Article(id=1243220383596393274, tenantId=1146029695717560320, journalId=1242844143416819734, issueId=1243220377556595432, articleNumber=null, orderNo=null, doi=10.15959/j.cnki.0254-0053.2025.03.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1744387200000, receivedDateStr=2025-04-12, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774336437366, onlineDateStr=2026-03-24, pubDate=1758729600000, pubDateStr=2025-09-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774336437366, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774336437366, creator=13701087609, updateTime=1774336437366, updator=13701087609, issue=Issue{id=1243220377556595432, tenantId=1146029695717560320, journalId=1242844143416819734, year='2025', volume='46', issue='3', pageStart='541', pageEnd='810', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774336435926, creator=13701087609, updateTime=1774336648182, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243221267898282005, tenantId=1146029695717560320, journalId=1242844143416819734, issueId=1243220377556595432, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243221267898282006, tenantId=1146029695717560320, journalId=1242844143416819734, issueId=1243220377556595432, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=704, endPage=714, ext={EN=ArticleExt(id=1243220383906771776, articleId=1243220383596393274, tenantId=1146029695717560320, journalId=1242844143416819734, language=EN, title=Design and Implementation of a Feeding Robot Based on Obstacle Avoidance Path Planning and Compliance Control, columnId=null, journalTitle=Chinese Quarterly of Mechanics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

With the rapid acceleration of population aging in China, the demand for feeding assistance among individuals with disabilities is becoming increasingly urgent. However, current feeding robots face several limitations such as poor adaptability to complex environments and safety concerns due to rigid structures. In this paper, a new six-degree-of-freedom feeding robot was developed that integrates obstacle avoidance path planning and compliance control. The robotic arm was designed employing a Bi-directional Rapidly-exploring Random Tree (Bi-RRT) algorithm to generate collision-avoidance trajectories, while inverse kinematics was solved using the Denavit-Hartenberg (D-H) parameter. At the control level, an impedance model-based compliance control strategy was introduced, and its compliant behavior under sudden external forces was verified through dynamic simulations. Prototype experiments demonstrated that the robot could effectively avoid obstacles and respond compliantly to external interference. While the robot achieved a 100% feeding success rate with solid and semi-liquid foods, it occasionally experienced spillage when feeding liquids due to structural limitations of the end-effector. This paper provides both a theoretical framework and practical guidance for enhancing the safety and environmental adaptability of feeding robots. Future work will focus on optimizing the end-effector design to further improve performance with liquid foods.

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随着我国人口老龄化程度加剧,失能老人自主进食需求日益迫切.针对现有喂食机器人环境适应性不足与刚性结构安全隐患等问题,本文提出一种集成避障路径规划与柔顺控制的新型6自由度喂食机器人系统.采用双向快速拓展随机树(Bidirectional Rapidly-exploring Random Tree,Bi-RRT)算法生成避障路径,并结合D-H(Denavit-Hartenberg)参数完成机械臂运动学逆解计算.在控制层面,引入基于阻抗模型的柔顺控制策略,通过动力学仿真验证其在突加外力作用下的柔顺特性.样机实验表明:该机器人可有效地规避障碍物,并在受到外力时体现出柔顺性.固体与半流质食物喂食成功率均达100%,流质食物因末端执行器结构限制存在撒漏情况.本研究为提升喂食机器人安全性与环境适应性提供了算法框架与工程实践参考,后续可通过优化末端执行器设计进一步改善流质食物的喂食效果.

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张锴,博士,副教授.研究方向:固体力学和数值仿真.E-mail:
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袁清,硕士生.研究方向:机器人控制与应用.E-mail:

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袁清,硕士生.研究方向:机器人控制与应用.E-mail:

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袁清,硕士生.研究方向:机器人控制与应用.E-mail:

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journalId=1242844143416819734, articleId=1243220383596393274, language=EN, label=Tab.1, caption=

D-H parameters of the feeding robotic arm

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Jointai-1/mmαi-1/degdi/mmθi/deg
10-90112θ1
22501800θ2
3250-1800θ3
409080θ4
50-90110θ5
60055θ6
), ArticleFig(id=1243220407327765014, tenantId=1146029695717560320, journalId=1242844143416819734, articleId=1243220383596393274, language=CN, label=表1, caption=

