阅读说明：本技术 一种应用于低成本芯片的扫地机器人清扫路径规划导航算法 (sweeping robot sweeping path planning navigation algorithm applied to low-cost chip ) 是由 陈振兵 詹伟 苟潇华 于 2019-09-30 设计创作，主要内容包括：本发明公开了一种应用于低成本芯片的扫地机器人清扫路径规划导航算法,其特征在于,包括控制层和算法层,包括以下步骤：步骤1：开启扫地机器人；步骤2：所述扫地机器人的控制层初始化算法模块中的plan模块,所述算法层返回所述plan模块的值至所述控制层中的pathPlan结构体,并保存pathPlan结构体；步骤3：所述扫地机器人进入弓扫模式；步骤4：计算当前坐标,检测所述扫地机器人是否会发生碰撞,根据检测结果将算法层获取行进方式并返回Action；步骤5：将Action导入所述控制层,根据method使用沿边或沿线控制；步骤6：扫地机器人判断清扫是否结束,若扫地机器人判断清扫未结束,则返回步骤4。(the invention discloses a sweeping path planning navigation algorithm of a sweeping robot applied to a low-cost chip, which is characterized by comprising a control layer and an algorithm layer, and the method comprises the following steps: step 1: starting the sweeping robot; step 2: a plan module in an algorithm module is initialized by a control layer of the sweeping robot, the algorithm layer returns the value of the plan module to a pathPlan structure in the control layer, and the pathPlan structure is stored; and step 3: the sweeping robot enters a bow sweeping mode; and 4, step 4: calculating current coordinates, detecting whether the sweeping robot collides or not, acquiring a traveling mode of an algorithm layer according to a detection result and returning to an Action; and 5: importing an Action into the control layer, and controlling along the edge or the line according to the method; step 6: and (4) judging whether the cleaning is finished or not by the cleaning robot, and if the cleaning is not finished by the cleaning robot, returning to the step 4.)

1. a sweeping robot sweeping path planning navigation algorithm applied to a low-cost chip is characterized by comprising a control layer and an algorithm layer, and comprises the following steps:

step 1: starting the sweeping robot;

Step 2: a plan module in an algorithm module is initialized by a control layer of the sweeping robot, the algorithm layer returns the value of the plan module to a pathPlan structure in the control layer, and the pathPlan structure is stored;

And step 3: the sweeping robot enters a bow sweeping mode;

And 4, step 4: calculating current coordinates, detecting whether the sweeping robot collides or not, acquiring a traveling mode of an algorithm layer according to a detection result and returning to an Action;

and 5: importing an Action into the control layer, and controlling along the edge or the line according to the method;

Step 6: and (4) judging whether the cleaning is finished or not by the cleaning robot, and if the cleaning is not finished by the cleaning robot, returning to the step 4.

2. the sweeping robot sweeping path planning navigation algorithm applied to the low-cost chip according to claim 1, wherein the sweeping robot acquiring the traveling mode comprises the following steps:

step 1: the sweeping robot receives the initial signal, judges whether the current mode is the edgewise mode, if so, executes the step 2, otherwise, executes the step 9;

step 2: the sweeping robot judges whether a coordinate system needs to be reconstructed, if so, the step 3 is executed, and if not, the step 4 is executed;

and step 3: the sweeping robot reconstructs a coordinate system by taking the position as an origin, and reconstructs 3 pre-planned paths, outputs the first one of the pre-planned paths, has a needRebuild mark of 1, finishes jumping out, and returns to Action;

And 4, step 4: the sweeping robot selects and judges that the robot jumps to 3 pre-planned paths along the edge, if the robot approaches to a first path, the step 5 is executed, if the robot approaches to a second path, the step 6 is executed, if the robot approaches to a third path, the step 7 is executed, and if the robot does not approach to the third path, the step 8 is executed;

and 5: the sweeping robot outputs the first one of the generated pre-planned paths, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, the jumping-out is finished, and the Action is returned;

