合控制方法的复杂.,1. 被动柔顺性 Example: RCC,2. 通过降低位置增益实现柔顺性 Consider a general spring with six degrees of freedom. Its action could be described by: where is a diagonal 66 matrix with three linear stiffness followed by three torsional stiffness on the diagonal. Problem: How could we make the end-effector of a manipulator exhibit this stiffness characteristic? Recalling the definition of the manipulator Jacobian:,Whereas a simple joint-based position control law: Salisbury suggests using: where is the desired stiffness of the end-effector in Catesian space. Essentially, through use of the Jacobian, a Cartesian stiffness has been transformed to a joint-space stiffness.,Example: Consider a two-link planar robot arm. Obtain the joint feedback gain matrix producing the endpoint stiffness:,Assuming that the link length is 1 for both links, the Jacobian is: So: Note that the joint feedback gain matrix is symmetric and that the matrix degenerates when the robot is at a singular. If it is non-singular, then: Therefore, the obtained join