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Register a new userRobot Calligraphy using Pseudospectral Optimal Control in Conjunction with a Novel Dynamic Brush Model
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Added by
Sen Wang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Chinese calligraphy is a unique art form with great artistic value but difficult to master. In this paper, we formulate the calligraphy writing problem as a trajectory optimization problem, and propose an improved virtual brush model for simulating the real writing process. Our approach is inspired by pseudospectral optimal control in that we parameterize the actuator trajectory for each stroke as a Chebyshev polynomial. The proposed dynamic virtual brush model plays a key role in formulating the objective function to be optimized. Our approach shows excellent performance in drawing aesthetically pleasing characters, and does so much more efficiently than previous work, opening up the possibility to achieve real-time closed-loop control.
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Chinese calligraphy is a unique art form with great artistic value but difficult to master. In this paper, we formulate the calligraphy writing problem as a trajectory optimization problem, and propose an improved virtual brush model for simulating the real writing process. Our approach is inspired by pseudospectral optimal control in that we parameterize the actuator trajectory for each stroke as a Chebyshev polynomial. The proposed dynamic virtual brush model plays a key role in formulating the objective function to be optimized. Our approach shows excellent performance in drawing aesthetically pleasing characters, and does so much more efficiently than previous work, opening up the possibility to achieve real-time closed-loop control.
Legged robot locomotion requires the planning of stable reference trajectories, especially while traversing uneven terrain. The proposed trajectory optimization framework is capable of generating dynamically stable base and footstep trajectories for multiple steps. The locomotion task can be defined with contact locations, base motion or both, making the algorithm suitable for multiple scenarios (e.g., presence of moving obstacles). The planner uses a simplified momentum-based task space model for the robot dynamics, allowing computation times that are fast enough for online replanning.This fast planning capabilitiy also enables the quadruped to accommodate for drift and environmental changes. The algorithm is tested on simulation and a real robot across multiple scenarios, which includes uneven terrain, stairs and moving obstacles. The results show that the planner is capable of generating stable trajectories in the real robot even when a box of 15 cm height is placed in front of its path at the last moment.
We present the design of a low-cost wheeled mobile robot, and an analytical model for predicting its motion under the influence of motor torques and friction forces. Using our proposed model, we show how to analytically compute the gradient of an appropriate loss function, that measures the deviation between predicted motion trajectories and real-world trajectories, which are estimated using Apriltags and an overhead camera. These analytical gradients allow us to automatically infer the unknown friction coefficients, by minimizing the loss function using gradient descent. Motion trajectories that are predicted by the optimized model are in excellent agreement with their real-world counterparts. Experiments show that our proposed approach is computationally superior to existing black-box system identification methods and other data-driven techniques, and also requires very few real-world samples for accurate trajectory prediction. The proposed approach combines the data efficiency of analytical models based on first principles, with the flexibility of data-driven methods, which makes it appropriate for low-cost robots. Using the learned model and our gradient-based optimization approach, we show how to automatically compute motor control signals for driving the robot along pre-specified curves.
A mobility mechanism for robots to be used in tight spaces shared with people requires it to have a small footprint, to move omnidirectionally, as well as to be highly maneuverable. However, currently there exist few such mobility mechanisms that satisfy all these conditions well. Here we introduce Omnidirectional Balancing Unicycle Robot (OmBURo), a novel unicycle robot with active omnidirectional wheel. The effect is that the unicycle robot can drive in both longitudinal and lateral directions simultaneously. Thus, it can dynamically balance itself based on the principle of dual-axis wheeled inverted pendulum. This letter discloses the early development of this novel unicycle robot involving the overall design, modeling, and control, as well as presents some preliminary results including station keeping and path following. With its very compact structure and agile mobility, it might be the ideal locomotion mechanism for robots to be used in human environments in the future.
Optimal control is a popular approach to synthesize highly dynamic motion. Commonly, $L_2$ regularization is used on the control inputs in order to minimize energy used and to ensure smoothness of the control inputs. However, for some systems, such as satellites, the control needs to be applied in sparse bursts due to how the propulsion system operates. In this paper, we study approaches to induce sparsity in optimal control solutions -- namely via smooth $L_1$ and Huber regularization penalties. We apply these loss terms to state-of-the-art DDP-based solvers to create a family of sparsity-inducing optimal control methods. We analyze and compare the effect of the different losses on inducing sparsity, their numerical conditioning, their impact on convergence, and discuss hyperparameter settings. We demonstrate our method in simulation and hardware experiments on canonical dynamics systems, control of satellites, and the NASA Valkyrie humanoid robot. We provide an implementation of our method and all examples for reproducibility on GitHub.
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