喂食机械臂D-H参数表

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Jointai-1/mmαi-1/degdi/mmθi/deg
10-90112θ1
22501800θ2
3250-1800θ3
409080θ4
50-90110θ5
60055θ6
), ArticleFig(id=1243220407533285915, tenantId=1146029695717560320, journalId=1242844143416819734, articleId=1243220383596393274, language=EN, label=Tab.2, caption=

Testing results of the three types of food

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Food type1st attempt2nd attempt3rd attempt4th attempt5th attempt
Peanuts
Porridge
Soy milkSpillSpill
), ArticleFig(id=1243220407734612511, tenantId=1146029695717560320, journalId=1242844143416819734, articleId=1243220383596393274, language=CN, label=表2, caption=

三种食物的测试结果

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Food type1st attempt2nd attempt3rd attempt4th attempt5th attempt
Peanuts
Porridge
Soy milkSpillSpill
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基于避障路径规划和柔顺控制方法的喂食机器人设计和实现
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袁清 1 , 吕浩阳 2 , 李蔚 2 , 朱睿 3 , 柏文霞 3 , 张锴 1
力学季刊 | 2025,46(3): 704-714
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力学季刊 | 2025, 46(3): 704-714
基于避障路径规划和柔顺控制方法的喂食机器人设计和实现
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袁清1 , 吕浩阳2, 李蔚2, 朱睿3, 柏文霞3, 张锴1
作者信息
  • 1.同济大学 航空航天与力学学院,上海 200092
  • 2.同济大学 医学院,上海 200092
  • 3.同济大学 附属养志康复医院,上海 201619
  • 袁清,硕士生.研究方向:机器人控制与应用.E-mail:

通讯作者:

张锴,博士,副教授.研究方向:固体力学和数值仿真.E-mail:
Design and Implementation of a Feeding Robot Based on Obstacle Avoidance Path Planning and Compliance Control
Qing YUAN1 , Haoyang LÜ2, Wei LI2, Rui ZHU3, Wenxia BAI3, Kai ZHANG1
Affiliations
  • 1.School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
  • 2.School of Medicine, Tongji University, Shanghai 200092, China
  • 3.Yangzhi Rehabilitation Hospital, Tongji University, Shanghai 201619, China
出版时间: 2025-09-25 doi: 10.15959/j.cnki.0254-0053.2025.03.012
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随着我国人口老龄化程度加剧,失能老人自主进食需求日益迫切.针对现有喂食机器人环境适应性不足与刚性结构安全隐患等问题,本文提出一种集成避障路径规划与柔顺控制的新型6自由度喂食机器人系统.采用双向快速拓展随机树(Bidirectional Rapidly-exploring Random Tree,Bi-RRT)算法生成避障路径,并结合D-H(Denavit-Hartenberg)参数完成机械臂运动学逆解计算.在控制层面,引入基于阻抗模型的柔顺控制策略,通过动力学仿真验证其在突加外力作用下的柔顺特性.样机实验表明:该机器人可有效地规避障碍物,并在受到外力时体现出柔顺性.固体与半流质食物喂食成功率均达100%,流质食物因末端执行器结构限制存在撒漏情况.本研究为提升喂食机器人安全性与环境适应性提供了算法框架与工程实践参考,后续可通过优化末端执行器设计进一步改善流质食物的喂食效果.

喂食机器人  /  机械臂  /  避障  /  柔顺控制

With the rapid acceleration of population aging in China, the demand for feeding assistance among individuals with disabilities is becoming increasingly urgent. However, current feeding robots face several limitations such as poor adaptability to complex environments and safety concerns due to rigid structures. In this paper, a new six-degree-of-freedom feeding robot was developed that integrates obstacle avoidance path planning and compliance control. The robotic arm was designed employing a Bi-directional Rapidly-exploring Random Tree (Bi-RRT) algorithm to generate collision-avoidance trajectories, while inverse kinematics was solved using the Denavit-Hartenberg (D-H) parameter. At the control level, an impedance model-based compliance control strategy was introduced, and its compliant behavior under sudden external forces was verified through dynamic simulations. Prototype experiments demonstrated that the robot could effectively avoid obstacles and respond compliantly to external interference. While the robot achieved a 100% feeding success rate with solid and semi-liquid foods, it occasionally experienced spillage when feeding liquids due to structural limitations of the end-effector. This paper provides both a theoretical framework and practical guidance for enhancing the safety and environmental adaptability of feeding robots. Future work will focus on optimizing the end-effector design to further improve performance with liquid foods.