Step 6: the sweeping robot generates a new path for 1 time, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, jumping out is finished, and an Action is returned;

and 7: the sweeping robot generates new paths for 2 times, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, jumping out is finished, and an Action is returned;

and 8: the sweeping robot outputs the last Action and the jumping-out is finished;

And step 9: the sweeping robot judges whether collision occurs at present, if so, the sweeping robot acquires the direction of a corresponding edge according to the current traveling path, outputs an edge mode, modifies the current edge traveling mode, and finishes jumping out, otherwise, executes the step 10;

step 10: the sweeping robot judges whether the end point of the current path is reached, if yes, the sweeping robot generates 1 time of new paths and outputs the first one of the pre-planned paths, the needRebuid is marked as 0, and the jumping-out is finished, otherwise, the step 11 is executed;

step 11: and the sweeping robot outputs the first one of the pre-planned paths, the needRebuid is marked as 0, and the jumping-out is finished.

3. the sweeping robot sweeping path planning navigation algorithm applied to the low-cost chip according to claim 2, wherein after the machine reaches the current line end point or transits to any one of the pre-planned paths along the edge, a path generation method is invoked to generate a new path which is continuous with the last path of the pre-planned path, the original second and third paths in the pre-planned path are lifted to the first and second positions at one time, the new path is placed at the third position, and the new path generation rule is as follows:

(1) setting the starting point of the new path as the end point of the last pre-planned route, and recording as (startX, startY);

(2) if the type of the last preplanned route is not 2, the new path end point coordinate is (startX + offset, startY), the type is 2, the angle is 0, otherwise, the 3 rd step and the 4 th step are executed;

(3) if the type of the second preplanned path is 1, the new path end point coordinate is (startX, startY-maxLen), the type is 3, and the angle is-90;

(4) And if the type of the second and planned path is 3, the new path end point coordinate is (startX, startY + maxLen), the type is 1, and the angle is 90.

4. The sweeping robot sweeping path planning navigation algorithm applied to the low-cost chip is characterized in that the sweeping robot constructs 3 pre-planned paths each time, and constructs a new planned path and reorients coordinates after the sweeper reaches the end point of each path so as to turn around and continue to cover an uncleaned area.

5. the sweeping robot sweeping path planning navigation algorithm applied to the low-cost chip is characterized in that an obstacle is encountered during the process of advancing along the planned route, the obstacle or the edge of a wall is swept in an edge mode, whether a route which is transited to the pre-planned route is calculated during the process of going along the route, and the exit along the edge is carried out.

Technical Field

the invention relates to the technical field of robots, in particular to a sweeping path planning navigation algorithm of a sweeping robot, which is applied to a low-cost chip.

Background

with the continuous development and progress of science and technology, more and more families begin to use the sweeping robot, and when the sweeping robot carries out sweeping work, a sweeping path needs to be planned to avoid collision with obstacles in a working interval, and the current sweeping path planning method applied to the sweeping robot has the following defects: the cost is high, and the cost of computing equipment is high due to the fact that in the prior art, a map needs to be stored, memory consumption is large, and a chip with more than 512kb needs to be used; the sweeping robot can start a sweeping task after exploring a working space and constructing a map in advance, and needs to spend a long time for exploring when a large space is swept; the cleaning path planning algorithm applied to the low-cost chip at present is mostly in a random collision type, the cleaning coverage rate and the cleaning efficiency are low, the normal use requirement cannot be met, and the user experience is poor; most of the solutions commonly used have low coverage of the edges of rooms where large amounts of debris are stacked.

disclosure of Invention

Technical problem to be solved

Aiming at the defects of the prior art, the invention provides a sweeping path planning navigation algorithm of a sweeping robot applied to a low-cost chip, and solves the problems of high cost, low sweeping coverage rate and sweeping efficiency and poor user experience of the sweeping robot.

