Alex Ansari

Optimal control-on-request: An application in real-time assistive balance control

This paper presents a method for shared control where real-time bursts of optimal control assistance are applied by an observer on-demand to aid a simulated figure in maintaining balance. The proposed Assistive Controller (AC) calculates the optimal burst control fast, in real time, while accounting for nonlinearities of the dynamic model. The short duration of the AC signals allows a rapid transfer of control authority between the nominal and the assistive controller. This scheme avoids prolonged loss of nominal control authority on the part of the figure while facilitating the real-time integration of an external observers guidance through the assistive control. We demonstrate the benefits of this control scheme in simulation using the Robot Operating System (ROS), in a context where the nominal controller fails to stabilize the figure and the AC is activated intermittently to not only keep it from falling but to additionally push it back to the upright position. The example signifies the efficiency of the proposed model-based AC even in the absence of force/pressure sensors. This approach presents an opportunity for using exoskeletons in balance support, fall prevention, and therapy. In particular, our simulation results indicate that a therapist equipped with an AC interface can, with minimal effort, increase active participation on the part of the patient while ensuring their safety.

Control-on-request: Short-burst assistive control for long time horizon improvement

This paper introduces a new control-on-request (COR) method that improves the capability of existing shared control interfaces. These COR enhanced interfaces allow users to request on-demand bursts of assistive computer control authority when manual / shared control tasks become too challenging. To enable the approach, we take advantage of the short duration of the desired control responses to derive an algebraic solution for the optimal switching control for differentiable nonlinear systems. These solutions minimize control authority while generating immediate and optimal degrees of improvement in system trajectories. The technique avoids the iterative constrained optimization required to derive traditional finite horizon optimal switching control solutions for nonlinear system and allows optimal control responses on time-frames otherwise infeasible. An interactive example illustrates how users can use COR interfaces to request real-time bursts of control assistance to help stabilize an unstable system.

Real-time trajectory synthesis for information maximization using Sequential Action Control and least-squares estimation

This paper presents the details and experimental results from an implementation of real-time trajectory generation and parameter estimation of a dynamic model using the Baxter Research Robot from Rethink Robotics. Trajectory generation is based on the maximization of Fisher information in real-time and closed-loop using a form of Sequential Action Control. On-line estimation is performed with a least-squares estimator employing a nonlinear state observer model computed with trep, a dynamics simulation package. Baxter is tasked with estimating the length of a string connected to a load suspended from the gripper with a load cell providing the single source of feedback to the estimator. Several trials are presented with varying initial estimates showing convergence to the actual length within a 6 second time-frame.

Sequential Action Control for Tracking of Free Invariant Manifolds

Abstract This paper presents a hybrid control method that controls to unstable equilibria of nonlinear systems by taking advantage of systems’ stable manifold of free dynamics. Resulting nonlinear controllers are closed-loop and can be computed in real-time. Thus, we present a computationally efficient approach to optimization-based switching control design using a manifold tracking objective. Our method is validated for the cart-pendulum and the pendubot inversion problems. Results show the proposed approach conserves control effort compared to tracking the desired equilibrium directly. Moreover, the method avoids parameter tuning and reduces sensitivity to initial conditions. Finally, when compared to existing energy based swing-up strategies, our approach does not rely on pre-derived, system-specific switching controllers. We use hybrid optimization to automate switching control synthesis on-line for nonlinear systems.

Model-Based Reactive Control for Hybrid and High-Dimensional Robotic Systems

Sequential action control (SAC) is a recently developed algorithm for optimal control of nonlinear systems. Previous work by the authors demonstrates that SAC performs well on several benchmark control problems. This work demonstrates applicability of SAC to a variety of robotic systems; we show that SAC can also be easily applied to hybrid systems without any modification and that its scalability facilitates application to high-dimensional systems. First, SAC is applied to a popular hybrid dynamic running model known as the spring-loaded inverted pendulum (SLIP). The results show that SAC can achieve dynamic hopping without using prescribed touchdown angles/leg stiffness. Moreover no specialized hybrid methods are necessary to handle the contact dynamics, despite the nonsmooth nature of the problem. The same SAC-controlled SLIP model is also implemented in a game for the Android operating system, demonstrating the minimal computational requirements for implementing SAC. Our second example involves successful stabilization and tracking control of a nonlinear, constrained dynamic model of a humanoid marionette with 56 states and 8 inputs. Finally, a discussion that includes best practices on tuning parameters of the SAC algorithm as well as the challenges of hardware implementation is also provided, along with a video that shows the resulting simulations for each example.