feeding robot  /  robotic arm  /  collision avoidance  /  compliance control
袁清, 吕浩阳, 李蔚, 朱睿, 柏文霞, 张锴. 基于避障路径规划和柔顺控制方法的喂食机器人设计和实现. 力学季刊, 2025 , 46 (3) : 704 -714 . DOI: 10.15959/j.cnki.0254-0053.2025.03.012
Qing YUAN, Haoyang LÜ, Wei LI, Rui ZHU, Wenxia BAI, Kai ZHANG. Design and Implementation of a Feeding Robot Based on Obstacle Avoidance Path Planning and Compliance Control[J]. Chinese Quarterly of Mechanics, 2025 , 46 (3) : 704 -714 . DOI: 10.15959/j.cnki.0254-0053.2025.03.012
根据第七次全国人口普查的调查结果[1],我国60岁及以上人口的比重高达18.7%,与第六次人口普查的结果相比增加了5.44个百分点.随着我国老龄化程度不断增加,失能老人的数量逐渐增多[2-3].中风、多发性硬化、帕金森等疾病导致这些老人无法自行进食,生活质量严重下降,需要借助他人帮助喂食.庞大的失能老人数量导致社会照护资源紧缺.为缓解老年人照护压力,改善这部分老人的生活质量,有必要研发一款辅助喂食机器人,帮助他们实现自主进食.
对于存在运动障碍的特殊人群,无法自主完成进食是他们生活中的一大难题,而喂食机器人的出现为他们生活质量的提高带来了新的希望[4-6]
目前,市面上已经存在一些商业化的喂食机器人产品.较早的是1987年由Mike Topping公司研制的Handy1机器人[7],用于协助一名11岁的脑瘫男孩在没有护工帮助的条件下完成自主进食.日本Secom公司在2003年研发了My Spoon机器人[8],使用者可以用手、脚或者嘴巴通过一个操作杆来控制机器人进行喂食,其优点是体积较小,可以被放置在餐桌上,且不会占用太多空间.美国Desin公司在2016年也推出了一款喂食机器人Obi[9],其拥有两个控制按钮,一个用于在机器人四个餐格中选择想要的食物,另一个用于开始或停止喂食动作,开始后整个喂食的过程是自动的.Obi还具有拖动示教的功能,可以由照护人员根据实际情况调整喂食的位置,让使用者能够更加舒适地进食.除此以外.还有Winsford feeder[10],MANUS[11],Meal buddy[12],Mealtime partner[13],Neater Eater[14]等机器人,也都实现了基本的喂食功能.但这些喂食机器人都只能沿着预先设定好的路线进行往复运动,不能主动地适应使用者的口部位置差异,对周边的环境也缺乏感知能力,使得其应用场景较为局限,缺乏实用性.近几年来,基于视觉识别的喂食机器人逐渐得到国外学者的关注[15-17],其相比上述商业喂食机器人拥有更强的适应性,喂食动作能够根据使用者的口部位置进行实时调整.此外,Perera等[18-19]还研究了将眼电图和脑电图作为喂食机器人的控制信号的方法,扩展了喂食机器人的交互方式.
国内对于喂食机器人也已有部分研究.在2010年,张立勋等[20]研究了喂食机器人的轨迹规划问题,为国内喂食机器人的研究打下了一定基础.上海理工大学的刘飞等[21-23]研发了一款I-feed喂食机器人,并且对喂食机器人的语音控制、实时面部状态识别、拖动示教等方面做了较为深入的研究.北京航空航天大学的陈殿生等[24]提出了一种基于关节阻抗控制的喂食机器人,实现了较好的柔顺性.李抒桐等[25]也设计了一款结构简单的喂食机器人,并进行了静力学和运动学分析.
