What you're looking for is custom routing. When you initialize the application, you can add something like the following to your FrontController:
$front = Zend_Controller_Front::getInstance();
$front->setParam('useDefaultControllerAlways', false);
$front->setControllerDirectory('application/controllers');
$front->getRouter()->addRoute('mycontrol', new Zend_Controller_Router_Route('/action/:param1/:param2/:param3', array(
'controller' => 'mycontrol',
'module' => 'default',
'action' => 'action',
'param1' => ''),
'param2' => ''),
'param3' => ''))
);
Then, in your controller (i.e. in MycontrolController->actionAction()) you can access the parameters as
$param1 = $this->_request->getParam('param1', $default = '');
$param2 = $this->_request->getParam('param2', $default = '');
$param3 = $this->_request->getParam('param3', $default = '');