(II) technical scheme

in order to achieve the purpose, the invention is realized by the following technical scheme: a sweeping robot sweeping path planning navigation algorithm applied to a low-cost chip comprises a control layer and an algorithm layer, and comprises the following steps:

step 1: starting the sweeping robot;

step 2: a plan module in an algorithm module is initialized by a control layer of the sweeping robot, the algorithm layer returns the value of the plan module to a pathPlan structure in the control layer, and the pathPlan structure is stored;

and step 3: the sweeping robot enters a bow sweeping mode;

And 4, step 4: calculating current coordinates, detecting whether the sweeping robot collides or not, acquiring a traveling mode of an algorithm layer according to a detection result and returning to an Action;

And 5: importing an Action into the control layer, and controlling along the edge or the line according to the method;

step 6: and (4) judging whether the cleaning is finished or not by the cleaning robot, and if the cleaning is not finished by the cleaning robot, returning to the step 4.

preferably, the sweeping robot acquiring and traveling mode comprises the following steps:

step 1: the sweeping robot receives the initial signal, judges whether the current mode is the edgewise mode, if so, executes the step 2, otherwise, executes the step 9;

step 2: the sweeping robot judges whether a coordinate system needs to be reconstructed, if so, the step 3 is executed, and if not, the step 4 is executed;

and step 3: the sweeping robot reconstructs a coordinate system by taking the position as an origin, and reconstructs 3 pre-planned paths, outputs the first one of the pre-planned paths, has a needRebuild mark of 1, finishes jumping out, and returns to Action;

And 4, step 4: the sweeping robot selects and judges that the robot jumps to 3 pre-planned paths along the edge, if the robot approaches to a first path, the step 5 is executed, if the robot approaches to a second path, the step 6 is executed, if the robot approaches to a third path, the step 7 is executed, and if the robot does not approach to the third path, the step 8 is executed;

And 5: the sweeping robot outputs the first one of the generated pre-planned paths, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, the jumping-out is finished, and the Action is returned;

step 6: the sweeping robot generates a new path for 1 time, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, jumping out is finished, and an Action is returned;

And 7: the sweeping robot generates new paths for 2 times, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, jumping out is finished, and an Action is returned;

and 8: the sweeping robot outputs the last Action and the jumping-out is finished;

and step 9: the sweeping robot judges whether collision occurs at present, if so, the sweeping robot acquires the direction of a corresponding edge according to the current traveling path, outputs an edge mode, modifies the current edge traveling mode, and finishes jumping out, otherwise, executes the step 10;

Step 10: the sweeping robot judges whether the end point of the current path is reached, if yes, the sweeping robot generates 1 time of new paths and outputs the first one of the pre-planned paths, the needRebuid is marked as 0, and the jumping-out is finished, otherwise, the step 11 is executed;

Step 11: and the sweeping robot outputs the first one of the pre-planned paths, the needRebuid is marked as 0, and the jumping-out is finished.

preferably, after the machine reaches the current line end point or transits to any one of the pre-planned paths along the edge, the path generation method is invoked to generate a new path which is continuous with the last path of the pre-planned path, the original second and third paths in the pre-planned path are lifted to the first and second positions at one time, the new path is placed at the third position, and the new path generation rule is as follows:

(1) Setting the starting point of the new path as the end point of the last pre-planned route, and recording as (startX, startY);

(2) if the type of the last preplanned route is not 2, the new path end point coordinate is (startX + offset, startY), the type is 2, the angle is 0, otherwise, the 3 rd step and the 4 th step are executed;

(3) If the type of the second preplanned path is 1, the new path end point coordinate is (startX, startY-maxLen), the type is 3, and the angle is-90;

(4) if the type of the second and planned path is 3, the new path end point coordinate is (startX, startY + maxLen), the type is 1, and the angle is 90.

preferably, the sweeping robot constructs 3 pre-planned paths each time, and constructs a new planned path and reorients coordinates after the sweeper reaches the end point of each path so as to realize turning around and continuously covering an uncleaned area.

preferably, the obstacle is encountered during the process of advancing along the planned route, the obstacle or the wall edge is cleaned in an edge mode, whether the route transits to the pre-planned route is calculated during the process of going along the route, and the exit along the edge is carried out.