综合分析目前国内外已有的喂食机器人,基本都以仿人手的串联机械臂为主,并已经能够一定程度上实现辅助喂食的基本功能.然而,喂食这一生活场景相比工业机械臂所处的工业场景,其工作环境更为复杂多变,对周边环境的感知能力有更高要求.同时,由于机器人本身结构刚性较大,在发生意外碰撞等突发事件时可能会对使用者造成人身伤害,具有潜在的安全隐患[26-28].因此,适应性和安全性对于喂食机器人显得尤为重要.基于此,本文设计了一款新型的智能避障辅助喂食机器人,通过避障路径规划和柔顺控制方法来提高喂食机器人的适应性和安全性,使其具有较好的应对突发碰撞事件的能力.
整个喂食机器人分为两个主要部分:计算平台和喂食机械臂,如图1所示.计算平台根据环境信息生成机械臂的避障运动路径,并根据柔顺控制算法向喂食机械臂发送动作指令.而喂食机械臂用于执行具体喂食动作,并向计算平台反馈关节电机运动情况.
使用时喂食机器人需要稳固放置在餐桌或支架上,以保证机器人不会出现滑动和倾倒等意外情况,安装示意图如图2所示.此外,使用者的口部必须位于机械臂的工作空间内(口部位置距机械臂基座直线距离≤500 mm),因此机械臂基座的位置与使用者不可相距过远.
在进行喂食任务的过程中,需要机械臂能够适应使用者口部的位置变化,并根据环境情况调整运动路径,这对机械臂的灵活性有一定要求.本文设计的喂食机械臂共有6个自由度,关节布置如图3所示,可以完成空间中任意位置、任意朝向的喂食动作.
机械臂的关节布置遵循Pieper原则,即机械臂存在三个相邻且互相平行的关节轴(关节2、3、4),这样的设计能够简化后续运动学分析的求解方程,易于得到有效的封闭解.为了便于后续开展喂食机械臂的算法编写,首先需要根据机械臂的设计方案确定其所对应的D-H参数.D-H参数是机器人学中用于描述机械臂运动学的一种参数化方法,由Denavit和Hartenberg于1955年提出[29],其能够用简洁的数学形式描述机械臂的各个关节之间的位置和姿态关系,因而被广泛地用于机器人的运动学分析和控制算法的设计.对于机械臂上每一组相邻关节,都可以用四个参数来描述它们之间的关系,分别是:杆件长度a、杆件扭角α、关节距离d、关节转角θ,其定义如图4所示.
按照D-H参数中对关节轴方向的要求来建立机械臂的关节坐标系,如图5所示.并以此确定各个连杆的D-H参数,汇总于表1
为了保障喂食过程中的安全,避免喂食机械臂与使用者的身体或环境中其他障碍碰撞而产生意外伤害事故,本文使用双向快速拓展随机树(Bidirectional Rapidly-exploring Random Tree,Bi-RRT)方法来生成避障路径[30-31].其原理是通过从起点和终点出发,按照一定距离的步长向外进行探索产生新的节点,同时规定节点不能落在障碍物区域内,当两颗生长树相遇时就形成了一条从起点到终点的连续折线路径.路径生成过程如图6所示.
算法具体实现步骤如下:
1.初始化整个空间,定义起点、终点、采样点数n、步长t等信息;
2.在空间中随机产生一个点Xrand;
3.在已知树的点集合中找到距离这个随机点最近的点Xnear;
4.在Xnear到Xrand的直线方向上从Xnear以步长t截取点Xnew;
5.判断从Xnear到Xnew之间是否存在障碍物,若存在则舍弃该点;
6.将Xnew点加入到树集合中;
7.循环2~6,直到有一棵树上的Xnew点能够与另一棵树上的节点成功连接.
上一节通过Bi-RRT方法得到了一条从起点到终点的连续折线路径,但生成的折线路径中往往存在大量不必要的大角度转向,这不利于机械臂的稳定运行.并且大量冗余的路径也会导致食物运送过程中的等待时间过长,一定程度上降低喂食动作的执行效率,从而影响使用者的体验.因此,还需要对避障路径进一步作平滑处理.
本文采用的路径平滑方法如图7所示.首先在保持路径的总体形状和目标点不变的前提下,尝试用直线连接路径上的非相邻点,若这条直线路径在可行空间内且未接触障碍物就可以替代中间的折线路径段,从而达到去除冗余路径的目的.在完成路径的缩短简化后,使用样条曲线将原先的折线路径拟合为连续可导的光滑曲线,并进行碰撞区域检查来确保最终的平滑路径能够正确地避开空间中设置的障碍物.
在上一节中生成的是机械臂末端的轨迹曲线,为了实现机械臂的实时控制,还需将该轨迹转化为机械臂的实时位姿,即6个关节的角度曲线.本文通过建立机械臂关节坐标系确定其D-H参数,并对机械臂开展运动学分析来求解关节角度.
