This paper proposes a method to generate feasible trajectories for robotic systems with predefined sequences of switched contacts. The proposed trajectory generation method relies on sampling-based methods, optimal control, and reach-ability analysis. In particular, the proposed method is able to quickly test whether a simplified model-based planner, such as the Time-to-Velocity-Reversal planner, provides a reachable contact location based on reachability analysis of the multi-body robot system. When the contact location is reachable, we generate a feasible trajectory to change the contact mode of the robotic system smoothly. To perform reachability analysis efficiently, we devise a method to compute forward and backward reachable sets based on element-wise optimization over a finite time horizon. Then, we compute robot trajectories by employing optimal control. The main contributions of this study are the following. Firstly, we guarantee whether planned contact locations via simplified models are feasible by the robot system. Secondly, we generate optimal trajectories subject to various constraints given a feasible contact sequence. Lastly, we improve the efficiency of computing reachable sets for a class of constrained nonlinear systems by incorporating bi-directional propagation (forward and backward). To validate our methods we perform numerical simulations applied to a humanoid robot walking.
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Efficient Trajectory Generation for Robotic Systems Constrained by Contact Forces
In this work, we propose a trajectory generation method for robotic systems with contact force constraint based on optimal control and reachability analysis. Normally, the dynamics and constraints of the contact-constrained robot are nonlinear and coupled to each other. Instead of linearizing the model and constraints, we directly solve the optimal control problem to obtain the feasible state trajectory and the control input of the system. A tractable optimal control problem is formulated which is addressed by dual approaches, which are sampling-based dynamic programming and rigorous reachability analysis. The sampling-based method and Partially Observable Markov Decision Process (POMDP) are used to break down the end-to-end trajectory generation problem via sample-wise optimization in terms of given conditions. The result generates sequential pairs of subregions to be passed to reach the final goal. The reachability analysis ensures that we will find at least one trajectory starting from a given initial state and going through a sequence of subregions. The distinctive contributions of our method are to enable handling the intricate contact constraint coupled with system’s dynamics due to the reduction of computational complexity of the algorithm. We validate our method using extensive numerical simulations with a legged robot.
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- Award ID(s):
- 1724360
- PAR ID:
- 10122271
- Date Published:
- Journal Name:
- ArXiv.org
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Summary A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation transforms the chance constrained optimal control problem into a deterministic optimal control problem that can be solved numerically. The new method developed in this paper approximates the chance constraints using Markov Chain Monte Carlo sampling and kernel density estimators whose kernels have integral functions that bound the indicator function. The nonlinear constraints resulting from the application of kernel density estimators are designed with bounds that do not violate the bounds of the original chance constraint. The method is tested on a nontrivial chance constrained modification of a soft lunar landing optimal control problem and the results are compared with results obtained using a conservative deterministic formulation of the optimal control problem. Additionally, the method is tested on a complex chance constrained unmanned aerial vehicle problem. The results show that this new method can be used to reliably solve chance constrained optimal control problems.
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Accepted Manuscript1.0
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