.png){kind=icon}
返回
Collocation methods for second and higher order systems
.png){kind=icon}
OA
AI
DOI：10.1007/s10514-023-10155-z.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are often governed by a second or higher order ODE involving configuration variables and their time derivatives. To apply a collocation method, therefore, the usual practice is to resort to the well known procedure of casting an Mth order ODE into M first order ones. This manipulation, which in the continuous domain is perfectly valid, leads to inconsistencies when the problem is discretized. Since the configuration variables and their time derivatives are approximated with polynomials of the same degree, their differential dependencies cannot be fulfilled, and the actual dynamics is not satisfied, not even at the collocation points. This paper draws attention to this problem, and develops improved versions of the trapezoidal and Hermite-Simpson collocation methods that do not present these inconsistencies. In many cases, the new methods reduce the dynamics transcription error in one order of magnitude, or even more, without noticeably increasing the cost of computing the solutions.
Keyword:
Collocation methods
Trajectory optimization
Optimal control
Second and higher order systems
期刊
IF:
4.3
论文数:
1.7K
被引数:
5.0K
机构
引用论文
分享收藏Effect of Exercise Training on the Mental and Physical Well-Being of Caregivers for Persons Living With Chronic Illnesses: A Systematic Review and Meta-Analysis运动训练对慢性病患者照顾者身心健康的影响: 系统综述和荟萃分析
PREAI
分享收藏High prevalence of non‐alcoholic fatty liver disease among healthy male blood donors of urban India.png)
JGH Open
OAAI
JGH OpenIF0
OAAI分享收藏CasADi: a software framework for nonlinear optimization and optimal controlCasADi: 非线性优化和最优控制的软件框架
PREAI
分享收藏
查看更多内容