(III) advantageous effects

the invention provides a sweeping path planning navigation algorithm of a sweeping robot applied to a low-cost chip. The method has the following beneficial effects: the invention has high execution efficiency and little dependence on the memory; the cost is low, the dependence on the memory is extremely small, and the STM chip can smoothly run with other robot algorithms in an STM32F0x0 chip with the lowest cost; the obstacle avoidance and the steering can be carried out in a planned way in the cleaning process without searching a map firstly; the coverage efficiency is far higher than that of all random collision cleaning algorithms by using the continuously-folded zigzag line; when the wall-type solar energy collecting device touches the edge of a room or an obstacle, the coverage rate of the obstacle or the edge of the room is improved by walking along the wall.

drawings

FIG. 1 is a schematic diagram of an algorithm invocation flow of the present invention;

FIG. 2 is a schematic view of a single step acquisition motion of the present invention;

FIG. 3 is a schematic diagram of the initialized and constructed pre-planned route of the present invention;

FIG. 4 is a schematic view of the cleaning end judgment of the present invention;

FIG. 5 is a schematic diagram of the cleaning end reconstruction pre-planned route of the present invention;

FIG. 6 is a schematic diagram of the edge, line mode switching of the present invention;

FIG. 7 is a first schematic diagram illustrating a first exit edgewise determination according to the present invention;

FIG. 8 is a second schematic diagram illustrating a determination of exit margin according to the present invention;

FIG. 9 is a third schematic view of a determination of exit edgewise of the present invention;

FIG. 10 is a fourth schematic diagram illustrating exit edgewise determination according to the present invention.

Detailed Description

the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1 to 10, an embodiment of the present invention provides a sweeping path planning navigation algorithm for a sweeping robot applied to a low-cost chip, including a control layer and an algorithm layer, including the following steps:

Step 1: starting the sweeping robot;

step 2: a plan module in an algorithm module is initialized by a control layer of the sweeping robot, the algorithm layer returns the value of the plan module to a pathPlan structure in the control layer, and the pathPlan structure is stored;

And step 3: the sweeping robot enters a bow sweeping mode;

and 4, step 4: calculating current coordinates, detecting whether the sweeping robot collides or not, acquiring a traveling mode of an algorithm layer according to a detection result and returning to an Action;

and 5: importing an Action into the control layer, and controlling along the edge or the line according to the method;

step 6: and (4) judging whether the cleaning is finished or not by the cleaning robot, and if the cleaning is not finished by the cleaning robot, returning to the step 4.

the sweeping robot acquiring and advancing mode comprises the following steps:

Step 1: the sweeping robot receives the initial signal, judges whether the current mode is the edgewise mode, if so, executes the step 2, otherwise, executes the step 9;

step 2: the sweeping robot judges whether a coordinate system needs to be reconstructed, if so, the step 3 is executed, and if not, the step 4 is executed;

and step 3: the sweeping robot reconstructs a coordinate system by taking the position as an origin, and reconstructs 3 pre-planned paths, outputs the first one of the pre-planned paths, has a needRebuild mark of 1, finishes jumping out, and returns to Action;

and 4, step 4: the sweeping robot selects and judges that the robot jumps to 3 pre-planned paths along the edge, if the robot approaches to a first path, the step 5 is executed, if the robot approaches to a second path, the step 6 is executed, if the robot approaches to a third path, the step 7 is executed, and if the robot does not approach to the third path, the step 8 is executed;

and 5: the sweeping robot outputs the first one of the generated pre-planned paths, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, the jumping-out is finished, and the Action is returned;

step 6: the sweeping robot generates a new path for 1 time, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, jumping out is finished, and an Action is returned;

and 7: the sweeping robot generates new paths for 2 times, the needRebuild mark is 0, the current mode is modified to be walking along a straight line, jumping out is finished, and an Action is returned;

and 8: the sweeping robot outputs the last Action and the jumping-out is finished;

and step 9: the sweeping robot judges whether collision occurs at present, if so, the sweeping robot acquires the direction of a corresponding edge according to the current traveling path, outputs an edge mode, modifies the current edge traveling mode, and finishes jumping out, otherwise, executes the step 10;

Step 10: the sweeping robot judges whether the end point of the current path is reached, if yes, the sweeping robot generates 1 time of new paths and outputs the first one of the pre-planned paths, the needRebuid is marked as 0, and the jumping-out is finished, otherwise, the step 11 is executed;

step 11: and the sweeping robot outputs the first one of the pre-planned paths, the needRebuid is marked as 0, and the jumping-out is finished.