Minimal parametric sensitivity trajectories for nonlinear systems

Trajectory optimization techniques can be used to minimize error norms on both state and controls with respect to a reference. However, without sufficient control authority, resulting controllers can be sensitive to variations in model parameters. This paper presents a method to incorporate parametric sensitivity in optimal control calculations to develop optimally insensitive trajectories which can be better tracked under open loop and limited gain feedback conditions. As it builds on existing nonlinear optimal control theory, the approach can be easily implemented and applies to a variety of system types. The effectiveness of the technique is demonstrated using a simplified vehicle model. Controllers developed are capable of tracking highly aggressive and dynamically infeasible paths while minimizing sensitivity to variations in modeled friction.

Dynamic Task Execution Using Active Parameter Identification With the Baxter Research Robot

This paper presents experimental results from the real-time parameter estimation of a system model and subsequent trajectory optimization for a dynamic task using the Baxter Research Robot from Rethink Robotics. An active estimator maximizing Fisher information is used in real time with a closed-loop, nonlinear control technique known as sequential action control. Baxter is tasked with estimating the length of a string connected to a load suspended from the gripper with a load cell providing the single source of feedback to the estimator. Following the active estimation, a trajectory is generated using the trep software package that controls Baxter to dynamically swing a suspended load into a box. Several trials are presented with varying initial estimates showing that the estimation is required to obtain adequate open-loop trajectories to complete the prescribed task. The result of one trial with and without the active estimation is also shown in the accompanying video.

Minimal sensitivity control for hybrid environments

This paper presents a method to develop trajectories which remain optimally insensitive to sudden changes in dynamics. The approach is applied to two example systems that model a vehicles attempt to navigate through potentially hazardous areas of the state space. Through these simplified examples, we show how to automatically plan trajectories which either avoid or adjust controls to safely pass through critical regions of the state space.

Assistive Optimal Control-on-Request with Application in Standing Balance Therapy and Reinforcement

This chapter develops and applies a new control-on-request (COR) method to improve the capability of existing shared control interfaces. These COR enhanced interfaces allow users to request on-demand bursts of assistive computer control authority when manual/shared control tasks become too challenging. To enable the approach, we take advantage of the short duration of the desired control responses to derive an algebraic solution for the optimal switching control for differentiable nonlinear systems. Simulation studies show how COR interfaces present an opportunity for human–robot collaboration in standing balance therapy . In particular, we use the Robot Operating System (ROS) to show that optimal control-on-request achieves both therapy objectives of active patient participation and safety. Finally, we explore the potential of a COR interface as a vibrotactile feedback generator to dynamically reinforce standing balance through sensory augmentation.

Minimum sensitivity control for planning with parametric and hybrid uncertainty

This paper introduces a method to minimize norms on nonlinear trajectory sensitivities during open-loop trajectory optimization. Specifically, we derive new parametric sensitivity terms that measure the variation in nonlinear (continuous-time) trajectories due to variations in model parameters, and hybrid sensitivities, which account for variations in trajectory caused by sudden transitions from nominal dynamics to alternative dynamic modes. We adapt continuous trajectory optimization to minimize these sensitivities while only minimally changing a nominal trajectory. We provide appended states, cost, and linearizations, required so that existing open-loop optimization methods can generate minimally sensitive feedforward trajectories. Although there are several applications for sensitivity optimization, this paper focuses on robot motion planning, where popular sample-based planners rely on local trajectory generation to expand tree/graph structures. While such planners often use stochastic uncertainty propagation to model and reduce uncertainty, this paper shows that trajectory uncertainty can be reduced by minimizing first-order sensitivities. Simulated vehicle examples show parametric sensitivity optimization generates trajectories optimally insensitive to parametric model uncertainty. Similarly, minimizing hybrid sensitivities reduces uncertainty in crossing mobility hazards (e.g. rough terrain, sand, ice). Examples demonstrate the process yields a planner that uses approximate hazard models to automatically and optimally choose when to avoid hazardous terrain and when controls can be adjusted to traverse hazards with reduced uncertainty. Sensitivity optimization offers a simple alternative to stochastic simulation and complicated uncertainty modeling for nonlinear systems.