根据表1中机械臂的D-H参数,可以写出其相邻两个关节的姿态变换矩阵为
式中,i为关节编号,为从关节i-1到关节i的姿态变换矩阵,i=0时为基坐标系(世界坐标系).在该矩阵中,杆件长度a、杆件扭角α、关节距离d都是已知量,由机器人的结构决定,而关节转角θ为待求参数.对于本研究中的六自由度机器人,可以由D-H参数获得六组姿态变换矩阵.将这些姿态变换矩阵相乘,得到如下结果
式中,表示机器人末端相对于基坐标系的姿态变换矩阵,描述了机器人末端所处的位置和朝向,其应当与等式右侧沿关节顺序逐一进行变换的结果相同.机器人末端相对于基坐标系的姿态变换矩阵可由路径规划的结果确定,其形式为
因此式(2)中只有关节转角θ是未知量,其本质上是一组关于关节转角θ的代数方程组,通过求解该方程组即可得到在运动过程中机器人各个关节处的转角.
根据喂食机械臂的D-H参数,在Simulink中创建相同构型的6自由度机械臂模型,并对上述避障路径规划算法进行初步验证,如图8所示.仿真结果显示机械臂能够正确地绕开柱状障碍物,到达使用者的口部前方.
确定喂食机器人的关节转角数据后,编写柔顺控制部分,首先建立喂食机器人的动力学模型
式中,T为关节电机输出的力矩,Text为外部阻碍产生的力矩.根据柔顺控制的原理[32],为使机械臂与环境发生突发撞击时具有柔顺性,指定阻抗模型为
其中,含有下标d的项代表期望角度/角速度/角加速度.当Text=0时,即机械臂未受障碍物阻挡时,有θ=θd,此时柔顺控制将不发挥作用.
将式(4)代入式(5),得到阻抗控制律为
为了确保上述算法能够达到预期效果,本文利用Matlab和Adams进行联合仿真,对喂食机器人开展动力学分析,得到图9图10的仿真结果.
图10中可以看出,相比传统的位置控制方法,柔顺控制方法下的机械臂在遭遇外界阻碍时产生的接触力更小.这是因为柔顺控制通过控制关节的力矩,使其在受到外力时能够做出适当的回退,这种柔顺特性使得机械臂在发生碰撞后能够自动调整自身的位置或与环境的接触力,避免接触力过大产生风险.同时由于柔顺控制引入了类似弹簧-阻尼的模型来使机械臂模拟出弹性行为,当机械臂与障碍物发生接触时,这种弹性特性能够吸收部分碰撞能量,从而减小碰撞瞬间接触力的峰值.
在完成算法编写和仿真验证后,搭建喂食机器人实物样机.图11展示了喂食机械臂部分,其中结构件均为3D打印PLA材质,在机械臂关节处使用了6个伺服电机.所有电机通过总线连接到一个电机控制板.此外,喂食机器人配备了急停按钮,以确保实验过程安全.
实验首先测试了喂食机器人对于不同食物种类的适用性,选取了花生(固体)、粥(半流质)、豆浆(流质)三类具有代表性的食物,如图12所示.将盛有食物的喂食碗统一放置在机械臂正前方固定位置,每种食物分别进行五次喂食测试,观察记录机械臂运动过程中食物是否出现撒漏的情况.
表2中记录了机器人喂食不同食物的测试结果,其中花生和粥的喂食成功率达到100%,但豆浆在喂食过程中存在撒漏的情况.这主要是因为机械臂的硬件条件不适用于流质食物的喂食,特别是勺状的喂食器在机械臂运动过程中容易因关节的摆动发生撒漏.因此,后续的实验主要使用固体和半流质食物进行喂食.
为评估喂食机器人对不同食物容器位置的适应性,将盛有食物的碗放置在机械臂的前后左右4个方位上(碗中心距离机械臂底座中心≥200 mm,且在机械臂的有效工作空间内),机械臂均能从碗中顺利舀起食物并送至使用者口部,如图13所示.
图14展示了喂食碗放置在正前方时喂食机器人6个关节的转角变化情况.由于碗放置在正前方,因此机械臂在喂食过程中基本只在平面内进行运动,此时主要转动的关节应为关节2、关节3、关节4,图14中的曲线体现了这一点.各关节转角曲线平滑无异常点,机械臂执行的实际末端路径与规划的路径基本一致.从机械臂舀取食物到送至使用者口中整个过程耗时约5.4 s.
为进一步验证避障路径规划算法对于不同喂食场景的有效性,设计了如下三个不同场景
场景1:喂食碗放置在机械臂正前方
场景2:喂食碗放置在机械臂侧面(距离机械臂底座中心≥100 mm)