After the machine reaches the current line end point or transits to any one of the pre-planned paths along the edge, a path generation method is called to generate a new path which is continuous with the last path of the pre-planned path, the second and third paths in the pre-planned path are lifted to the first and second positions at one time, the new path is placed at the third position, and the generation rule of the new path is as follows:

(1) Setting the starting point of the new path as the end point of the last pre-planned route, and recording as (startX, startY);

(2) If the type of the last preplanned route is not 2, the new path end point coordinate is (startX + offset, startY), the type is 2, the angle is 0, otherwise, the 3 rd step and the 4 th step are executed;

(3) if the type of the second preplanned path is 1, the new path end point coordinate is (startX, startY-maxLen), the type is 3, and the angle is-90;

(4) if the type of the second and planned path is 3, the new path end point coordinate is (startX, startY + maxLen), the type is 1, and the angle is 90.

the sweeping robot constructs 3 pre-planned paths each time, and constructs a new planned path and a redirection coordinate after the sweeper reaches the end point of each path so as to realize turning around and continuously covering an uncleaned area.

When the obstacle is encountered in the process of advancing along the planned route, the obstacle enters an edgewise mode to clean the obstacle or the edge of the wall, whether the route transits to the pre-planned route or not is calculated in the process of going along the planned route, and the edgewise exit is carried out.

the invention generates and changes the route:

(1) Pre-construction at initialization: in most cases, when the user uses the sweeping robot, the sweeping robot is placed in the central part of the passageway, so that when the sweeping robot starts to sweep, the current orientation (x axis) of the sweeping robot is the middle of the coverage area. In the initial phase, the following future 3 lines will be generated according to the incoming configuration (see fig. 3).

(2) judging the current path end point: in the cleaning process, the control layer repeatedly calls the get _ current _ action () method to obtain the suggested route, if the sweeping robot does not collide with obstacles and does not reach the terminal, the sweeping robot quickly goes out of the last returned route, and the sweeping robot is controlled to continue to walk along the current route. And if the sweeping robot reaches the end point of the line, outputting the next line of the line, and generating a new line to be placed in the pre-planned line array. The current line end point judgment method is as follows:

knowing that the coordinates of the starting point of the current route are (x1, y1), and the coordinates of the current sweeping robot are (x2, y 2);

If the current line type is 2 (side), judging whether x2-x1 is larger than or equal to offset, if so, arriving, otherwise, not arriving;

if the current line type is not 2 (side), judging whether the absolute value of y2-y1 is larger than or equal to maxLen, if so, arriving, otherwise, not arriving.

The C + + code is as follows:

(3) Path dynamic generation in the cleaning process: when the sweeping robot reaches the current line end point or transits to any one of the pre-planned paths along the edge, a path generation method is called to generate a new path which is continuous with the last path of the pre-planned path, the original second path in the pre-planned path is lifted to the position of the first path, the original 3 rd path is lifted to the position of the second path, and the new path is placed at the third position. The new path is generated as follows:

Setting the starting point of the new path as the end point of the last pre-planned route, and recording as (startX, startY);

if the type of the last pre-planned route is not 2, the new path end point coordinate is (startX + offset, startY), the type is 2, and the angle is 0. Otherwise, executing the step 3 and the step 4;

if the type of the second preplanned path is 1, the new path end point coordinate is (startX, startY-maxLen), the type is 3, and the angle is-90;

if the type of the second and planned path is 3, the new path end point coordinate is (startX, startY + maxLen), the type is 1, and the angle is 90.

(4) and (3) judging the end: the sweeping robot turns back along the zigzag shape and continuously covers along the X axis, and finally reaches the obstacle, so that the sweeping robot cannot enter the next planned route, and at the moment, the sweeping robot must enter the edgewise mode and finally enter the uncovered area, as shown in fig. 4. By judging the current machine coordinate, when the sweeping robot enters an uncovered area, the needRebuild is output to be 1, and a navigation route after the end is planned again, and after the control layer judges that the needRebuild is 1, the current coordinate, namely the code disc, is reset to be 0, so that the uncovered area is continuously covered.

generation after the end: when the control layer acquires that the needrebuiled is 1, the coordinate system is reconstructed, an old coordinate system (gray) is used as an origin according to the coordinates of the current sweeping robot, the head orientation is used as an x-axis to construct a new coordinate (blue coordinate in the figure), and 3 pre-planned routes (0, 1 and 2 in the figure) are constructed along the direction far away from the wall body, as shown in the following figure 5, if the current is the left edge wall, the method for generating 3 routes is as follows:

If the front of the energy is the right edge wall, the method for generating 3 routes is as follows:

the invention controls the switching of the mode along the edge line: in the actual operation process of the sweeping robot, the sweeping robot faces various irregular room edges, and the sweeping robot can reasonably switch two working modes along the edge line during sweeping, so that the walking route of the sweeping robot can be as shown in fig. 6 for the edges with various shapes or inclinations:

Entering an edgewise mode and determining the edgewise mode, if the current mode is an edgewise straight walking mode, namely the nowMethod is 1, and when the control layer calls the get recommended travel mode (get _ current _ action), entering the obstacle to be 1, namely collision occurs, setting the nowMethod to be 2, and determining the edgewise direction through the following logics:

if the type of the first strip in the pre-planned path is 1 (go), the edgewise direction is a left edgewise direction;

if the type of the first strip in the pre-planned path is 3 (return), the edge direction is a right edge;

if the first type in the pre-planned path is 2 and the latter type is 1, the edge direction is a right edge;

If the first type in the pre-planned path is 2 and the latter type is 3, the edgewise direction is left edgewise.

The invention adopts the following edge-following mode: if the current traveling mode is the edgewise mode, i.e. nowMethod is 2, and the coordinate system does not need to be reconstructed, it will be logically determined whether to exit the edgewise mode or not.

If the type of the first pre-planned route is 1 and the type of the second pre-planned route is 2, judging to jump to the route as shown in FIG. 7;

if the type of the first pre-planned route is 2 and the type of the second pre-planned route is 1, judging to jump to the route as shown in FIG. 8;

If the type of the first pre-planned route is 3 and the type of the second pre-planned route is 2, judging to jump to the route as shown in FIG. 9;

if the first pre-planned route is of type 2 and the second is 3, the transition to that route is determined as shown in FIG. 10.

if the transition is to the first one in the pre-planned route, any one of the following conditions is met, namely the transition is successful, otherwise, the transition is invalid: a if the first pre-planned route is of type 1 and the current Y coordinate minus the Y coordinate beginning to enter the edge is greater than 320 (machine diameter); b if the first pre-planned route is 2 and the x coordinate value of the current x coordinate value minus the x coordinate value of the starting edge is greater than 320; c if the first pre-planned route is of type 3 and the starting edge Y coordinate minus the current Y coordinate value is greater than 320.

Definition of the related data structure of the present invention:

Point coordinate points:

type (B)	Field(s)	description of the invention
			int	x	x coordinate
int	y	y coordinate

Path route:

Action output behavior:

The pathPlan algorithm module stores parameters:

design of API, path _ plan _ init module initialization method:

inputting:

and outputting the pathPlan structure, calling in sequence before acquiring the suggested route, storing the returned pathPlan structure in a global variable, and transmitting a pointer of the variable when acquiring the suggested behavior by calling each time.

get _ current _ action gets the current proposed travel:

inputting:

And (3) outputting: an Action structure.

route generation and route replacement, pre-construction during initialization:

Serial number	Starting point	terminal point	Type (B)	angle of rotation
					0	(0,0)	(offset,0)	2 (side)	0
1	(offset,0)	(offset,-maxLen/2)	1 (go)	90
					2	(offset,-maxLen/2)	(offset×2,-maxLen/2)	2 (side)	0

it is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.

although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.