场景3:喂食碗放置在机械臂侧面,且在喂食碗和使用者之间布置标准障碍物(直径80 mm圆柱体,模拟餐桌上的水杯等物体)
对上述每个场景进行喂食实验,喂食机械臂均能够正确地从碗中舀取食物并送至使用者口中.各场景的路径规划结果如图15所示.
对于有障碍物的场景(图15右),算法给出的路径显示其并未与障碍物发生干涉,路径与障碍物的最小距离≥50 mm,且机械臂能够正确执行该避障路径,没有发生碰撞,避障路径规划算法达到预期效果.
为验证柔顺控制算法的有效性,在机械臂运行时施加外力,观察到其能够顺着外力方向进行回退,体现出柔顺性.在外力撤去后,机械臂通过柔顺控制补偿返回到受力前姿态.图16中展示了在机械臂小臂上施加向下外力时机械臂的柔顺响应,此时外力主要影响的关节为关节2和关节3.在外力作用下,柔顺控制算法使得关节2、关节3的转角发生变化,使得机械臂呈现被下压的运动趋势,减少碰撞可能造成的伤害.同时,关节2、关节3产生补偿力矩,与外力实现平衡.在干扰外力撤去后,关节2、关节3重新恢复到受力前转角,补偿力矩随之逐渐降低.该过程中关节2、关节3的转角和力矩曲线如图17所示.
本文设计了一款较为智能的辅助喂食机器人,对比目前其它喂食机器人在复杂喂食环境的安全性有显著提高,特别是考虑了餐桌上可能会导致碰撞的障碍物(如水杯、花瓶等),并为此设计了包含自动避障路径规划和柔顺控制方法的主被动相结合的防碰撞系统,有效地降低了碰撞事故发生的可能性.
本文采用快速扩展随机树方法,结合运动学分析,实现了喂食机器人的自动避障路径规划,提高了其在复杂环境中工作的灵活性.根据柔顺控制的原理编写控制算法,并通过动力学仿真验证了喂食机械臂对外力能够产生柔顺响应.在此基础上搭建了实物样机,进一步验证了上述功能的实际效果.本文为喂食机器人的新型设计和部分算法实现提供基本参考,并为未来喂食机器人的安全性改进提供可行思路.后续可以对末端喂食器进一步改进,减少喂食机器人在运送流质食物时出现的撒漏情况.
  • 上海市残疾人联合会科技攻关项目(2024KJ1002)
  • 同济大学“医学+X”交叉研究项目(20250648YB07)
  • 国家临床重点专科建设项目(Z155080000004)
  • 上海市康复医学重中之重研究中心(2023ZZ02027)
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doi: 10.15959/j.cnki.0254-0053.2025.03.012
  • 接收时间:2025-04-12
  • 首发时间:2026-03-24
  • 出版时间:2025-09-25
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  • 收稿日期:2025-04-12
基金
上海市残疾人联合会科技攻关项目(2024KJ1002)
同济大学“医学+X”交叉研究项目(20250648YB07)
国家临床重点专科建设项目(Z155080000004)
上海市康复医学重中之重研究中心(2023ZZ02027)
作者信息
    1.同济大学 航空航天与力学学院,上海 200092
    2.同济大学 医学院,上海 200092
    3.同济大学 附属养志康复医院,上海 201619

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张锴,博士,副教授.研究方向:固体力学和数值仿真.E-mail:
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2种不同金属材料的力学参数

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占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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